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Prediction of Maximal Heart Rate

1

JEPonline

Journal of Exercise Physiologyonline

Official Journal of The American

Society of Exercise Physiologists (ASEP)

ISSN 1097-9751

An International Electronic Journal

Volume 5 Number 2 May 2002

Commentary

THE SURPRISING HISTORY OF THE “HRmax=220-age” EQUATION

ROBERT A. ROBERGS AND ROBERTO LANDWEHR

Exercise Physiology Laboratories, The University of New Mexico, Albuquerque, NM

ABSTRACT

THE SURPRISING HISTORY OF THE “HRmax=220-age” EQUATION. Robert A. Robergs, Roberto

Landwehr. JEPonline. 2002;5(2):1-10. The estimation of maximal heart rate (HRmax) has been a feature of

exercise physiology and related applied sciences since the late 1930’s. The estimation of HRmax has been

largely based on the formula; HRmax=220-age. This equation is often presented in textbooks without

explanation or citation to original research. In addition, the formula and related concepts are included in most

certification exams within sports medicine, exercise physiology, and fitness. Despite the acceptance of this

formula, research spanning more than two decades reveals the large error inherent in the estimation of HRmax

(Sxy=7-11 b/min). Ironically, inquiry into the history of this formula reveals that it was not developed from

original research, but resulted from observation based on data from approximately 11 references consisting of

published research or unpublished scientific compilations. Consequently, the formula HRmax=220-age has no

scientific merit for use in exercise physiology and related fields. A brief review of alternate HRmax prediction

formula reveals that the majority of age-based univariate prediction equations also have large prediction errors

(>10 b/min). Clearly, more research of HRmax needs to be done using a multivariate model, and equations may

need to be developed that are population (fitness, health status, age, exercise mode) specific.

Key Words: Cardiovascular function, Estimation, Error, Exercise prescription, Fitness.

INTRODUCTION

This short manuscript has been written to provide insight into the history of the maximal heart rate (HRmax)

prediction equation; HRmax=220–age. Surprisingly, there is no published record of research for this equation.

As will be explained, the origin of the formula is a superficial estimate, based on observation, of a linear best fit

to a series of raw and mean data compiled in 1971 (1). However, evidence of the physiological study of

maximal heart rate prediction dates back to at least 1938 from the research of Sid Robinson (2).

Research since 1971 has revealed the error in HRmax estimation, and there remains no formula that provides

acceptable accuracy of HRmax prediction. We present the majority of the formulae that currently exist to

Prediction of Maximal Heart Rate

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estimate HRmax, and provide recommendations on which formula to use, and when. We also provide

recommendations for research to improve our knowledge of the between subjects variability in HRmax.

THE IMPORTANCE OF MAXIMAL HEART RATE

Heart rate is arguably a very easy cardiovascular measurement, especially in comparison to the invasive or

noninvasive procedures used to estimate stroke volume and cardiac output. Consequently, measurement of

heart rate is routinely used to assess the response of the heart to exercise, or the recovery from exercise, as well

as to prescribe exercise intensities (3). Given that the increase in heart rate during incremental exercise mirrors

the increase in cardiac output, maximal heart rate is often interpreted as the upper ceiling for an increase in

central cardiovascular function. Indeed, research for the last 100 years has demonstrated that heart rate does in

fact have a maximal value (4); one that cannot be surpassed despite continued increases in exercise intensity or

training adaptations.

Perhaps the most important application of the heart

rate response to exercise has been the use of

submaximal heart rate, in combination with resting

and maximal heart rate, to estimate VO2max. In

many instances, maximal heart rate estimation is

recommended by using the formula HRmax=220-

age. Based on this application, heart rate responses

to exercise have been used to calculate exercise

intensities, such as a percent of maximal heart rate

(%HRmax) or a percent of the heart rate reserve

(%HRR) (Table 1).

HISTORY OF MAXIMAL HEART RATE

PREDICTION

Due to our interest in improving the accuracy of maximal heart rate estimation, we have tried to research the

origin of the formula HRmax=220-age (Tables 2 and 3). As far as we could determine from books and

research, the first equation to predict maximal heart rate was developed by Robinson in 1938 (2). His data

produced the equation HRmax=212-0.77(age), which obviously differs from the widely accepted formula of

HRmax=220-age. As we will explain below, there are numerous HRmax prediction equations (Table 3), yet it

is the history of the HRmax=220-age equation that is most interesting.

