Am J Hum
Biol. Author manuscript; available in PMC 2014 Feb 26. Published in final edited form as: PMCID: PMC3935487 NIHMSID: NIHMS555165 The purpose of this study was to examine how well two commonly used age-based prediction equations for maximal heart rate
(HRmax) estimate the actual HRmax measured in Black and White adults from the HERITAGE Family Study. A total of 762 sedentary subjects (39% Black, 57% Females) from HERITAGE were included. HRmax was measured during maximal exercise tests using cycle ergometers. Age-based HRmax was predicted using the Fox (220-age) and Tanaka (208 – 0.7 × age) formulas. The standard error of estimate (SEE) of predicted HRmax was 12.4 and 11.4 bpm for the Fox and Tanaka formulas, respectively, indicating a wide-spread of measured-HRmax values are compared to their age-predicted values. The SEE (shown as Fox/Tanaka) was higher in Blacks (14.4/13.1 bpm) and Males (12.6/11.7 bpm) compared to Whites (11.0/10.2 bpm) and Females (12.3/11.2 bpm) for both formulas. The SEE was higher in subjects above the BMI median (12.8/11.9 bpm)
and below the fitness median (13.4/12.4 bpm) when compared to those below the BMI median (12.2/11.0 bpm) and above the fitness median (11.4/10.3) for both formulas. Our findings show that based on the SEE, the prevailing age-based estimated HRmax equations do not precisely predict an individual’s measured-HRmax. Maximal heart rate (HRmax) is commonly
used in exercise physiology and clinical practice for preventive and diagnostic purposes. For example, HRmax is used to develop exercise prescriptions, estimate aerobic fitness levels, and is often a criterion for achieving maximal exertion in the determination of maximal aerobic capacity (Physical Activity Guidelines Advisory Committee, 2008;
Thompson, 2010). Since a direct measurement of HRmax is not always feasible, researchers, clinicians, fitness instructors, and exercise practitioners often employ age-based prediction equations to calculate HRmax. The most widely used age-based HRmax prediction equation is the formula generated by
Fox et al. (1971) of HRmax = 220-age. The Fox et al. formula is known to be quite variable, with a standard error of estimate (SEE) of predicted HRmax of 7–12 beats per minute (bpm) (Robergs and Landwehr, 2002;
Thompson, 2010). Several other age-based HRmax prediction equations have emerged from laboratory studies and are summarized by Robergs and Landwehr (2002). In 2001, Tanaka et al. performed a meta-analysis of 351 studies involving 18,712 subjects, including objective criteria for
maximal exertion, along with cross-validation in a laboratory study of 514 subjects. From this data, the authors derived the following formula to predict HRmax: 208 – 0.7 × age, which was the same for both men and women, and had a SEE of ~10 bpm (Tanaka et al., 2001). Currently, the Tanaka equation is becoming widely used, either alone or in combination with the Fox
equation (220-age), to predict HRmax in clinical studies. There is large inter-individual variation in HRmax values across a given population. Such a level of heterogeneity would equate to large differences in estimated HRmax derived from linear equations compounding the imprecision of these formulas. Estimated values of HRmax depend greatly on individual physiology and lifestyle factors
(Whaley et al. 1992; Zhu et al., 2010). However, few well-controlled laboratory studies with actual measures of HRmax, including objective measures of maximal exertion, have examined the validity of these estimates, particularly those from the Tanaka
formula, and factors associated with their accuracy in the general population. Furthermore, to our knowledge the accuracy of age-predicted equations to predict HRmax between ethnic groups has not been examined. Therefore, the purpose of the present study was to examine the association between estimated HRmax using the Tanaka et al. (2001) (208 – 0.7 × age)
and Fox et al. (1971) (220-age) formulas and measured HRmax in sedentary Black and White adults from the HERITAGE Family Study. The sample, study design and exercise training protocol of the HERITAGE Family Study has been described elsewhere
