PFT predicted values by 2022 race-neutral GLI equations, ages 3 to 95

 
Input
 
Sex Female

Male
Age  
Height  
Measured FEV1  
Measured FVC  

 
Results
 
Important: Inputs must be complete to perform calculation.

 
 
Measured FEV1/FVC ratio  
 
Predicted FEV1  
FEV1 percent predicted  
FEV1 Z-score  
FEV1 LLN  
FEV1 ULN  
 
Predicted FVC  
FVC percent predicted  
FVC Z-score  
FVC LLN  
FVC ULN  
 
Predicted FEV1/FVC ratio  
FEV1/FVC percent predicted  
FEV1/FVC ratio Z-score  
FEV1/FVC LLN  
FEV1/FVC ULN  
 
Decimal Precision  
 

 

 
Notes
  • For most accurate calculation, input fractional ages where possible, especially for young individuals.
  • The FEV1/FVC predicted ratio is population based and calculated independently from the FEV1 and FVC. Therefore, there may be minor differences from the predicted value shown here, and the value calculated from simple division of the predicted FEV1 by predicted FVC.
  • The Z-score is the number of standard deviations a value is from the predicted (mean) value. A negative Z-score represents data below the mean and a positive Z-score represents data above the mean.
  • Lower and upper limits of normal pulmonary function tests are calculated using the Z-score equation where Z-score is set to -1.645 for the LLN (5th percentile), and 1.645 for ULN (95th percentile).
  • PFT: pulmonary function test; GLI: Global Lung Function Initiative; FEV1: forced expiratory volume at 1 second; FVC: forced vital capacity; LLN: lower limit of normal; ULN: upper limit of normal.

 
Equations used
 
Measured values
FEV1/FVC ratio = Measured FEV1 / Measured FVC
Predicted values
Female FEV1 = e(-10.901689 + (2.385928 * ln(Height)) - (0.076386 * ln(Age)) + M spline)
Female FVC = e(-12.055901 + (2.621579 * ln(Height)) - (0.035975 * ln(Age)) + M spline)
Female FEV1/FVC = e(0.9189568 - (0.1840671 * ln(Height)) - (0.0461306 * ln(Age)) + M spline)
Male FEV1 = e(-11.399108 + (2.462664 * ln(Height)) - (0.011394 * ln(Age)) + M spline)
Male FVC = e(-12.629131 + (2.727421 * ln(Height)) + (0.009174 * ln(Age)) + M spline)
Male FEV1/FVC = e(1.022608 - (0.218592 * ln(Height)) - (0.027586 * ln(Age)) + M spline)
Percent predicted values
FEV1 percent predicted = 100 * Measured FEV1 / Predicted FEV1
FVC percent predicted = 100 * Measured FVC / Predicted FVC
FEV1/FVC ratio percent predicted = 100 * Measured FEV1/FVC ratio / Predicted FEV1/FVC ratio
Z-score calculation
Z-score = ((Measurement/M)L - 1) / (L * S)
LMS values for female FEV1 Z-score
L = 1.21388
M = Predicted FEV1
S = e(-2.364047 + 0.129402 * ln(Age) + S spline)
LMS values for female FVC Z-score
L = 0.899
M = Predicted FVC
S = e(-2.310148 + 0.120428 * ln(Age) + S spline)
LMS values for female FEV1/FVC ratio Z-score
L = 6.6490 - 0.9920 * ln(Age);
M = Predicted FEV1/FVC ratio
S = e(-3.171582 + 0.144358 * ln(Age) + S spline)
LMS values for male FEV1 Z-score
L = 1.22703
M = Predicted FEV1
S = e(-2.256278 + 0.080729 * ln(Age) + S spline)
LMS values for male FVC Z-score
L = 0.9346;
M = Predicted FVC
S = e(-2.195595 + 0.068466 * ln(Age) + S spline)
LMS values for male FEV1/FVC ratio Z-score
L = 3.8243 - 0.3328 * ln(Age)
M = Predicted FEV1/FVC ratio
S = e(-2.882025 + 0.068889 * ln(Age) + S spline)

 

 
Calculation Details and Variables
  • Age-based M and S spline coefficients are listed in the tables below.
  • Linear interpolation is used to obtain M and S spline values between listed ages.

 
References
  1. Bowerman C, Bhakta NR, Brazzale D, et al. A Race-neutral Approach to the Interpretation of Lung Function Measurements. Am J Respir Crit Care Med. 2023; 207:768. PubMed ID: 36383197 PubMed Logo
  2. Quanjer PH, Stanojevic S, Cole TJ, et al. ERS Global Lung Function Initiative. Multi-ethnic reference values for spirometry for the 3-95-yr age range: the global lung function 2012 equations. Eur Respir J. 2012; 40:1324. PubMed ID: 22743675 PubMed Logo