The Formula: “HRmax=220-Age”

Within textbooks, failure to cite the original research regarding the formula HRmax=220-age indirectly affirms

a connection to Karvonen. This association exists due to the textbook presentation of HRmax prediction with

the concept of a heart rate reserve, which was devised by Karvonen (3). Ironically, the study of Karvonen was

not of maximal heart rate. To clarify, Dr. Karvonen was contacted in August of 2000 and subsequent

discussion indicated that he never published original research of this formula, and he recommended that we

research the work of Dr. Åstrand to find the original research.

Another citation for the formula is Åstrand (7). Once again, this study was not concerned with HRmax

prediction. We were able to discuss this topic with Dr. Åstrand in September 2000 while he was in

Albuquerque to receive his Lifetime Achievement Award in Exercise Physiology from the American Society of

Exercise Physiologists. Dr. Åstrand stated that he did not publish any data that derived this formula. However,

Table 1: Use of heart rate to estimate

exercise intensities that coincide with

%VO2max.

%VO2max % HRmax %HRR*^

40 63 40

50 69 50

60 76 60

70 82 70

80 89 80

90 95 90

*based on Karvonen method (HR=HRrest +

((intended fraction) * (HRmax - HRrest)));

^%HRR equals the intended fraction expressed as %

Adapted from Heyward V. (5) and Swain et al. (6)

Prediction of Maximal Heart Rate

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he did comment that in past presentations he had stated that such a formula appears close to research findings,

and would be a convenient method to

use.

Interestingly, Åstrand published

original HRmax data for 225 subjects

(115 male, 110 female) for ages 4 to 33

years in one of his earlier texts (8). The

data are from either treadmill or cycle

ergometer exercise tests to VO2max,

with no knowledge of protocol

characteristics. This data is presented

in Figure 1a and b. When data for ages

>10 years are used (Figure 1b), there is

a significant correlation (r=0.43), yet

considerable error (Sxy=11 b/min).

The resulting formula is; HRmax =

216.6–0.84(age). Despite the similarity

of the prediction equation to

HRmax=220–age, the notable feature

of this data set is the large error of

prediction. Interestingly, in two other

studies, Åstrand found that the average

decrease in HRmax for women was 12

beats in 21 years (9) and 19 beats in 33

years (10). For men, the decrease in

HRmax was 9 beats in 21 years (9) and

~26 in 33 years (10). If the formula

HRmax=220-age is correct, the slope

for HR decrement with increasing age

would be 1. In addition, Åstrand’s data

Table 2: The research and textbooks, and the citations used or

not used, in crediting the source of the HRmax=220-age

formula.

Publication Year Citation

Research

Engels et al. 1998 Fox & Haskell, 1971

O’Toole et al. 1998 ACSM. 1995

Tanaka 2001 Fox & Haskell, 1971

Vandewalle & Havette 1987 Astrand, 1986

Whaley et al. 1992 Froelicher,1987

Textbooks

ACSM 2001 ACSM, 2000

Baechle & Earle 2000 No Citation

Baumgartner & Jackson 1995 No Citation

Brooks et al. 2000 No Citation

Fox et al. 1989 No Citation

Garret & Kirkendall 2000 No Citation

Heyward 1997 No Citation

McArdle, Katch & Katch 1996 Londeree, 1982

McArdle, Katch & Katch 2000 No Citation

Nieman 1999 No citation

Plowman & Smith 1997 Miller et al. 1993

Powers & Howley 1996 No Citation

Robergs & Roberts 1997 Hagberg et al, 1985

Robergs & Roberts 2000 No Citation

Roberts et al. 1997 Asmussen, 1959

Rowland 1996 No Citation

Wasserman et al. 1994 No Citation

Wilmore & Costill 1999 No Citation

a.

2 6 10 14 18 22 26 30 34

160

175

190

205

220

235

250

Age (years)

HRmax (b/min)

Figure 1: Data of HRmax for a) 225

subjects, 4 to 33 years, and b) a subset of

the subjects, ages 11 to 33 years, n=196.

Prediction of Maximal Heart Rate

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indicates that HRmax prediction from such

formula should not be used on children 10 years

or younger, as HRmax follows a different age

associated change for children. In addition, the

likelihood that children attain a true HRmax

during exercise testing can be questioned.

It appears that the correct citation for the origin of

HRmax=220-age is Fox et al. (1). However, and

as explained by Tanaka et al. (11), Fox did not

derive this equation from original research. We

evaluated the original manuscript of Fox et al. (1),

which was a large review of research pertaining to

physical activity and heart disease. In a section

subtitled “Intensity”, a figure is presented that

contains the data at question, and consists of

approximately 35 data points. No regression

analysis was performed on this data, and in the

figure legend the authors stated that;

“….no single line will adequately represent the

data on the apparent decline of maximal heart

rate with age. The formula maximum heart

rate=220–age in years defines a line not far

from many of the data points..”