(Bouchard et al., 1995). Briefly, 834 Black and White sedentary subjects (16- to 65-years-old) from 218 families were recruited to participate in an endurance exercise training study. All results presented in this manuscript are based on baseline data. The study protocol was approved by the Institutional Review Boards at each of the five participating centers. Written informed
consent was obtained from each participant. Details of the exercise tests, measurements, and protocols are found elsewhere (Skinner et al., 1999). Each subject completed two maximal exercise tests at baseline on a SensorMedics Ergometrics 800S cycle ergometer (Yorba Linda, CA) connected to a SensorMedics
2900 metabolic measurement cart. Before, during, and after each exercise test, heart rate and blood pressure (BP) measurements were taken. Specifically, heart rate was determined using an electrocardiogram with values recorded during the last 15 s of each stage, while BP was obtained during the last minute of each stage using a Colin STBP-780 automated BP unit (San Antonio, TX). The criteria for attaining maximal oxygen uptake (VO2max)/maximal exertion was defined as reaching one of
the following criteria: respiratory exchange ratio (RER) of > 1.1, plateau in O2 uptake (change of <100 ml/min in the last three 20 s intervals), and HR within 10 bpm of age-predicted HRmax (220-age). Measured-HRmax was defined as the highest value attained during either of the two maximal exercise tests. Reproducibility of the HRmax
measurements was determined from maximal exercise test data obtained (a) on two separate days in a sample of 390 subjects (198 men and 192 women) from the main HERITAGE cohort, (b) across four days (four separate tests) in an Intracenter Quality Control (ICQC) substudy with 55 subjects who were not part of the main study, and (c) across two weeks in a Traveling Crew Quality Control (TCQC) substudy with the same eight subjects who were tested at each of the four centers
(Skinner et al., 1999). Reproducibility was evaluated using technical errors (TE): defined as the within-subject standard deviation as derived from repeated measures over a given period of time (a combination of measurement error plus day-to-day variation); coefficients of variation (CV) for repeated measures: derived from the TE and the measurement mean, and intraclass
correlation coefficients (ICC): computed from the within-subject variance compared to the overall measurement variance. The reproducibility values for HRmax were TE = 5.4, CV = 2.9, and ICC = 0.88 in the main HERITAGE cohort; TE = 3.7, CV = 2.0, ICC = 0.88 in the ICQC substudy, and TE = 3.9, CV = 2.1, ICC = 0.87 in the TCQC substudy (Skinner et al., 1999). Given that we are examining the associations between measured HRmax and estimated HRmax and that one of the criteria for attaining maximal exertion was a heart rate within 10 bpm of age-predicted HRmax, we excluded subjects who reached maximal exertion exclusively via age-predicted HRmax from the analyses. A total of 832 subjects (38% Black, 56% Females) achieved
VO2max using one or more of the criteria. Of these, 70 subjects (8.4%) achieved maximal exertion based on reaching either the heart rate criteria or both the heart rate and VO2 plateau criteria. Unfortunately, our records did not allow us to determine whether or not a subject met the VO2 plateau criteria. Thus, in order to remain conservative, we excluded all 70 subjects from our analyses. Our final sample size was 762 subjects (39% Black, 57% Females). Statistical analysesAll statistical analyses were performed with SAS version 9.1 (SAS Institute, Cary, NC). Pearson correlation coefficients were used to test the relationships between measured HRmax and age-predicted HRmax using the Fox et al. (Fox-HRmax) and Tanaka et al. (Tanaka-HRmax) formulas in the total sample, by ethnicity, and by sex. The differences between measured and age-predicted HRmax values were calculated as predicted Fox-HRmax –measured-HRmax and predicted Tanaka-HRmax–measured-HRmax. Thus, a negative value represents an underestimation of measured-HRmax by the age-based prediction equation and a positive value an overestimation. The correlations of Fox-HRmax–measured-HRmax and Tanaka-HRmax–measured-HRmax with age, body mass index (BMI), and fitness level (measured by VO2max) were also tested. Differences in continuous and categorical variables between groups (e.g., ethnicity, sex, age groups, etc.) were assessed using t-tests and chi-square tests, respectively. The