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Age-predicted maximal heart rate revisitedFree Access

Clinical study: exercise testing

J Am Coll Cardiol, 37 (1) 153–156



We sought to determine a generalized equation for predicting maximal heart rate (HRmax) in healthy adults.


The age-predicted HRmaxequation (i.e., 220 − age) is commonly used as a basis for prescribing exercise programs, as a criterion for achieving maximal exertion and as a clinical guide during diagnostic exercise testing. Despite its importance and widespread use, the validity of the HRmaxequation has never been established in a sample that included a sufficient number of older adults.


First, a meta-analytic approach was used to collect group mean HRmaxvalues from 351 studies involving 492 groups and 18,712 subjects. Subsequently, the new equation was cross-validated in a well-controlled, laboratory-based study in which HRmaxwas measured in 514 healthy subjects.


In the meta-analysis, HRmaxwas strongly related to age (r = −0.90), using the equation of 208 − 0.7 × age. The regression equation obtained in the laboratory-based study (209 − 0.7 × age) was virtually identical to that obtained from the meta-analysis. The regression line was not different between men and women, nor was it influenced by wide variations in habitual physical activity levels.


1) A regression equation to predict HRmaxis 208 − 0.7 × age in healthy adults. 2) HRmaxis predicted, to a large extent, by age alone and is independent of gender and habitual physical activity status. Our findings suggest that the currently used equation underestimates HRmaxin older adults. This would have the effect of underestimating the true level of physical stress imposed during exercise testing and the appropriate intensity of prescribed exercise programs.


Maximal heart rate (HRmax) is one of the most commonly used values in clinical medicine and physiology. For example, a straight percentage of HRmaxor a fixed percentage of heart rate reserve (HRmax− heart rate at rest) is used as a basis for prescribing exercise intensity in both rehabilitation and disease prevention programs (1,2). Moreover, in some clinical settings, exercise testing is terminated when subjects reach an arbitrary percentage of their age-predicted maximal heart rate (e.g., 85% of HRmax) (3). Maximal heart rate also is widely used as a criterion for achieving peak exertion in the determination of maximal aerobic capacity (1,4,5).

Because maximal exercise testing is not feasible in many settings, HRmaxis often estimatedusing the age-predicted equation of 220 − age. However, the validity of the age-predicted HRmaxequation has not been established, particularly in a study sample that included an adequate number of older adults (e.g., >60 years of age). The latter limitation is crucial in that older adults demonstrate the highest prevalence of cardiovascular and other chronic diseases. As such, this is the most prevalent population undergoing diagnostic exercise testing, representing a key clinical target for exercise prescription. Importantly, older adults are a population in which there is often a reluctance or an inability to measure HRmaxdirectly, owing to concerns related to the physiologic stress imposed by strenuous exercise. Thus, ironically, the 220 − age HRmaxprediction equation is used in this population more than in any other.

Accordingly, the aim of the present study was to determine an equation for predicting HRmaxin healthy, nonmedicated humans ranging widely in age. To address this aim, we first used a meta-analytic approach in which group mean HRmaxvalues were obtained from the published data. Subsequently, we cross-validated the newly derived equation in a well-controlled, laboratory-based study. With each approach, we attempted to establish the generalizability of the equation by determining whether gender or habitual physical activity status exerted a significant modulatory influence on the HRmax-age relation.


Meta-analytic study

Meta-analysis is a set of quantitative procedures for systematically integrating and analyzing the findings of previous research. Meta-analysis in the present study was conducted as described previously in detail by our laboratory (6). As an initial step, an extensive search of the published data was conducted to identify as many studies as possible in which HRmaxwas measured. Initially, this was done by using computer searches. In addition, extensive hand searching and cross-referencing were performed using bibliographies of already retrieved studies. The following criteria for inclusion were used: 1) English language studies published in peer-reviewed journals; 2) data on men and women reported separately; 3) at least five subjects per group; 4) only the most recently published results of a particular study group; 5) adult subjects; 6) maximal exertion documented by using objective criteria (5); and 7) only healthy (e.g., nonischemic electrocardiographic response), nonmedicated and nonsmoking groups. A list of reports included in the meta-analysis can be obtained from the authors upon request. Because the studies included in the meta-analysis used different terms to describe the aerobic exercise status of their subject groups, we classified and analyzed the groups into three arbitrarily defined categories: 1) endurance-trained, referring to regular performance of vigorous endurance exercise ≥3 times/week for over one year; 2) active, referring to occasional or irregular performance of aerobic exercise ≤2 times/week; and 3) sedentary, referring to no performance of any aerobic exercise. Data from treadmill and cycle ergometers were evaluated together and separately. There were no differences in the results between the two analyses. Therefore, data from both exercise modes were pooled and are presented together. This meta-analysis included a total of 351 studies involving 492 subject groups (161 female and 331 male groups) and 18,712 subjects. Because we have previously shown that weighted results by sample size were not significantly different from unweighted results (6), no weighting scheme was used in the present meta-analysis.