 
  Appendix

 
M and S spline coefficients for females 3 to 95 years
 
 FEV1FVCFEV1/FVC ratio
AgeMSMSMS
3-0.2095507780.313300389-0.13635550.26866539-0.0613314020.080526237
3.25-0.2006664340.288280448-0.1303403750.247291282-0.05869480.077631527
3.5-0.192467480.265145552-0.1247856310.227528531-0.056294710.074930735
3.75-0.1848882120.243660411-0.1196434890.20917695-0.0541363530.072381303
4-0.1779132130.223661208-0.1148957270.192097646-0.0522382310.069945704
4.25-0.1715274540.205011666-0.1105261260.17617495-0.0506174990.067589726
4.5-0.1656975330.187599579-0.1065131990.161313729-0.0492826720.065283288
4.75-0.1603655990.171342117-0.1028295020.147444278-0.0482192050.063005418
5-0.1554786340.156163622-0.0994491080.134502704-0.0473774810.060745687
5.25-0.1509847130.141994266-0.0963456930.122430067-0.0466881890.058496974
5.5-0.1467866430.128779429-0.0934728680.111182404-0.046076610.05625979
5.75-0.1427818910.116471401-0.09078170.100721949-0.0454655080.054039438
6-0.1388901270.105023469-0.0882327960.091010919-0.0447843540.051845823
6.25-0.135048490.094390462-0.0857939910.082012215-0.0439712710.049692078
6.5-0.1312080760.084528851-0.0834344780.073690041-0.0429858840.047589678
6.75-0.1273308650.075397095-0.0811261010.066010098-0.0418147840.045544128
7-0.1233872230.066955942-0.0788460870.05893963-0.0404638340.043555518
7.25-0.1193541820.059168418-0.0765760690.052447494-0.0389494620.041618684
7.5-0.1152130760.051999337-0.0743006590.04650368-0.0372950780.039726691
7.75-0.1109377460.045410721-0.0720006310.041073944-0.0355244810.037872312
8-0.1065001680.039364403-0.0696560940.036122984-0.033661710.03604702
8.25-0.1018783250.033825477-0.0672509480.031618633-0.0317247110.034243441
8.5-0.0970552460.028762004-0.0647722930.027531571-0.0297290110.032456688
8.75-0.0920180860.024144699-0.0622098690.023835014-0.0276871480.030682778
9-0.08675850.019945763-0.0595559910.020503561-0.0255863440.028926881
9.25-0.0812831620.016129752-0.0568090520.017504253-0.0234065580.02719917
9.5-0.0756066010.012658692-0.0539708950.014801576-0.021136140.025508116
9.75-0.069742350.009498632-0.0510436090.012363893-0.0187676290.023860817
10-0.0637028990.006619247-0.0480294290.010163041-0.016295740.022262836
10.25-0.0574998010.003993386-0.0449306880.008173904-0.0137227360.020716771
10.5-0.051143750.001596692-0.0417497810.006374035-0.0110597550.019223017
10.75-0.044645293-0.000592797-0.0384893470.004743263-0.0083222450.017780285
11-0.038030844-0.002596684-0.0351575020.003261599-0.0055274630.016386321
11.25-0.031341549-0.004436324-0.0317674290.001909129-0.0026951170.015039025
11.5-0.024614507-0.00613098-0.0283311510.0006679580.0001525070.013735544
11.75-0.017882376-0.00769796-0.024859376-0.0004779210.0029934250.012473357
12-0.011173899-0.009152836-0.021361643-0.0015428410.005806550.011249676
12.25-0.004514363-0.010509632-0.017846457-0.002539650.0085718260.010061673
12.50.002074002-0.011780991-0.014321405-0.0034798670.011269920.008906173
12.750.008571669-0.012978324-0.010793251-0.0043738330.0138831330.00778063
130.014961115-0.014111829-0.007268505-0.005230790.0163968420.00668324
13.250.021224088-0.015189926-0.003756437-0.0060587120.0187990620.005612291
13.50.027343303-0.016219896-0.000266838-0.0068646220.0210799550.004566151
13.750.033303622-0.0172083440.003191571-0.0076548380.0232326150.003543593
140.039091821-0.0181612670.00661104-0.0084350440.0252527610.00254365
14.250.044696388-0.0190841160.009984681-0.0092103540.0271385650.001565448
14.50.050107341-0.0199818460.013306389-0.0099853690.0288894520.000607958
14.750.055316062-0.0208589640.016570757-0.0107642250.030506261-0.000329721
150.060315153-0.021719570.019773006-0.0115506420.031991009-0.00124848
15.250.065098312-0.0225673950.022908924-0.012347960.033346812-0.002149073
15.50.069660283-0.0234058250.025974817-0.0131591620.034577516-0.003032036
15.750.074000208-0.0242374410.02896791-0.0139860620.035687564-0.003897727
160.078122708-0.0250638810.031886451-0.0148290470.036681939-0.004746278
16.250.082032722-0.0258865840.034729011-0.0156883450.037566018-0.005577625
16.50.085735078-0.0267068640.037494406-0.0165641320.038345273-0.006391723
16.750.089234496-0.027525920.040181666-0.0174565410.039025155-0.007188664
170.092535584-0.0283448450.042790016-0.0183656640.039611046-0.007968582
17.250.09564284-0.0291646360.045318858-0.0192915580.040108339-0.008731663
17.50.098560654-0.0299862040.047767752-0.0202342480.040522416-0.0094781
17.750.101293308-0.0308103780.0501364-0.021193730.040858451-0.010208079
180.103844979-0.0316379110.05242463-0.0221699750.041121214-0.010921835
18.250.106219737-0.0324694920.054632386-0.0231629310.041315187-0.011619668
18.50.108421553-0.0333057440.056759717-0.0241725280.041444392-0.012302024
18.750.11045482-0.0341470930.058806964-0.0251984820.041512563-0.012969396
190.112327738-0.0349928530.060776064-0.0262390750.041523375-0.013622212
19.250.114049843-0.0358419010.062669582-0.027292050.041480594-0.014260787
19.50.115630128-0.0366931910.064489976-0.0283553030.041388018-0.014885384
19.750.11707707-0.0375457530.066239598-0.0294268710.041249279-0.015496245
200.118398662-0.0383986820.067920702-0.0305049270.041067832-0.016093567
20.250.119602445-0.0392511410.069535447-0.0315877690.040846973-0.016677547
20.50.120695538-0.040102350.071085903-0.032673810.040589982-0.017248381
20.750.121684663-0.0409515850.072574055-0.0337615710.04029999-0.017806264
210.122576169-0.0417981730.074001808-0.0348496740.039979943-0.018351395
21.250.123376059-0.0426414910.075370992-0.0359368350.039632607-0.018883953
21.50.124090005-0.0434809590.076683362-0.0370218570.039260496-0.019404038
21.750.124723373-0.0443160390.077940607-0.0381036260.038866043-0.019911739
220.125281242-0.0451462330.07914435-0.0391811040.038451661-0.020407135
22.250.125768417-0.0459710780.080296151-0.0402533240.038019647-0.020890282
22.50.12618943-0.046790090.081397515-0.0413193330.03757198-0.021361156
22.750.126548393-0.047602180.082449915-0.0423776350.037110507-0.021819688
230.126849083-0.0484059210.083454792-0.0434264460.036636994-0.022265797
23.250.127095082-0.0491999770.084413528-0.0444640930.036153054-0.022699429
23.50.12728979-0.0499831040.085327456-0.045489020.035659967-0.023120605
23.750.127436434-0.0507541420.08619786-0.0464997730.035158884-0.023529361
240.127538078-0.0515120110.087025974-0.0474950.034650922-0.023925738
24.250.127597631-0.0522557080.087812991-0.0484734430.034137106-0.024309772
24.50.12761786-0.0529842970.08856006-0.0494339290.033618194-0.02468147
24.750.12760139-0.0536969130.089268287-0.0503753690.033094916-0.025040809
250.12755072-0.0543927480.089938741-0.0512967510.032567993-0.025387753
25.250.127468223-0.0550710560.090572454-0.0521971350.032038124-0.025722253
25.50.127356157-0.0557311440.09117042-0.0530756490.03150591-0.026044201
25.750.127216669-0.0563723720.091733602-0.0539314870.03097194-0.026353481