We decided to replicate the approach used by

Fox et al (1), using the original data presented in

their manuscript. As we could not find all

manuscripts due to inaccurate citations, we

reproduced the data from the figure and

presented it in Figure 2. We fit a linear

regression to the data set and derived the following equation; HRmax=215.4 – 0.9147(age), r=0.51, Sxy=21

b/min. Thus, even the original data from which observation established the HRmax=220-age formula does no

support this equation.

REVIEW OF RESEARCH OF MAXIMAL HEART RATE

We retrieved as much of the research on HRmax as is possible. This was a daunting task, as many of the

original research and review studies on this topic did not provide complete references, or citations of the

original research of this topic. We collated 43 formulae from different studies, and these are presented in Table

3, along with pertinent statistics when possible.

To verify if there was a trend towards the equation HRmax=220-age, we selected 30 equations from the ones

presented in Table 3 (excluded equations derived from non-healthy subjects). The equations were used to re-

calculate HRmax for ages 20 to 100 years of age, and a new regression equation was calculated from the data

(Figure 3). The regression equation yielded a prediction formula; HRmax=208.754-0.734(age), r=0.93 and

Sxy=7.2, which is very close to that derived by Tanaka et al. (11) (Table 3).

b.

10 14 18 22 26 30 34

160

180

200

220

240 HRmax = (-0.8421*age) + 216.6

r2 = 0.1859 ; Sy.x = 11 b/min

Age (years)

HRmax (b/min)

0 10 20 30 40 50 60 70

140

150

160

170

180

190

200

210

220 Robinson

Astrand

Astrand2

Bruce

Binkhorst

Anderson

Lester

Kasch

Saltin

Hollman

Unknown

HRmax = 215.4 - (0.9147*Age)

Age (yr)

HRmax (b/min)

Figure 2. A reproduced figure from the data of Fox et al. (1)

which was used to derive the original HRmax=220-age formula.

Blue line represents line of best fit. Red line represents 220-age.

Prediction of Maximal Heart Rate

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Table 3. The known univariate prediction equations for maximal heart rate.

Study N Population Mean Age

(range) Regression

(HRmax=) r2 Sxy

Univariate Equations

Astrand, in

Froelicher (2) 100

Healthy Men – cycle

ergometer 50 (20 - 69) 211-0.922a N/A

N/A

Brick, in Froelicher

(2) ?

Women N/A 226-age N/A

N/A

Bruce (12) 1295

CHD 52±8 204-1.07a 0.13

22

Bruce (12) 2091

Healthy Men 44±8 210-0.662a 0.19

10

Bruce (12) 1295

Hypertension 52±8 204-1.07a 0.24

16

Bruce (12) 2091

Hypertension + CHD 44±8 210-0.662a 0.10

21

Cooper in

Froelicher (2) 2535

Healthy Men 43(11 - 79) 217-0.845a N/A

N/A

Ellestad in

Froelicher (2) 2583

Healthy Men 42(10-60) 197-0.556a N/A

N/A

Fernhall (13) 276

Mental Retardation 9-46 189-0.56a 0.09

13.8

Fernhall (13) 296

Healthy W & M N/A 205-0.64a 0.27

9.9

Froelicher (2) 1317

Healthy Men 38.8(28-54) 207-0.64a 0.18

10

Graettinger (14) 114

Healthy Men (19-73) 199-0.63a 0.22

N/A

Hammond (15) 156

Heart Disease 53.9 209-age 0.09

19

Hossack (16) 104

Healthy Women (20-70) 206-0.597a 0.21

N/A

Hossack (16) 98

Healthy Men (20-73) 227-1.067a 0.40

N/A

Inbar (17) 1424

Healthy W & M 46.7(20-70) 205.8-.685a 0.45

6.4

Jones (18) 100

Healthy W & M cycle

ergometer (15 – 71) 202-0.72a 0.52

10.3

Jones N/A ?

Healthy W &M 210-0.65a 0.04

N/A

Jones (18) 60

Healthy Women (20-49) 201-0.63a

N/A

Lester (19) 48

W & M Trained 205-0.41a 0.34

N/A

Lester (19) 148

W & M Untrained 43(15 – 75) 198-0.41a N/A

N/A

Londeree (20) ?