SEE was calculated as: SEE=Σ(Y− Ypred)2n−2, where Y = measured-HRmax and Ypred = age-based predicted HRmax from either the Fox or Tanaka formula. RESULTSBasic characteristicsThe basic characteristics of the HERITAGE subjects can be found in Table 1. Briefly, the HERITAGE cohort was comprised of 39% Black and 57% Female subjects with an average age of 34 years and body mass index (BMI) of 26.5 kg/m2. There were significant differences between ethnic groups for age, BMI, cardiorespiratory fitness level (i.e., VO2max) and resting and exercise BP, with Black subjects on average being younger and heavier, with lower fitness and higher resting and exercise BP levels compared to White subjects (Table 1). Similarly, significant sex differences were found, with males having significantly higher fitness, resting BP, and maximum exercise SBP levels compared to females. Lastly, as shown in Table 2, on average Blacks and females had significantly higher resting heart rate values as compared to Whites and males, respectively. TABLE 1Descriptive characteristics, shown as mean (standard deviation) with minimum and maximum values of HERITAGE subjects by ethnicity and sex
TABLE 2Means and standard deviations, with minimum and maximum and standard error of estimate values indicated for measured-HRmax and predicted-HRmax in HERITAGE subjects by ethnicity and sex
Mean values of measured and age-predicted HRmaxThe mean values of measured and age-predicted HRmax values can be seen in Table 2. The mean Fox-HRmax value for the total group was significantly higher than the mean values of both measured-HRmax and Tanaka-HRmax (P < 0.0001). In the total sample, the Fox-HRmax formula overestimated measured-HRmax by 1.8 ± 12.2 bpm, as the difference with measured-HRmax varied from an overestimation of 49 bpm to an underestimation of 43 bpm. The mean difference between Tanaka-HRmax and measured-HRmax was 0.03 ± 11.4 bpm in the total sample, ranging from an over-estimation of 44 bpm to an underestimation of 38 bpm. There were significant sex (P ≤ 0.04) and ethnicity (P < 0.0001) differences in the mean values for the differences between both age-predicted HRmax formulas and measured-HRmax (Table 2). For example, measured-HRmax was significantly higher (~4 bpm) in Whites as compared to Blacks. Both formulas significantly overestimated measured-HRmax in Blacks, while the Tanaka-HRmax formula significantly underestimated measured-HRmax in Whites. In females the Fox-HRmax formula significantly overestimated measured-HRmax, while there were no mean differences between measured-HRmax and either Fox-HRmax or Tanaka-HRmax (Table 2). Accuracy of age-predicted HRmaxThe correlation of measured-HRmax with age-predicted HRmax was 0.60 in the total sample (P < 0.0001). Bland-Altman plots of the difference between age-predicted HRmax and measured HRmax values are shown in sex-ethnicity subgroups for Fox-HRmax and Tanaka-HRmax in Figures 1 and 2, respectively. Although the age-predicted HRmax values were similar to measured HRmax values on average, there was a large spread in the accuracy of the predictions. As can be seen by the slopes in Figures 1 and 2, at lower measured HRmax values both prediction formulas tended to overestimate measured HRmax, while tending to underestimate measured HRmax at higher measured HRmax values.  Bland-Altman plots of the difference between age-predicted HRmax using the Fox formula (220-age) and measured HRmax by ethnicity and sex subgroups in HERITAGE. Horizontal lines are shown for the mean difference and the 95% confidence intervals of the mean difference. Bland-Altman plots of the difference between age-predicted HRmax using the Tanaka formula (208–0.7 × age) and measured HRmax by ethnicity and sex subgroups in HERITAGE. Horizontal lines are shown for the mean difference and the 95% confidence intervals of the mean difference. The lack of accuracy of the age-predicted HRmax formulas is further exhibited by the SEE values for the prediction formulas in the total sample and by ethnicity and sex (Table 1, Figures 1 and 2). Overall, the SEE was 12.4 and 11.4 bpm for the prediction of measured-HRmax using the Fox-HRmax and Tanaka-HRmax formulas, respectively. The SEE of the prediction was greater in Blacks as compared to Whites for both formulas, with the Fox-HRmax formula in Blacks