260.127051801-0.0569941450.092262928-0.05476390.030436775-0.026649986
26.250.126863497-0.0575959180.092759294-0.0555721980.029900922-0.026933591
26.50.126653605-0.0581771850.093223569-0.0563557430.029364778-0.027204135
26.750.126423886-0.0587374820.093656591-0.0571139470.028828721-0.027461456
270.126175989-0.0592763790.094059159-0.0578462690.028293127-0.02770541
27.250.125910729-0.0597933860.094431748-0.0585521840.02775831-0.027935854
27.50.125628046-0.0602879420.094774488-0.0592311770.027224383-0.02815258
27.750.125327849-0.0607595230.095087501-0.0598827760.026691425-0.028355363
280.125010063-0.0612076480.095370919-0.0605065490.026159498-0.028543983
28.250.124674625-0.0616318710.095624883-0.06110210.025628669-0.028718229
28.50.124321487-0.0620317840.095849543-0.0616690690.025098954-0.028877899
28.750.123950611-0.062407010.096045056-0.0622071310.024570364-0.029022808
290.123561972-0.0627572080.096211588-0.0627159910.024042924-0.02915278
29.250.123155555-0.0630820640.096349308-0.0631953850.023516679-0.029267656
29.50.122731356-0.0633812940.096458395-0.0636450740.022991634-0.029367323
29.750.12228938-0.0636546390.09653903-0.064064850.022467786-0.0294517
300.121829639-0.0639018670.0965914-0.0644545260.021945143-0.029520715
30.250.121352156-0.064122770.096615698-0.0648139390.021423732-0.029574291
30.50.120856959-0.0643171620.096612118-0.0651429510.020903543-0.029612323
30.750.120344086-0.0644848770.096580859-0.0654414410.020384574-0.029634695
310.119813578-0.0646257720.096522124-0.0657093090.019866836-0.029641288
31.250.119265485-0.0647397190.096436118-0.0659464740.019350344-0.029631988
31.50.118699862-0.0648266120.096323047-0.0661528730.018835079-0.029606697
31.750.118116769-0.0648863580.096183123-0.0663284560.01832102-0.02956533
320.117516272-0.0649188830.096016555-0.0664731930.017808159-0.029507811
32.250.11689844-0.0649241270.095823558-0.0665870650.017296508-0.029434052
32.50.116263337-0.064902050.09560434-0.0666700750.016786103-0.029343937
32.750.115610789-0.0648527720.095358993-0.0667223740.016276995-0.029237351
330.114940426-0.0647765510.095087507-0.0667442440.015769248-0.029114184
33.250.11425189-0.0646736480.094789882-0.0667359710.015262907-0.028974329
33.50.113544848-0.0645443230.094466124-0.0666978390.014757941-0.02881769
33.750.112818987-0.0643888360.094116253-0.0666301320.01425432-0.028644174
340.112074018-0.0642074460.093740296-0.0665331340.01375205-0.028453694
34.250.111309671-0.0640004080.09333829-0.0664071240.013251166-0.028246166
34.50.110525694-0.0637679770.092910278-0.0662523840.012751779-0.028021478
34.750.109721855-0.0635104080.092456314-0.0660691920.012254028-0.027779521
350.108897938-0.0632279520.091976457-0.0658578250.01175805-0.027520198
35.250.108053744-0.0629208580.091470772-0.0656185580.01126399-0.027243418
35.50.10718909-0.0625893760.090939334-0.0653516650.010772024-0.026949102
35.750.106303807-0.0622337530.09038222-0.0650574190.010282322-0.026637179
360.105397742-0.0618542310.089799516-0.0647360880.009795055-0.026307581
36.250.104470754-0.0614510550.089191311-0.0643879410.009310404-0.025960248
36.50.103522716-0.0610244660.0885577-0.0640132450.008828527-0.025595139
36.750.102553512-0.0605747010.087898782-0.0636122630.008349571-0.025212224
370.10156304-0.0601019980.087214661-0.0631852570.007873685-0.024811479
37.250.100551206-0.0596065910.086505445-0.0627324880.007401022-0.024392889
37.50.09951793-0.0590887130.085771246-0.0622542130.006931769-0.023956434
37.750.09846314-0.0585485950.085012178-0.0617506890.006466103-0.023502104
380.097386774-0.0579864650.084228359-0.0612221680.006004177-0.02302989
38.250.096288781-0.0574025490.083419913-0.0606689020.005546138-0.022539783
38.50.095169115-0.0567970720.082586962-0.0600911390.005092181-0.022031774
38.750.094027742-0.0561702550.081729634-0.0594891280.004642508-0.021505862
390.092864634-0.055522320.080848058-0.0588631120.004197303-0.020962052
39.250.091679801-0.0548535620.079942413-0.0582134290.003756737-0.020400368
39.50.090473337-0.0541644810.079013007-0.057540660.003320988-0.019820854
39.750.08924535-0.0534555990.078060162-0.0568454110.002890241-0.019223559
400.087995951-0.0527274220.077084193-0.0561282720.002464665-0.018608539
40.250.086725254-0.0519804420.076085413-0.0553898160.002044417-0.017975858
40.50.085433373-0.0512151420.075064129-0.0546306040.001629632-0.01732559
40.750.084120424-0.0504319880.074020641-0.0538511780.001220432-0.016657815
410.082786527-0.0496314360.072955247-0.0530520680.000816928-0.015972615
41.250.0814318-0.048813930.071868237-0.0522337910.00041921-0.015270087
41.50.080056364-0.0479799040.0707599-0.051396852.73E-05-0.014550367
41.750.078660343-0.0471297770.069630518-0.050541732-0.000358627-0.013813603
420.077243858-0.0462639620.068480368-0.049668916-0.000738675-0.013059946
42.250.075807035-0.0453828580.067309723-0.048778866-0.001112787-0.012289555
42.50.074349998-0.0444868550.066118854-0.047872033-0.001480951-0.011502605
42.750.072872874-0.0435763330.064908025-0.04694886-0.001843151-0.010699277
430.071375788-0.0426516640.063677496-0.046009776-0.002199378-0.009879752
43.250.069858869-0.0417132080.062427524-0.0450552-0.002549641-0.009044224
43.50.068322244-0.0407613190.061158361-0.04408554-0.002893988-0.008192897
43.750.066766041-0.0397963390.059870257-0.043101194-0.003232475-0.00732597
440.065190389-0.0388186040.058563454-0.042102551-0.00356516-0.006443637
44.250.063595417-0.0378284410.057238196-0.041089988-0.0038921-0.005546084
44.50.061981254-0.0368261690.055894717-0.040063875-0.004213344-0.004633501
44.750.06034803-0.0358120980.054533253-0.039024572-0.004528952-0.003706078
450.058695875-0.0347865340.053154032-0.037972429-0.004838988-0.002764011
45.250.057024917-0.033749770.051757281-0.036907788-0.005143522-0.001807502
45.50.055335286-0.0327020980.050343224-0.035830985-0.005442638-0.000836784
45.750.053627113-0.0316437980.048912078-0.034742344-0.005736430.000147902
460.051900526-0.0305751460.047464061-0.033642183-0.0060249970.00114632
46.250.050155656-0.0294964110.045999385-0.032530813-0.0063084430.002158235
46.50.048392631-0.0284078540.044518261-0.031408536-0.0065868660.003183381
46.750.046611581-0.0273097330.043020893-0.030275648-0.0068603710.004221496
470.044812637-0.0262022990.041507489-0.029132437-0.0071290560.005272321
47.250.04299605-0.0250858530.039978359-0.02797925-0.0073930180.006335607
47.50.041162239-0.0239607690.038433958-0.026816511-0.007652360.007411112
47.750.039311623-0.0228274180.036874743-0.025644638-0.0079071950.008498597
480.037444612-0.021686160.035301158-0.024464041-0.0081576480.009597827
48.250.035561607-0.0205373460.033713638-0.023275117-0.0084038460.010708564
48.50.033663002-0.0193813170.032112605-0.022078252-0.0086459250.011830572
48.750.031749179-0.0182184060.030498473-0.020873824-0.008884020.012963615