National Level Athletes N/A 206.3-0.711a 0.72

N/A

Miller (21) 89

W & M Obese 42 200-0.48a 0.12

12

Morris, in

Froelicher (2) 1388

Heart Disease 57(21 – 89) 196-0.9a 0.00

N/A

Morris, in

Froelicher (2) 244

Healthy Men 45(20 – 72) 200 -0.72a 0.30

15

Ricard (22) 193

Treadmill W&M 209 -0.587a 0.38

9.5

Ricard (22) 193

W & M - cycle

ergometer 200 -0.687a 0.44

9.5

Robinson 1938 in

Froelicher (2) 92

Healthy Men 30(6 - 76) 212 -0.775a 0.00

N/A

Rodeheffer (23) 61

Healthy Men 25 - 79 214-1.02a 0.45

N/A

Schiller 24) 53

Women Hispanic 46(20-75) 213.7-0.75a 0.56

N/A

Schiller (24) 93

Women Caucasian 42(20-75) 207 -0.62a 0.44

N/A

Sheffield (25) 95

Women 39(19 - 69) 216 -0.88a 0.58

N/A

Tanaka (11) ?

Sedentary W&M 211 -0.8a 0.81

N/A

Tanaka (11) ?

Active W&M 207 -0.7a 0.81

N/A

Tanaka (11) ?

Endurance trained W&M

206 -0.7a 0.81

N/A

Prediction of Maximal Heart Rate

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Study N Population Mean Age

(range) Regression

(HRmax=) r2 Sxy

Univariate Equations

Tanaka (11)

Women & Men 208-0.7a 0.81

N/A

Whaley (26) 754

Women 41.3(14-77) 209-0.7a 0.37

10.5

Whaley (26) 1256

Men 42.1(14-77) 214-0.8a 0.36

10.7

W=women, M=men

Table 4. The known multivariate prediction equations for maximal heart rate.

Study and Equations r2

Londeree (20)

PMHR = 196.7+1.986xC2+5.361xE+1.490xF4+3.730xF3+4.036xF2-00006xA4-0.542xA2 0.77

PMHRI = 199.1+0.119xAEF4+0.112xAE+6.280xEF3+2.468xC2+3.485xF2-.00006xA4-0.591xA

0.78

PMHRC = 205-3.574xT1+8.316xE-7.624xF5-.00004xA4-0.624xA2 0.85

PMHRCI = 205-0.116xAEF3-0.223xAF5+0.210xAE+6.876xEF3+2.091xC2-3.310xT1-

0.0005xA4-0.654xA 0.86

PMHR (National Collegiate Athletes) = 202.8-0.533xA-00006xA4 0.73

PMHR=predicted maximal heart rate, C=Cross Sectional, I=interaction; a=A=age; A2=age; A4= (age4)/1000; C#=continent ( if

European, then C2=1, otherwise C2=0); E=ergometer (if treadmill, then E=1, if bicycle then E=0); F#=fitness level (if sedentary,

F2=1, otherwise F2=0; if active then F3=1, otherwise F3=0, if endurance trained, then F4=1, otherwise F4=0; Type # =type of

exercise protocol (if continuous and incremental, then T1=1, otherwise T1=0). Multiple letters interaction terms which should be

multiplied together.

Interestingly, Londeree (20) developed a

multivariate equation using the variables age, age2,

age4/1000, ethnicity, mode of exercise, activity

levels, and type of protocol used to assess HR

(Table 4). However, no statistical results pertaining

to significant increases in the explanation of

variance in HRmax using a mutivariate model was

provided by the authors. The same criticism

applies to the study of Tanaka et al. (11). As

Zavorsky (27) showed that endurance training

lowers HRmax, and others have shown the exercise

mode specificity of HRmax (28,29,30), an original

study of HRmax using multiple independent

variables is long overdue.

The data from research of HRmax are clear in

showing the large error of HRmax prediction using

just a y-intercept and slope when age is the sole independent variable. Furthermore, the results and regression

equations need to be recognized as being mode–specific (28,29,30). It is unfortunate that the mode-specificity

of HRmax prediction equations is not clearly addressed in textbooks of exercise physiology and exercise

prescription. Finally, even a multivariate model of HRmax prediction and variance explanation does not reduce

the error of HRmax prediction.

20 30 40 50 60 70 80

140

150

160

170

180

190

200 Compiled studies average

220-age

Londeree meta-analysis

Tanaka meta-analysis

Age (yrs)

Maximal Heart Rate

(b/min)

Regression Lines

Figure 3. Regression lines from data obtained from 220-

age,

the mean of 30 studies from Table 3, and the meta analyses

of Londeree (28) and Tanaka (47).