Laboratory-based study

Five-hundred fourteen subjects (237 men and 277 women) were studied (age range 18 to 81 years). All of the subjects were apparently healthy and free of overt coronary artery disease, as determined by a medical history questionnaire. Subjects >50 years of age were further evaluated by physical examination and by rest and maximal exercise electrocardiography ECG (3). None of the subjects smoked or used any medications other than hormone replacement (postmenopausal women). To eliminate the potentially confounding influence of severe obesity, only subjects with a body mass index <35 kg/m2were included. Two different groups were studied: endurance exercise-trained and sedentary. The endurance-trained subjects (n = 229) had been training for at least the past two years. The subjects in the sedentary group (n = 285) performed no regular physical exercise. Before participation, the subjects gave their written, informed consent to participate in this investigation. This study was reviewed and approved by the Human Research Committee at the University of Colorado at Boulder.

Maximal heart rate was determined by a continuous, incremental treadmill protocol, as previously described in detail by our laboratory (4). Heart rates were continuously monitored with electrocardiography. Minute oxygen consumption (V̇o2) also was measured using on-line, computer-assisted, open-circuit spirometry (4). After a warm-up period of 6 to 10 min, each subject ran or walked at a comfortable but brisk speed. The treadmill grade was increased 2.5% every 2 min until volitional exhaustion. At the end of each stage, the subjects were asked to rate their perception of effort using a Borg category scale (6 to 20 rating). Maximal heart rate was defined as the highest value recorded during the test. To ensure that each subject achieved maximal exertion, at least three of the following four criteria were met by each subject: 1) a plateau in V̇o2with increasing exercise intensity (<100 ml); 2) a respiratory exchange ratio of at least 1.15; 3) a maximal respiratory rate of at least 35 breaths/min; and 4) a rating of perceived exertion of at least 18 units on the Borg scale (5).

Statistical analysis

Linear regression analyses were performed to determine the association among variables. In all cases, age was used as the predictor variable. Pearson product-moment correlation coefficients were used to indicate the magnitude and direction of relations among variables. The slopes of regression lines were compared using analysis of covariance. Forward stepwise multiple regression analyses were used to identify significant independent determinants for the age-related declines in HRmax. To do so, only those variables that had significant univariate correlations with HRmax(e.g., age, body mass) were entered in the model. All data were reported as the pooled mean value ± SD. The statistical significance level was set, a priori, at p < 0.01 for all analyses.


Meta-analytic study

Figure 1illustrates the decline in HRmaxin men and women included in the meta-analysis. Maximal heart rate was strongly and inversely related to age in both men and women (r = −0.90). The rate of decline and the y intercepts were not different between men and women nor among sedentary (211 − 0.8 × age), active (207 − 0.7 × age) and endurance-trained (206 − 0.7 × age) subjects. The regression equation, when all the subjects were combined, was 208 − 0.7 × age. Stepwise regression analysis revealed that age alone explained ∼80% of the individual variance in HRmax.

Figure 1.
Figure 1.

Relation between maximal heart rate (HRmax) (group mean values) and subject group age obtained from the meta-analysis.

Laboratory-based study

The maximal respiratory exchange ratio (1.17 ± 0.06) and maximal rating of perceived exertion (19.1 ± 0.8) were not different across ages, suggesting consistently similar voluntary maximal efforts. The relation between HRmaxand age obtained in the laboratory-based study is presented in Figure 2. Maximal heart rate was inversely related to age in both men and women. There was substantial variation in HRmaxacross the entire age range, with standard deviations ranging from 7 to 11 beats/min. The regression equation for HRmax(209 − 0.7 × age) was virtually identical to that obtained from the meta-analysis. Again, no significant differences in the HRmaxregression equation were observed between men and women or between sedentary (212 − 0.7 × age) and endurance-trained (205 − 0.6 × age) subjects.

Figure 2.
Figure 2.

Relation between maximal heart rate (HRmax) and age obtained from the prospective, laboratory-based study.


The primary findings of the present study are as follows. First, a regression equation for estimating HRmaxis 208 − 0.7 × age in healthy adult humans, which is significantly different from the traditional 220 − age equation. Second, HRmaxis predicted, to a large extent, by age alone and is independent of gender and physical activity status. These results were first obtained in a meta-analysis of previously published studies and then confirmed in a prospective, well-controlled, laboratory-based study. Our findings suggest that the prevailing equation significantly underestimates HRmaxin older adults. This would have the effect of underestimating the true level of physical stress imposed during exercise testing, as well as the intensity of exercise programs that are based on HRmax-derived target heart rate prescriptions.