490.029820512-0.0170489380.028871645-0.0196622-0.009118270.014107461
49.250.027877369-0.0158732260.027232515-0.018443737-0.0093488180.015261871
49.50.025920107-0.014691580.025581467-0.017218782-0.009575810.016426599
49.750.023949075-0.0135042980.023918876-0.015987674-0.0097993960.017601398
500.021964617-0.0123116710.022245107-0.014750744-0.0100197270.018786028
50.250.019967067-0.0111139830.020560519-0.013508312-0.0102369540.019980255
50.50.017956753-0.0099115110.018865459-0.012260691-0.0104512220.021183826
50.750.015933993-0.0087045250.017160268-0.011008186-0.0106626760.022396491
510.013899103-0.0074932860.015445279-0.009751093-0.010871460.023618005
51.250.011852387-0.0062780490.013720817-0.008489702-0.0110777150.024848125
51.50.009794146-0.0050590650.011987197-0.007224294-0.0112815550.026086606
51.750.007724671-0.0038365760.010244731-0.005955144-0.0114830910.02733321
520.005644251-0.0026108170.008493719-0.004682517-0.0116824320.028587701
52.250.003553166-0.0013820190.006734458-0.003406675-0.011879680.029849846
52.50.001451689-0.0001504060.004967235-0.002127871-0.0120749240.03111941
52.75-0.000659910.0010838030.003192332-0.000846351-0.0122682510.032396162
53-0.0027813680.0023203950.0014100250.000437644-0.0124597480.033679874
53.25-0.004912430.003559163-0.0003794180.00172388-0.0126494910.034970326
53.5-0.0070528420.004799905-0.0021757350.003012129-0.0128375370.036267301
53.75-0.0092023580.006042424-0.0039786690.004302168-0.013023940.037570585
54-0.0113607380.007286528-0.005787970.005593781-0.0132087610.038879969
54.25-0.0135277460.008532031-0.0076033920.006886757-0.0133920620.040195248
54.5-0.0157031490.009778749-0.0094246980.008180891-0.0135738930.041516215
54.75-0.0178867230.011026506-0.0112516530.009475983-0.0137543040.042842662
55-0.0200782460.012275129-0.0130840280.010771837-0.013933350.044174387
55.25-0.02227750.013524449-0.0149216020.012068264-0.0141110840.045511192
55.5-0.0244842740.014774302-0.0167641550.013365079-0.0142875560.046852881
55.75-0.026698360.016024528-0.0186114750.0146621-0.0144628150.048199257
56-0.0289195540.017274972-0.0204633540.015959154-0.0146369180.04955013
56.25-0.0311476570.018525481-0.0223195880.017256069-0.0148099240.050905309
56.5-0.0333824740.019775907-0.0241799780.018552678-0.0149818950.052264604
56.75-0.0356237850.021026114-0.0260443150.019848832-0.0151528990.053627827
57-0.0378712980.022275989-0.027912350.021144425-0.015323010.054994794
57.25-0.0401247140.023525426-0.0297838340.022439359-0.0154923020.056365323
57.5-0.042383740.024774323-0.0316585220.023733539-0.0156608390.057739236
57.75-0.044648090.026022577-0.0335361750.025026872-0.0158286830.059116358
58-0.0469174840.027270092-0.0354165630.026319268-0.0159958980.060496516
58.25-0.049191650.028516771-0.0372994560.027610639-0.0161625450.061879537
58.5-0.0514703220.029762522-0.0391846340.028900899-0.0163286820.06326524
58.75-0.0537532370.031007254-0.041071880.030189965-0.0164943660.064653451
59-0.0560401410.032250877-0.0429609810.031477755-0.0166596570.066043998
59.25-0.0583307850.033493307-0.0448517330.032764191-0.016824620.067436715
59.5-0.0606249250.034734459-0.0467439310.034049194-0.016989320.068831428
59.75-0.0629223230.035974251-0.0486373810.035332691-0.0171538310.070227968
60-0.0652227470.037212604-0.0505318880.036614607-0.017318230.071626168
60.25-0.0675259690.03844944-0.0524272660.037894872-0.0174825880.073025865
60.5-0.0698317660.039684684-0.054323330.039173416-0.0176469510.074426892
60.75-0.0721399210.040918261-0.0562199010.040450171-0.017811360.075829089
61-0.0744502220.042150101-0.0581168050.041725073-0.0179758580.077232297
61.25-0.0767624610.043380133-0.0600138710.042998056-0.0181404840.078636368
61.5-0.0790764350.044608289-0.061910930.044269058-0.0183052680.080041161
61.75-0.0813919450.045834504-0.0638078220.045538019-0.0184702390.081446545
62-0.0837087980.047058712-0.0657043850.04680488-0.0186354320.082852388
62.25-0.0860268030.04828085-0.0676004650.048069582-0.0188008770.084258563
62.5-0.0883457750.049500859-0.069495910.049332071-0.0189665780.085664945
62.75-0.0906655340.050718677-0.0713905710.050592291-0.0191325350.087071413
63-0.09298590.051934248-0.0732843050.051850189-0.0192987470.088477845
63.25-0.0953067030.053147514-0.0751769680.053105715-0.0194652080.089884128
63.5-0.0976277710.054358421-0.0770684250.054358817-0.0196318990.091290157
63.75-0.099948940.055566915-0.0789585380.055609447-0.0197987950.09269583
64-0.1022700480.056772944-0.0808471780.056857557-0.0199658770.09410105
64.25-0.1045909360.057976458-0.0827342150.058103101-0.0201331260.095505717
64.5-0.106911450.059177408-0.0846195240.059346035-0.0203005250.096909732
64.75-0.1092314390.060375745-0.0865029830.060586313-0.020468060.098312995
65-0.1115507540.061571423-0.0883844710.061823895-0.0206357190.099715411
65.25-0.1138692520.062764396-0.0902638730.063058739-0.020803490.101116884
65.5-0.1161867910.063954621-0.0921410730.064290804-0.0209713560.102517317
65.75-0.1185032330.065142054-0.0940159610.065520051-0.0211393020.103916611
66-0.1208184440.066326654-0.0958884290.066746443-0.0213073110.105314674
66.25-0.123132290.067508381-0.0977583690.067969942-0.0214753690.106711416
66.5-0.1254446440.068687194-0.0996256790.069190513-0.0216434510.108106747
66.75-0.1277553790.069863056-0.1014902570.070408121-0.0218115330.109500577
67-0.1300643730.07103593-0.1033520050.071622733-0.0219795950.110892819
67.25-0.1323715040.072205778-0.1052108260.072834314-0.0221476120.112283384
67.5-0.1346766560.073372567-0.1070666280.074042835-0.0223155530.113672192
67.75-0.1369797120.074536262-0.1089193170.075248263-0.0224833860.115059161
68-0.1392805620.07569683-0.1107688040.076450568-0.0226510770.116444212
68.25-0.1415790950.076854245-0.1126150110.077649728-0.0228185980.117827268
68.5-0.1438752030.078008502-0.1144578830.078845736-0.0229859150.119208245
68.75-0.1461687840.079159603-0.1162973740.08003859-0.0231530020.120587065
69-0.1484597340.080307548-0.1181334380.08122829-0.0233198290.121963649
69.25-0.1507479530.081452336-0.1199660310.082414833-0.0234863740.12333792
69.5-0.1530333450.082593969-0.1217951080.083598218-0.0236526210.1247098
69.75-0.1553158150.083732447-0.1236206280.084778446-0.0238185550.126079215
70-0.1575952680.084867772-0.1254425490.085955514-0.0239841620.127446089
70.25-0.1598716140.085999946-0.1272608320.087129423-0.0241494280.128810351
70.5-0.1621447640.087128969-0.1290754380.088300173-0.0243143380.130171928
70.75-0.1644146320.088254844-0.1308863280.089467764-0.0244788770.131530751
71-0.1666811330.089377572-0.1326934670.090632196-0.0246430340.132886752
71.25-0.1689441840.090497157-0.1344968180.09179347-0.0248067950.134239865
71.5-0.1712037040.091613599-0.1362963470.092951587-0.0249701520.135590027
71.75-0.1734596150.092726901-0.1380920190.094106547-0.0251330960.136937182