Prediction of Maximal Heart Rate

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What is an Acceptable Error of HRmax Prediction?

Given the precision of HR measurement, the measurement error of HRmax is small and attributable to the

exercise protocol and subject motivation. Consequently, HRmax measurement is likely to be accurate to within

±2 b/min, if the subject truly attains maximal exertion. Nevertheless, another factor to consider is the impact of

prediction error on the application of HRmax. For the estimation of two exercise intensities (Table 5), HRmax

prediction errors (HRmax–predicted=error) of 2, 4, 6 and 8 b/min cause negligible error. For example, a HR of

150 b/min, which lies in the center of the “true” heart rate prescription range, remains within the recommended

heart rate ranges for all error examples. However, as revealed in Table 3, errors in HRmax estimation can be in

excess of 11 b/min. Consequently, it is likely that current equations used to estimate HRmax are not accurate

enough for prescribing exercise training heart rate ranges for a large number of individuals.

Table 5. Estimations of error in submaximal exercise intensities and VO2max when using HRmax

estimated with errors of 2, 4, 6, and 8 b/min (underestimated prediction of HRmax).

HR values For Given HRmax Error (True-Estimated, b/min (%))

Intensity True 2 (1) 4 (2.1) 6 (3.1) 8 (4.2)

Submaximal exercise intensities

60-80% HRR 135-164 134-162 133-160 132-159 130-157

VO2max

YMCA* (mL/min) 4200 4083 6967 3850 3733

Error (mL/min)

0 117 233 350 467

Error (%)

0 2.8 5.6 8.3 11.11

Calculations are based on assuming a resting heart rate of 50 b/min, for a 25 year old person with a HRmax=192 b/min ; HRR=heart

rate reserve ; for YMCA protocol, heart rates and workloads were assumed to be (HR:kgm/min) 90:150, 125:750, 153:1200,

respectively.

When the prediction of HRmax is used in the estimation of VO2max, as it is in the YMCA method, there can be

considerable errors in estimated VO2max (Table 5). For example, when HRmax is underestimated by 6 b/min,

there is a resulting error in estimated VO2max of 350 mL/min. This equates to an error of -8.3%, or -4.7

mL/kg/min for a 75 kg person.

The data of Table 5 help in selecting a suitable error in HRmax estimation. The error can be larger for purposes

of prescribing training heart rate ranges than in the estimation of VO2max. For purposes of prescribing training

heart rate ranges, errors ≤8 b/min are likely to be acceptable. However, for VO2max, it can be argued that

prediction errors in HRmax need to be <±3 b/min.

CONCLUSIONS AND RECOMMENDATIONS

Based on this review of research and application of HRmax prediction, the following recommendations can be

made;

1. Currently, there is no acceptable method to estimate HRmax.

2. If HRmax needs to be estimated, then population specific formulae should be used. However, the most

accurate general equation is that of Inbar (17) (Table 3); HRmax=205.8-0.685(age). Nevertheless, the error

(Sxy=6.4 b/min) is still unacceptably large.

3. An acceptable prediction error for HRmax for application to estimation of VO2max is <±3 b/min. Thus, for

a person with a HRmax of 200 b/min, error equals ±1.5%. If this precision is not possible, then there is no

justification for using methods of VO2max estimation that rely on HRmax prediction formulae.

Prediction of Maximal Heart Rate

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4. Additional research needs to be performed that develops multivariate regression equations that improve the

accuracy of HRmax prediction for specific populations, and modes of exercise.

5. The use of HRmax is most prevalent in the fitness industry, and the people who work in these facilities

mainly have a terminal undergraduate degree in exercise science or related fields. These students/graduates

need to be better educated in statistics to recognize and understand the concept of prediction error, and the

practical consequences of relying on an equation with a large standard error of estimate (Sxy).

6. Textbooks in exercise physiology and exercise prescription should contain content that is more critical of the

HRmax=220-age or similar formulae. Authors need to stress the mode-specificity of HRmax, provide alternate,

research substantiated formula, and express all content of items 1-5, above. Similarly, academic coverage of

HRmax needs to explain how this error detracts from using HRmax estimation in many field tests of physical

fitness and in exercise prescription.

Address for correspondence: Robert A. Robergs, Ph.D., FASEP, EPC, Director-Exercise Physiology

Laboratories, Exercise Science Program, Department of Physical Performance and Development, Johnson

Center, Room B143, The University of New Mexico, Albuquerque, NM 87131-1258, Phone: (505) 277-2658,

FAX: (505) 277-9742; Email: rrobergs@unm.edu

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