Comparison with the traditional equation

The original reports proposing the 220 − age HRmaxequation appear to be reviews by Fox and Haskell in the 1970s (7,8). The age-predicted equation was determined “arbitrarily” from a total of 10 studies. The highest age included was <65 years, with the majority of subjects being ≤55 years old. Because of these limitations, there have been some attempts to establish a more appropriate equation to predict HRmax(9–11). However, similar to the original reports by Fox and Haskell (7,8), these studies probably or definitely included subjects with cardiovascular disease who smoked and/or were taking cardiac medications. Each of these conditions influences HRmaxindependent of age (10,12,13). Therefore, the present study is the first to determine the age-predicted equation for healthy, unmedicated and nonsmoking adult humans. Another unique aspect of the present study is that each subject achieved a verified maximal level of effort, as established by conventional maximal exercise criteria (e.g., a plateau in V̇o2, maximal respiratory exchange ratio >1.15).

We obtained the regression equation of 208 − 0.7 × age to predict HRmaxin the present study. When this equation was compared with the traditional 220 − age equation (Fig. 3), it is clear that the traditional equation overestimates HRmaxin young adults, intersects with the present equation at age 40 years and then increasingly underestimates HRmaxwith further increases in age. For example, at age 70 years, the difference between the two equations is ∼10 beats/min. Considering the wide range of individual subject values around the regression line for HRmax(SD ∼10 beats/min), the underestimation of HRmaxcould be >20 beats/min for some older adults. Although the present HRmaxequation provides a more accurate estimation of HRmaxon average, as with previous equations, it may not precisely predict true HRmaxin some individuals, because of the standard deviation. As such, despite the convenience and ease of use of age-predicted HRmax, direct measurements of HRmaxshould be used as an indicator of physical stress whenever possible. Alternatively, individuals may choose to use more subjective end points of exercise, such as breathlessness and/or a fatigue level considered to be “somewhat hard” to “hard” on the Borg perceived exertion scale (2).

Figure 3.
Figure 3.

Regression lines depicting the relation between maximal heart rate (HRmax) and age obtained from the results derived from our equation (208 − 0.7 × age) (solid linewith 95% confidence interval), as compared with the results derived from the traditional 220 − age equation (dashed line). Maximal heart rates predicted by traditional and current equations, as well as the differences between the two equations, are shown in the table format at the top.

Clinical implications

These differences in HRmaxcould have a number of important clinical implications for older adults. First, because exercise testing is terminated when subjects reach a certain percentage of predicted HRmax(e.g., 85% HRmax) in some clinical settings (3), use of the prevailing prediction equation would result in premature termination of the test and possibly failure to attain required exertion levels for diagnostic validity. Second, for physical activity intervention programs, an aerobic exercise prescription based on the traditional equation would result in a target heart rate below the intended intensity which may also be optimal for producing health benefits). Third, in fitness and health settings, maximal aerobic capacity is commonly predicted by extrapolating submaximal heart rate to age-predicted HRmax(e.g., YMCA cycle protocol) (1). Under these conditions, use of the prevailing equation would result in an underestimation of aerobic fitness levels.

Factors influencing HRmax

We found that the rate of decline in maximal heart rate was not associated with either gender or physical activity status. More importantly, a large portion of variability was explained by age alone. These results collectively indicate that the same age-based equation can be used for various groups of healthy adults to estimate their HRmaxvalues. We wish to emphasize, however, that because we excluded individuals with overt cardiovascular disease and smokers (10,12,13), the present equation may not be applicable to these subjects.


The mechanism underlying the age-related reduction in HRmaxis not clear. It has been postulated that the primary mechanism is related to an age-related decline in intrinsic heart rate (i.e., independent of autonomic influences) (14,15). In this context, it is interesting to note that the rate of decline in HRmaxobserved in the present study is very similar to that reported previously for intrinsic heart rate determined after cardiac autonomic blockade (−0.6 − 0.8 beats/min per year) (14,15). Moreover, consistent with the present findings, gender (14)and habitual physical activity (16)do not appear to influence intrinsic heart rate in humans. These results collectively suggest that a decrease in HRmaxwith age may primarily be due to the reduction in intrinsic heart rate.


The results of the present study fail to validate the traditional equation for predicting HRmaxacross the adult age range in healthy humans. Specifically, the traditional equation underestimates HRmaxpast age 40 years, markedly so in older adults. On the basis of the cross-confirmatory findings of our meta-analysis and complementary prospective study, we present a new equation for future use that should provide more precise results. These findings have important clinical implications related to exercise testing and prescription.

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maximal heart rate


minute oxygen consumption


☆ This work was supported by National Institutes of Health (Bethesda, Maryland) awards AG-00847, AG-06537 and AG-13038.