72-0.1757118380.093837067-0.1398838020.095258352-0.0252956210.138281271
72.25-0.17796030.094944099-0.1416716630.096407003-0.025457720.139622242
72.5-0.1802049250.096048-0.1434555730.097552501-0.0256193820.140960047
72.75-0.1824456440.097148773-0.1452355010.09869485-0.0257805980.142294642
73-0.1846823840.098246421-0.1470114170.099834049-0.0259413560.143625983
73.25-0.1869150790.099340949-0.1487832930.100970102-0.0261016480.14495403
73.5-0.1891436610.100432358-0.1505511010.10210301-0.0262614630.146278747
73.75-0.1913680650.101520654-0.1523148160.103232777-0.0264207940.147600102
74-0.1935882280.10260584-0.154074410.104359404-0.0265796340.148918067
74.25-0.1958040870.10368792-0.1558298590.105482895-0.0267379750.150232614
74.5-0.1980155820.104766898-0.1575811380.106603252-0.0268958070.151543718
74.75-0.2002226540.105842778-0.1593282240.107720478-0.0270531190.152851361
75-0.2024252440.106915564-0.1610710940.108834577-0.0272099010.154155521
75.25-0.2046232970.107985262-0.1628097250.109945552-0.0273661450.15545618
75.5-0.2068167590.109051875-0.1645440970.111053406-0.0275218470.156753321
75.75-0.2090055740.110115409-0.1662741870.112158143-0.0276770030.158046926
76-0.2111896920.111175867-0.1679999770.113259766-0.027831610.159336978
76.25-0.2133690610.112233255-0.1697214460.11435828-0.0279856650.160623465
76.5-0.2155436310.113287579-0.1714385760.115453689-0.0281391660.161906378
76.75-0.2177133550.114338842-0.1731513490.116545995-0.0282921080.163185714
77-0.2198781850.11538705-0.1748597460.117635204-0.0284444890.164461469
77.25-0.2220380750.116432208-0.1765637520.11872132-0.0285963090.165733639
77.5-0.224192980.117474322-0.1782633490.119804348-0.028747570.167002219
77.75-0.2263428570.118513397-0.1799585220.120884291-0.0288982760.168267206
78-0.2284876640.119549439-0.1816492560.121961154-0.029048430.169528598
78.25-0.2306273580.120582453-0.1833355350.123034943-0.0291980360.17078639
78.5-0.2327618990.121612444-0.1850173460.124105661-0.0293470980.172040582
78.75-0.2348912490.122639419-0.1866946760.125173314-0.0294956220.173291176
79-0.2370153690.123663383-0.188367510.126237907-0.0296436110.174538172
79.25-0.2391342220.124684343-0.1900358370.127299444-0.0297910720.17578157
79.5-0.2412477720.125702303-0.1916996440.128357931-0.029938010.177021374
79.75-0.2433559830.126717271-0.193358920.129413374-0.0300844340.178257586
80-0.2454588210.127729251-0.1950136530.130465777-0.0302303490.179490209
80.25-0.2475562530.128738251-0.1966638330.131515145-0.0303757630.180719247
80.5-0.2496482460.129744276-0.198309450.132561485-0.0305206830.181944707
80.75-0.251734770.130747332-0.1999504940.133604802-0.0306651170.183166598
81-0.2538157930.131747427-0.2015869550.1346451-0.0308090710.184384927
81.25-0.2558912850.132744566-0.2032188250.135682387-0.0309525530.185599703
81.5-0.2579612160.133738754-0.2048460940.136716667-0.0310955680.186810938
81.75-0.2600255610.13473-0.2064687550.137747947-0.0312381210.188018641
82-0.2620842980.135718311-0.2080868060.138776234-0.0313802170.189222825
82.25-0.2641374220.136703698-0.209700250.139801537-0.031521860.190423499
82.5-0.2661849570.137686177-0.2113091130.140823873-0.0316630560.191620676
82.75-0.2682269250.138665764-0.2129134140.141843256-0.0318038090.19281437
83-0.2702633470.139642476-0.2145131770.142859703-0.0319441240.194004593
83.25-0.2722942440.140616328-0.2161084210.143873227-0.0320840050.195191357
83.5-0.2743196370.141587335-0.2176991690.144883844-0.0322234580.196374678
83.75-0.2763395470.142555514-0.2192854410.145891569-0.0323624860.197554569
84-0.2783539950.143520879-0.2208672590.146896415-0.0325010940.198731045
84.25-0.2803630010.144483446-0.2224446420.147898398-0.0326392840.199904121
84.5-0.2823665870.145443229-0.2240176120.148897531-0.0327770610.20107381
84.75-0.2843647730.146400245-0.2255861890.14989383-0.032914430.202240127
85-0.2863575790.147354507-0.2271503930.150887308-0.0330513960.203403085
85.25-0.2883450260.148306031-0.2287102450.15187798-0.0331879620.2045627
85.5-0.2903271340.14925483-0.2302657650.152865858-0.0333241320.205718986
85.75-0.2923039240.150200921-0.2318169720.153850958-0.0334599070.20687196
86-0.2942754160.151144316-0.2333638870.154833293-0.0335952890.208021636
86.25-0.296241630.15208503-0.2349065290.155812877-0.0337302820.209168031
86.5-0.2982025850.153023078-0.2364449170.156789723-0.0338648870.210311159
86.75-0.3001583030.153958474-0.2379790720.157763845-0.0339991070.211451037
87-0.3021088010.154891231-0.2395090120.158735256-0.0341329460.21258768
87.25-0.3040541020.155821363-0.2410347570.159703969-0.0342664060.213721103
87.5-0.3059942230.156748885-0.2425563250.160669998-0.034399490.214851322
87.75-0.3079291850.157673809-0.2440737370.161633355-0.0345322020.215978351
88-0.3098590070.158596149-0.2455870090.162594055-0.0346645450.217102204
88.25-0.3117837080.159515919-0.2470961620.163552108-0.0347965220.218222898
88.5-0.3137033080.160433132-0.2486012140.164507529-0.0349281350.219340446
88.75-0.3156178270.161347801-0.2501021820.165460331-0.0350593860.220454866
89-0.3175272830.162259939-0.2515990870.166410525-0.0351902760.221566172
89.25-0.3194316950.163169559-0.2530919450.167358124-0.0353208080.222674379
89.5-0.3213310820.164076675-0.2545807750.168303141-0.0354509810.223779504
89.75-0.3232254630.164981299-0.2560655950.169245588-0.0355807990.224881562
90-0.3251148580.165883443-0.2575464230.170185478-0.0357102620.22598057
90.25-0.3269992840.166783121-0.2590232760.171122822-0.0358393730.227076542
90.5-0.3288787610.167680344-0.2604961720.172057633-0.0359681320.228169494
90.75-0.3307533070.168575126-0.261965130.172989923-0.036096540.229259442
91-0.332622940.169467478-0.2634301650.173919703-0.03622460.2303464
91.25-0.3344876780.170357413-0.2648912950.174846986-0.0363523130.231430384
91.5-0.336347540.171244943-0.2663485380.175771783-0.036479680.23251141
91.75-0.3382025460.17213008-0.2678019120.176694106-0.0366067030.233589493
92-0.3400527140.173012837-0.2692514330.177613968-0.0367333830.234664648
92.25-0.3418980620.173893224-0.2706971180.178531378-0.0368597210.23573689
92.5-0.3437386060.174771254-0.2721389840.17944635-0.036985720.236806235
92.75-0.3455743620.175646938-0.2735770460.180358892-0.0371113810.237872698
93-0.3474053450.176520288-0.2750113180.181269017-0.0372367050.238936294
93.25-0.3492315720.177391314-0.2764418190.182176735-0.0373616940.239997039
93.5-0.3510530690.178260029-0.2778685670.183082059-0.037486350.241054946
93.75-0.3528698620.179126446-0.2792915820.183985002-0.0376106730.242110032
94-0.3546819760.179990577-0.2807108860.184885577-0.0377346670.24316231
94.25-0.3564894320.180852434-0.2821264960.185783796-0.0378583320.244211795
94.5-0.358292220.181712024-0.2835384140.186679663-0.0379816690.245258502
94.75-0.3600903250.182569354-0.284946640.187573182-0.0381046810.246302444
95-0.3618837310.18342443-0.2863511750.188464355-0.0382273690.247343636

 
M and S spline coefficients for males 3 to 95 years
 
 FEV1FVCFEV1/FVC ratio
AgeMSMSMS
3-0.1197755940.184307362-0.0569425650.149455893-0.0349395380.01755124
3.25-0.1139554540.171160981-0.0542627730.138593778-0.0339256170.0221529
3.5-0.1084033080.158994969-0.0517467030.12854384-0.0330647070.026377944
3.75-0.1030896760.147679297-0.0493937720.119199604-0.0323747790.030225016
4-0.0980349020.137110566-0.0472176130.110476538-0.0318653470.033665118
4.25-0.0934008370.127211229-0.0452841070.102312293-0.031538990.03665079
4.5-0.0893237420.117916644-0.0436467060.094654776-0.0313799080.039135686
4.75-0.0858706330.109172031-0.0423340310.087459385-0.0313720240.041108046
5-0.083017780.100933825-0.04135020.080690062-0.0314923210.042596322
5.25-0.0807253620.093163853-0.040690620.074315006-0.0316874960.043662055
5.5-0.0789541470.085827647-0.0403463540.068305417-0.0318923790.044381505
5.75-0.0776255960.078894526-0.0402870430.062635308-0.0320509650.044814446
6-0.0766296830.072337153-0.0404653970.057281204-0.0321173660.04501273
6.25-0.0758756120.066130609-0.040841180.05222175-0.0320665480.04502296
6.5-0.0752902080.060252124-0.0413809210.047437478-0.0318939440.044882986
6.75-0.0748328880.054680771-0.0420550960.042910563-0.0315986290.044626511
7-0.0745142020.049397165-0.0428353530.038624578-0.0311757460.044271869
7.25-0.0743478060.044383519-0.0436975190.03456448-0.030628990.043819595
7.5-0.0743435020.039623524-0.0446213960.030716481-0.0299746710.043257301
7.75-0.0745080430.035102191-0.0455900690.027067926-0.0292351740.042569823
8-0.0748233240.030805517-0.0465805450.023607021-0.0284357290.041741105
8.25-0.07519160.026719872-0.0475416280.020322364-0.0275999740.040752118
8.5-0.075512830.022832583-0.0484237140.017203371-0.0267460360.039582986
8.75-0.075703890.019132025-0.0491858940.014240327-0.0258822230.038233467
9-0.0756958290.015607502-0.049794530.011424295-0.0249789450.036751685
9.25-0.0754316150.012249159-0.050222080.008747034-0.0239897890.03520758
9.5-0.0748604140.009047749-0.0504446750.006200837-0.0228753580.033668013
9.75-0.0739168450.005993827-0.0504340670.003777988-0.0216090780.032185617
10-0.0725378050.003078378-0.0501637990.001471157-0.0201739250.030798272
10.25-0.0706710540.00029313-0.049612291-0.000726394-0.018560.029531439
10.5-0.068273636-0.002369527-0.04876212-0.002820878-0.0167647090.028398948
10.75-0.065310536-0.004916603-0.047599405-0.004818033-0.0147906510.027407663
11-0.061753529-0.00735457-0.046113283-0.006723165-0.0126454590.026562318
11.25-0.057581415-0.009689409-0.044295848-0.008541194-0.0103421140.025863005
11.5-0.052812865-0.011926584-0.042152399-0.010276713-0.0078995620.025303362
11.75-0.047505135-0.014071079-0.039700947-0.011934022-0.0053412560.024874178
12-0.041712276-0.01612753-0.036958928-0.013517123-0.002691770.024563815
12.25-0.035483352-0.018100261-0.033942579-0.0150297432.39E-050.024359257
12.5-0.028862958-0.019993309-0.030667035-0.0164753620.0027799720.024243716
12.75-0.021891672-0.021810449-0.027146425-0.0178572280.0055508510.02419839
13-0.01460646-0.023555217-0.02339395-0.0191783810.0083119220.024204644
13.25-0.007041031-0.025230925-0.019421961-0.0204416680.0110408790.024245236
13.50.000772006-0.026840657-0.015243034-0.0216497540.0137177830.024304884
13.750.008773402-0.0283869-0.010885127-0.0228050960.0163251510.02437092
140.016886095-0.029871683-0.006386638-0.0239099710.0188472920.024432178
14.250.025040024-0.031296943-0.001782701-0.0249665210.02126960.024476893
14.50.033172115-0.0326645380.002894871-0.0259767690.0235791360.024493244
14.750.041225603-0.033976250.007617271-0.0269426230.0257657070.024471153
150.049149418-0.0352337930.012358413-0.0278658890.0278215110.0244019
15.250.056897642-0.0364388090.017094676-0.0287482730.0297409640.024278415
15.50.064429016-0.0375928790.021804675-0.0295913920.0315203660.02409507
15.750.071706506-0.0386975190.026469057-0.0303967770.0331581490.023847746
160.078696905-0.0397541880.031070313-0.0311658810.0346541660.023533943
16.250.085373739-0.0407642160.035592604-0.0319000130.0360095090.023152924
16.50.091728764-0.0417285370.040021563-0.0326000910.0372274980.022705226
16.750.09775948-0.0426479680.044344203-0.0332669080.0383128720.022191606
170.10346408-0.0435233230.048548818-0.0339012360.0392708830.021612804
17.250.108841384-0.0443554070.052624865-0.0345038270.0401068270.020969752
17.50.113890765-0.0451450170.056562868-0.0350754140.0408263210.020263937
17.750.118612098-0.0458929450.060354319-0.0356167110.0414353240.019497286
180.123005703-0.0465999670.063991603-0.0361284140.0419397180.018671858
18.250.127072297-0.0472668530.067467915-0.0366111980.0423453540.017789909
18.50.130812954-0.047894360.070777195-0.0370657240.0426586410.016854992
18.750.134229065-0.0484832340.073914063-0.0374926320.0428860160.015870864
190.137322301-0.0490342070.076873763-0.0378925470.0430337260.014840877
19.250.140094604-0.0495480030.079652118-0.0382660770.0431076970.013768374
19.50.142553-0.0500253710.082248345-0.0386137790.0431133680.012657416
19.750.144715578-0.0504671480.084668541-0.0389361250.0430557350.011512017
200.146600993-0.050874160.086919473-0.0392335670.0429394120.010335984
20.250.148226832-0.051247210.089007595-0.0395065510.0427688470.00913302
20.50.149609679-0.0515870760.090939061-0.0397555170.0425485860.007906602
20.750.150765184-0.0518945170.092719741-0.0399808940.0422830770.006660033
210.151708117-0.0521702680.094355241-0.0401831090.0419766430.005396413
21.250.152452425-0.0524150440.095850915-0.0403625780.0416333640.004118707
21.50.153011281-0.0526295410.097211879-0.0405197110.0412568780.00282972
21.750.153397135-0.0528144340.098443024-0.0406549110.0408505330.001531999
220.153621752-0.0529703810.099549029-0.0407685730.0404174610.000227949
22.250.15369626-0.0530980190.100534369-0.0408610850.039960552-0.00107999
22.50.153631182-0.053197970.101403331-0.0409328280.039482359-0.002389467
22.750.153436475-0.0532708380.102160019-0.0409841760.0389853-0.00369825
230.153121563-0.0533172120.102808364-0.0410154950.038471711-0.005004279
23.250.152695354-0.0533376870.103352414-0.0410271680.037943744-0.006305684
23.50.152166213-0.053332990.103797587-0.04101970.037403189-0.007600732
23.750.151542039-0.0533038680.10414958-0.0409936260.03685169-0.008887798
240.150830316-0.0532510420.104413805-0.040949460.036290841-0.010165307
24.250.150038139-0.0531752070.10459541-0.0408877010.035722131-0.011431734
24.50.149172229-0.0530770330.104699293-0.0408088290.035146854-0.012685512
24.750.148238961-0.0529571650.104730112-0.0407133070.034566225-0.013925127
250.147244378-0.0528162260.104692301-0.0406015840.033981428-0.01514917
25.250.146194214-0.0526548180.10459008-0.0404740930.033393577-0.01635626
25.50.145093904-0.0524735190.104427469-0.0403312530.032803597-0.017544681
25.750.143948606-0.0522728910.104208294-0.0401734690.032212316-0.018712685
260.142763215-0.0520534730.103936201-0.0400011330.031620531-0.019858591
26.250.141542372-0.0518157880.103614664-0.0398146240.031029015-0.020980785
26.50.140290484-0.0515603410.103246992-0.0396143090.030438422-0.022077715
26.750.139011733-0.051287620.102836341-0.0394005430.029849329-0.023147909
270.137710088-0.0509980970.102385718-0.039173670.029262244-0.024189964
27.250.136389316-0.0506922270.101897992-0.0389340230.028677634-0.025202541
27.50.135052993-0.0503704530.101375896-0.0386819250.028095899-0.026184314
27.750.13370446-0.0500332010.10082202-0.0384176910.027517402-0.027133962
280.132345912-0.0496809140.100238459-0.0381416560.026942503-0.028050214
28.250.130978568-0.0493140380.099626887-0.037854170.026371535-0.028931923
28.50.129603563-0.0489330080.098988891-0.0375555750.025804734-0.029778186
28.750.128221973-0.0485382430.098325994-0.0372461980.025242287-0.030588207
290.126834828-0.0481301480.097639652-0.0369263580.0246844-0.031361205
29.250.125443106-0.0477091140.096931261-0.0365963610.024131279-0.032096402
29.50.124047741-0.047275520.096202159-0.0362565050.023583073-0.032793049
29.750.122649622-0.0468297330.095453625-0.0359070770.023039887-0.033450455
300.121249596-0.0463721070.094686887-0.0355483540.022501808-0.034067995
30.250.11984847-0.0459029840.09390312-0.0351806070.021968905-0.034645147
30.50.118447015-0.0454226970.093103452-0.0348040940.021441167-0.035181631
30.750.117045962-0.0449315680.092288964-0.0344190690.020918542-0.035677253
310.11564601-0.0444299060.091460691-0.0340257740.020400952-0.036131842
31.250.114247825-0.0439180140.090619626-0.0336244470.019888292-0.036545282
31.50.11285204-0.0433961840.089766723-0.0332153170.019380366-0.036917567
31.750.11145926-0.0428646980.088902894-0.0327986050.018876933-0.037248713
320.110070059-0.042323830.088029015-0.0323745260.018377747-0.037538767
32.250.108684985-0.0417738470.087145926-0.031943290.017882577-0.037787807
32.50.107304559-0.0412150050.086254434-0.0315050960.0173912-0.037996034
32.750.105929279-0.0406475540.085355312-0.0310601430.016903399-0.038163668
330.104559617-0.0400717370.084449302-0.0306086190.016418939-0.038290925
33.250.103195985-0.0394877890.083537089-0.030150710.015937573-0.038377998
33.50.101838102-0.0388959430.08261885-0.0296866110.015458996-0.038425025
33.750.100485103-0.038296430.081694336-0.0292165210.014982889-0.038432125
340.099136143-0.0376894710.080763297-0.0287406370.014508933-0.038399416
34.250.097790409-0.0370752850.079825496-0.0282591480.014036849-0.038327004
34.50.096447126-0.0364540810.078880711-0.0277722370.013566473-0.038214999
34.750.095105549-0.0358260640.07792873-0.0272800820.01309769-0.038063486
350.093764967-0.0351914320.076969355-0.0267828550.012630404-0.037872532
35.250.092424697-0.0345503770.076002399-0.0262807220.012164561-0.037642211
35.50.091084086-0.0339030860.075027684-0.0257738450.011700136-0.037372631
35.750.089742509-0.0332497390.074045046-0.0252623810.011237103-0.037063915
360.088399368-0.0325905140.073054326-0.0247464820.010775431-0.036716206
36.250.087054089-0.0319255810.072055379-0.0242262960.010315107-0.036329688
36.50.085706124-0.0312551060.071048067-0.0237019650.009856156-0.035904622
36.750.084354948-0.0305792510.070032261-0.0231736280.00939863-0.035441292
370.083000059-0.0298981730.069007839-0.0226414190.008942585-0.034939952
37.250.081640976-0.0292120230.067974689-0.0221054710.008488068-0.034400872
37.50.080277239-0.0285209510.066932706-0.0215659080.008035079-0.033824379
37.750.078908408-0.0278251010.06588179-0.0210228540.007583618-0.033210809
380.077534064-0.0271246120.064821851-0.0204764290.007133684-0.032560508
38.250.076153802-0.026419620.063752803-0.0199267480.006685275-0.031873847
38.50.07476724-0.0257102590.062674569-0.0193739240.006238411-0.031151208
38.750.07337401-0.0249966570.061587075-0.0188180670.005793124-0.030392952
390.07197376-0.024278940.060490255-0.0182592820.005349458-0.029599422
39.250.070566155-0.0235572290.059384048-0.0176976720.004907443-0.02877097
39.50.069150874-0.0228316430.058268397-0.0171333380.004467099-0.027908004
39.750.067727613-0.0221022980.057143252-0.0165663780.004028433-0.027010938
400.06629601-0.0213693160.056008528-0.0159968910.003591451-0.026080176
40.250.064855563-0.020632840.054864057-0.0154249920.003156162-0.025116118
40.50.063405765-0.0198930120.053709668-0.0148507940.002722596-0.024119172
40.750.061946131-0.019149970.052545197-0.0142744060.002290793-0.023089744
410.060476196-0.0184038480.05137049-0.0136959330.001860799-0.022028226
41.250.058995517-0.0176547760.050185402-0.0131154790.001432648-0.020935001
41.50.057503667-0.0169028810.048989794-0.0125331430.001006361-0.019810437
41.750.056000239-0.0161482850.047783539-0.0119490230.000581943-0.018654887
420.054484844-0.0153911070.046566513-0.0113632110.000159386-0.017468703
42.250.052957109-0.0146314640.045338602-0.010775799-0.000261316-0.016252268
42.50.051416678-0.0138694680.044099697-0.010186877-0.000680136-0.015006035
42.750.04986321-0.0131052280.042849698-0.009596528-0.001097037-0.013730463
430.048296381-0.012338850.041588509-0.009004838-0.001511981-0.01242601
43.250.04671588-0.0115704380.040316042-0.008411887-0.001924938-0.011093151
43.50.045121411-0.0108000910.039032214-0.007817752-0.002335884-0.009732389
43.750.043512691-0.0100279080.037736948-0.007222512-0.002744805-0.008344222
440.04188945-0.0092539830.036430171-0.006626239-0.003151699-0.006929132
44.250.040251431-0.0084784070.035111819-0.006029005-0.00355657-0.005487604
44.50.03859839-0.0077012710.033781829-0.005430881-0.003959413-0.00402015
44.750.036930093-0.0069226620.032440144-0.004831934-0.004360223-0.002527274
450.035246319-0.0061426630.031086714-0.004232229-0.004759005-0.001009467
45.250.033546857-0.0053613580.029721489-0.003631832-0.0051557840.000532769
45.50.031831507-0.0045788250.028344428-0.003030803-0.0055506170.002098882
45.750.030100079-0.0037951430.026955491-0.002429203-0.0059435720.003688313
460.028352392-0.0030103870.025554642-0.00182709-0.0063347220.005300503
46.250.026588275-0.0022246310.024141852-0.001224522-0.0067241520.006934894
46.50.024807568-0.0014379460.022717092-0.000621554-0.0071119540.008590905
46.750.023010116-0.0006504010.021280337-1.82E-05-0.007498220.010267956
470.0211957750.0001379350.0198315680.000585371-0.0078830470.011965483
47.250.0193644090.0009269980.0183707670.001189225-0.0082665250.013682929
47.50.017515890.0017167240.0168979190.001793275-0.0086487260.015419752
47.750.0156501060.0025070490.0154130210.002397471-0.0090297120.017175427
480.013767150.0032978980.0139162230.003001762-0.009409540.01894945
48.250.0118672820.0040891860.0124078040.003606091-0.0097882540.020741347
48.50.0099507680.0048808290.0108880410.004210404-0.0101658480.022550727
48.750.0080178650.0056727450.0093572070.004814648-0.0105423050.024377222
490.0060688280.0064648560.0078155660.005418772-0.0109176160.026220461
49.250.0041039070.0072570850.0062633780.006022726-0.0112917690.028080074
49.50.0021233470.0080493570.0047008980.00662646-0.0116647390.029955659
49.750.000127390.00884160.0031283730.007229928-0.0120365030.031846813
50-0.0018837290.0096337440.0015460460.007833085-0.0124070480.033753141
50.25-0.0039097760.01042572-4.58E-050.008435886-0.0127763720.035674245
50.5-0.0059505230.011217462-0.0016470680.009038287-0.0131444950.037609715
50.75-0.0080057450.012008905-0.0032573960.009640248-0.0135114490.039559142
51-0.0100752210.012799988-0.0048766060.010241727-0.0138772720.041522129
51.25-0.0121587350.013590648-0.006504480.010842685-0.0142420020.043498275
51.5-0.0142560740.014380826-0.0081408060.011443085-0.0146056690.04548716
51.75-0.0163670270.015170467-0.0097853750.012042888-0.0149682990.047488369
52-0.0184913880.015959512-0.0114379840.012642058-0.0153299170.0495015
52.25-0.0206289560.01674791-0.0130984330.013240562-0.0156905510.051526157
52.5-0.0227795310.017535606-0.0147665260.013838365-0.0160502130.053561945
52.75-0.0249429180.01832255-0.0164420730.014435433-0.0164089210.055608475
53-0.0271189230.019108692-0.0181248860.015031736-0.0167666950.057665355
53.25-0.0293073580.019893984-0.0198147820.015627242-0.0171235470.059732195
53.5-0.0315080360.020678379-0.0215115830.016221921-0.0174794640.061808616
53.75-0.0337207750.021461831-0.0232151110.016815744-0.0178344330.063894248
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54.25-0.0381817170.023025735-0.026641670.018000709-0.0185414850.068091695
54.5-0.0404295680.023806101-0.0283643660.018591798-0.0188935380.070202794
54.75-0.0426887780.024585356-0.0300931240.019181922-0.0192445810.072321675
55-0.0449591780.02536346-0.0318277870.019771057-0.0195945960.074447997
55.25-0.04724060.026140376-0.0335681980.020359179-0.0199435730.076581435
55.5-0.0495328840.026916067-0.0353142070.020946264-0.0202915010.078721676
55.75-0.0518358670.027690496-0.0370656640.021532289-0.0206383640.08086842
56-0.0541493930.02846363-0.0388224250.022117233-0.0209841530.083021379
56.25-0.0564733050.029235434-0.0405843470.022701074-0.0213288570.085180262
56.5-0.0588074510.030005875-0.0423512910.02328379-0.0216724650.087344769
56.75-0.0611516810.030774922-0.0441231190.023865363-0.022014970.089514611
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57.5-0.0682431560.033073397-0.0494664660.025603028-0.0230358620.096053223
57.75-0.0706254850.033836572-0.0512561440.02617984-0.023373940.098241428
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58.25-0.0754151630.035358291-0.0548466770.027329755-0.0240467510.102628977
58.5-0.0778216130.036116785-0.056646990.027902827-0.0243815030.104827733
58.75-0.0802352220.036873671-0.0584503140.028474625-0.0247151760.107029437
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59.25-0.0850822280.038382526-0.0620649810.029614339-0.0253793710.111440611
59.5-0.0875148050.039134452-0.0638758280.03018223-0.0257099170.113649561
59.75-0.0899529010.039884683-0.0656886980.030748794-0.026039430.115860426
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60.25-0.0948441080.041379979-0.0693195780.031877891-0.0266953560.120286958
60.5-0.0972964720.042125006-0.0711371390.032440402-0.0270217830.122502132
60.75-0.0997528580.042868261-0.0729558210.033001541-0.0273472080.124718233
61-0.1022129130.043609727-0.0747754140.033561296-0.0276716490.126935006
61.25-0.1046762930.044349387-0.0765957090.034119659-0.0279951280.129152207
61.5-0.107142660.045087224-0.0784165040.034676619-0.0283176590.131369604
61.75-0.1096116850.045823222-0.0802376030.035232167-0.0286392620.133586973
62-0.1120830450.046557367-0.0820588110.035786295-0.0289599470.135804097
62.25-0.1145564260.047289644-0.083879940.036338993-0.0292797310.13802076
62.5-0.117031520.048020037-0.0857008060.036890254-0.0295986310.140236731
62.75-0.1195080270.048748535-0.087521230.03744007-0.0299166660.142451781
63-0.1219856520.049475123-0.0893410340.037988433-0.0302338550.144665683
63.25-0.1244641090.050199788-0.0911600490.038535336-0.0305502150.146878215
63.5-0.1269431180.050922519-0.0929781060.039080772-0.0308657540.149089165
63.75-0.1294224020.051643303-0.0947950410.039624734-0.0311804760.151298328
64-0.1319016960.052362129-0.0966106960.040167216-0.0314943840.153505505
64.25-0.1343807360.053078986-0.0984249140.040708212-0.0318074820.155710499
64.5-0.1368592660.053793864-0.1002375410.041247716-0.0321197810.157913119
64.75-0.1393370370.054506752-0.1020484310.041785722-0.0324312970.160113179
65-0.1418138040.05521764-0.1038574370.042322224-0.0327420420.162310495
65.25-0.1442893280.05592652-0.1056644170.042857219-0.0330520330.164504894
65.5-0.1467633750.056633383-0.1074692340.0433907-0.0333612820.166696219
65.75-0.1492357170.057338218-0.1092717510.043922664-0.0336698050.168884318
66-0.1517061320.05804102-0.1110718360.044453106-0.0339776140.171069048
66.25-0.1541744010.058741779-0.1128693610.044982021-0.0342847220.173250267
66.5-0.1566403110.059440488-0.11466420.045509406-0.0345911370.175427849
66.75-0.1591036550.060137139-0.1164562290.046035257-0.0348968650.177601671
67-0.1615642280.060831727-0.1182453290.046559571-0.0352019130.179771615
67.25-0.1640218330.061524244-0.1200313820.047082344-0.0355062830.181937564
67.5-0.1664762760.062214683-0.1218142750.047603573-0.0358099590.184099415
67.75-0.1689273650.06290304-0.1235938960.048123255-0.0361129230.18625707
68-0.1713749180.063589309-0.1253701350.048641387-0.0364151570.188410433
68.25-0.1738187520.064273483-0.1271428860.049157967-0.0367166430.190559412
68.5-0.176258690.064955558-0.1289120460.049672992-0.0370173570.192703925
68.75-0.1786945830.065635532-0.130677530.050186462-0.0373172760.194843891
69-0.1811263440.066313411-0.1324392980.05069838-0.0376163770.196979232
69.25-0.1835538950.066989202-0.1341973170.051208751-0.0379146390.199109876
69.5-0.1859771650.067662911-0.1359515570.051717581-0.0382120440.201235755
69.75-0.1883960790.068334547-0.1377019860.052224872-0.0385085740.203356801
70-0.1908105690.069004114-0.1394485770.05273063-0.038804210.205472949
70.25-0.1932205650.069671622-0.1411912990.05323486-0.0390989360.207584138
70.5-0.1956260.070337076-0.1429301260.053737566-0.039392730.209690323
70.75-0.198026810.071000484-0.1446650310.054238752-0.0396855680.21179146
71-0.2004229310.071661853-0.1463959870.054738424-0.039977430.213887511
71.25-0.2028143010.07232119-0.148122970.055236586-0.0402682980.215978436
71.5-0.205200860.072978501-0.1498459550.055733243-0.0405581560.218064202
71.75-0.207582550.073633794-0.1515649190.056228399-0.040846990.220144778
72-0.2099593130.074287076-0.1532798380.05672206-0.041134790.22222013
72.25-0.2123310930.074938354-0.1549906910.057214229-0.0414215450.224290225
72.5-0.2146978370.075587635-0.1566974570.057704912-0.041707250.226355034
72.75-0.2170594920.076234926-0.1584001140.058194114-0.0419918990.228414528
73-0.2194160060.076880233-0.1600986420.058681838-0.042275490.230468683
73.25-0.221767330.077523564-0.1617930240.05916809-0.0425580190.232517471
73.5-0.2241134140.078164926-0.1634832380.059652875-0.0428394820.234560872
73.75-0.2264542130.078804326-0.1651692690.060136197-0.0431198760.236598867
74-0.2287896790.079441771-0.1668510980.060618061-0.0433991980.238631437
74.25-0.2311197670.080077267-0.1685287090.061098472-0.0436774460.240658567
74.5-0.2334444350.080710822-0.1702020860.061577434-0.0439546220.242680246
74.75-0.235763640.081342442-0.1718712120.062054952-0.0442307270.244696464
75-0.2380773420.081972135-0.1735360740.062531032-0.0445057610.246707212
75.25-0.2403854990.082599908-0.1751966560.063005677-0.0447797280.248712479
75.5-0.2426880730.083225766-0.1768529450.063478893-0.0450526280.250712261
75.75-0.2449850270.083849718-0.1785049280.063950683-0.0453244630.25270655
76-0.2472763240.08447177-0.1801525920.064421054-0.0455952320.254695343
76.25-0.2495619280.085091929-0.1817959240.06489001-0.045864940.256678632
76.5-0.2518418040.085710202-0.1834349130.065357555-0.0461335910.258656407
76.75-0.254115920.086326595-0.1850695470.065823694-0.0464011950.260628661
77-0.2563842430.086941116-0.1866998170.066288432-0.0466677580.262595384
77.25-0.2586467410.08755377-0.1883257110.066751774-0.046933290.26455657
77.5-0.2609033840.088164566-0.1899472190.067213724-0.0471977990.266512217
77.75-0.2631541410.08877351-0.1915643330.067674287-0.0474612950.268462322
78-0.2653989860.089380608-0.1931770440.068133468-0.0477237860.270406884
78.25-0.2676378880.089985868-0.1947853420.068591271-0.0479852810.272345905
78.5-0.2698708220.090589295-0.196389220.069047702-0.0482457870.274279389
78.75-0.2720977620.091190897-0.197988670.069502764-0.0485053130.276207344
79-0.2743186820.091790681-0.1995836860.069956463-0.0487638670.278129776
79.25-0.2765335570.092388653-0.2011742590.070408804-0.0490214580.280046689
79.5-0.2787423650.092984819-0.2027603840.07085979-0.0492780960.281958087
79.75-0.2809450830.093579187-0.2043420550.071309426-0.0495337940.283863971
80-0.2831416880.094171762-0.2059192650.071757718-0.0497885630.285764342
80.25-0.2853321590.094762552-0.207492010.07220467-0.0500424130.287659206
80.5-0.2875164760.095351563-0.2090602840.072650286-0.0502953550.289548573
80.75-0.2896946180.095938802-0.2106240830.073094571-0.05054740.291432459
81-0.2918665680.096524275-0.2121834020.07353753-0.0507985580.29331088
81.25-0.2940323050.097107989-0.2137382380.073979168-0.0510488370.295183855
81.5-0.2961918140.09768995-0.2152885870.074419488-0.0512982460.297051402
81.75-0.2983450760.098270165-0.2168344450.074858496-0.0515467930.298913541
82-0.3004920750.098848639-0.218375810.075296195-0.0517944870.300770291
82.25-0.3026327990.099425381-0.2199126790.075732592-0.0520413360.302621674
82.5-0.3047672580.100000397-0.2214450660.076167691-0.0522873450.304467707
82.75-0.3068954870.100573699-0.2229729940.076601501-0.0525325240.306308409
83-0.3090175180.101145296-0.2244964860.077034028-0.0527768790.308143798
83.25-0.3111333850.101715197-0.2260155660.07746528-0.0530204180.309973891
83.5-0.3132431190.102283413-0.2275302560.077895263-0.0532631480.311798707
83.75-0.3153467520.102849953-0.2290405790.078323986-0.0535050770.313618262
84-0.3174443170.103414826-0.2305465590.078751454-0.0537462130.315432574
84.25-0.3195358460.103978043-0.2320482170.079177675-0.0539865640.31724166
84.5-0.321621370.104539612-0.2335455760.079602656-0.0542261380.319045536
84.75-0.3237009190.105099542-0.2350386580.080026404-0.0544649440.320844219
85-0.3257745250.105657843-0.2365274850.080448924-0.0547029920.322637725
85.25-0.327842220.106214524-0.2380120790.080870225-0.0549402880.324426071
85.5-0.3299040320.106769595-0.2394924620.081290313-0.0551768420.326209278
85.75-0.3319599930.107323063-0.2409686550.081709194-0.055412660.327987368
86-0.3340101320.107874938-0.2424406790.082126875-0.055647750.329760361
86.25-0.336054480.108425229-0.2439085560.082543362-0.055882120.33152828
86.5-0.3380930660.108973944-0.2453723070.082958662-0.0561157760.333291143
86.75-0.3401259190.109521092-0.2468319520.083372781-0.0563487260.335048971
87-0.3421530680.110066682-0.2482875120.083785727-0.0565809780.336801784
87.25-0.3441745430.110610723-0.2497390080.084197504-0.0568125390.338549603
87.5-0.3461903710.111153222-0.251186460.084608119-0.0570434140.340292453
87.75-0.3482005820.111694188-0.2526298890.085017578-0.057273610.342030359
88-0.3502052040.11223363-0.2540693140.085425888-0.0575031320.343763346
88.25-0.3522042650.112771555-0.2555047550.085833055-0.0577319870.345491441
88.5-0.3541977930.113307973-0.2569362330.086239085-0.057960180.34721467
88.75-0.3561858150.113842891-0.2583637670.086643983-0.0581877150.348933058
89-0.3581683580.114376316-0.2597873760.087047756-0.0584145970.35064663
89.25-0.3601454510.114908258-0.261207080.087450409-0.0586408320.352355414
89.5-0.362117120.115438724-0.2626228980.087851949-0.0588664240.354059434
89.75-0.3640833910.115967722-0.2640348490.088252381-0.0590913760.355758716
90-0.3660442930.116495259-0.2654429530.088651712-0.0593156920.357453286
90.25-0.3679998520.117021345-0.2668472280.089049946-0.0595393770.359143169
90.5-0.3699500930.117545985-0.2682476930.08944709-0.0597624350.36082839
90.75-0.3718950410.118069188-0.2696443660.089843148-0.0599848690.362508972
91-0.3738347210.118590961-0.2710372620.090238127-0.0602066850.364184941
91.25-0.3757691580.119111312-0.2724264010.090632032-0.0604278850.365856321
91.5-0.3776983810.119630248-0.2738118030.091024869-0.0606484750.367523134
91.75-0.379622420.120147777-0.2751934910.091416643-0.0608684570.369185406
92-0.3815413040.120663908-0.2765714860.091807362-0.0610878380.370843159
92.25-0.383455060.121178647-0.2779458090.09219703-0.0613066190.372496417
92.5-0.3853637120.121692002-0.2793164730.092585653-0.0615248060.374145204
92.75-0.3872672780.12220398-0.2806834940.092973235-0.0617424010.375789544
93-0.3891657810.122714586-0.2820468860.093359781-0.0619594090.37742946
93.25-0.391059240.123223828-0.2834066610.093745296-0.0621758310.379064976
93.5-0.3929476750.123731712-0.2847628340.094129784-0.0623916730.380696114
93.75-0.3948311070.124238244-0.2861154190.094513251-0.0626069370.382322899
94-0.3967095550.124743431-0.2874644280.0948957-0.0628216260.383945353
94.25-0.398583040.12524728-0.2888098760.095277137-0.0630357440.385563499
94.5-0.4004515810.125749796-0.2901517760.095657566-0.0632492940.387177359
94.75-0.4023151980.126250986-0.2914901410.096036991-0.0634622790.388786956
95-0.404173910.126750856-0.2928249840.096415417-0.0636747030.390392312

 

 

 
 

 
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