showing the largest SEE value of 14.4 bpm (Table 1). The SEE values were similar between men and women for both the Fox- and Tanaka-HRmax formulas (Table 1). When divided into sex-ethnicity groups, the SEE for both formulas was highest in Black males, while the SEE values were lowest in White females (Figures 1 and 2). Factors associated with the accuracy of age-predicted HRmaxThere was a large difference in the performance of the prediction formulas by age, as the SEE was higher in subjects above the age median of 30.4 years (13.5 bpm for Fox-HRmax, 12.9 bpm for Tanaka-HRmax) as compared to those below the age median (11.3 bpm for Fox-HRmax, 9.7 bpm for Tanaka-HRmax) for both formulas. Since the age-HRmax association has been previously shown to be modified by BMI and fitness level (Zhu et al., 2010), we examined if the prediction performance of the Fox and Tanaka formulas varied as a function of these variables. Stratified analyses showed that the age-predicted formulas performed worse in larger and less fit individuals. The SEE of age-predicted HRmax was higher in subjects above the BMI median of 25.5 kg/m2 as compared to those below the BMI median for both formulas (12.8 vs. 12.2 bpm for Fox-HRmax, 11.9 vs. 11.0 bpm for Tanaka-HRmax). Similarly, the SEE for both prediction formulas was higher in subjects below the cardiorespiratory fitness (measured VO2max) median of 2171 ml O2/min compared to subjects above the fitness median (13.4 vs. 11.4 bpm for Fox-HRmax, 12.4 vs. 10.3 bpm for Tanaka-HRmax). DISCUSSIONMeasured-HRmax, achieved during two maximal exercise tests that met predetermined criteria for attaining maximal exertion, was not strongly correlated with age-predicted HRmax using either the Fox et al. (1971) or Tanaka et al. (2001) formulas. Specifically, age-predicted HRmax explained only 36% and 26% of the total variance in measured-HRmax in the full cohort and black subjects, respectively. In the total sample, the SEE of the prediction for both formulas was between 11 and 12 bpm, which represents about 6% of the mean measured-HRmax in HERIT-AGE subjects and indicates a wide-spread of measured-HRmax values are compared to their age-predicted values. Thus, about 95% of the estimated HRmax values will fall within ±22 bpm of their corresponding measured-HRmax value. This is not very impressive considering the range of measured-HRmax in HERITAGE was only 79 bpm (136–216). For example, for individuals of the same age, fitness level, and BMI with a measured-HRmax of 200 bpm, the 95% confidence interval for the age-predicted HRmax value (using either the Fox or Tanaka formulas) would be 178–222 bpm, a range indicating limited clinical utility. This range would be even larger in Blacks, older adults, or individuals with high BMI and/or low fitness levels. Our results show that compared to mean values, the SEE is a more appropriate tool to compare measured and age-predicted HRmax values. These results are similar to a study that compared age-predicted maximum heart rate equations in college-aged subjects (N = 96) (Cleary et al., 2011). The authors found that the SEE for the Fox and Tanaka formulas was 12.7 and 9.3, respectively as compared to their criterion measure of HRmax. Our findings show that the prevailing age-based estimated HRmax equations do not accurately predict an individual’s measured-HRmax. Although the Tanaka-HRmax formula appears to slightly improve the prediction of an individual’s HRmax as compared to the Fox-HRmax formula, there is still substantial interindividual variation. The age-based HRmax predictions performed worse in Blacks as compared to Whites, as the SEE values for both formulas was higher in Blacks. Furthermore, both formulas significantly overestimated measured-HRmax in Blacks, while the Fox-HRmax formula overestimated measured-HRmax in females. Similarly, in a study of over 5,000 asymptomatic women, Gulati et al. (2010) found that the Fox et al. equation overestimates HRmax for age in women, with their results giving a formula of: Peak HR = 206 − 0.88 × age. We found that the accuracy of the age-based HRmax predictions was also affected by an individual’s BMI and current fitness level. There are several possible explanations for the differences in SEE observed between ethnic groups in the present study. One possibility is that the differences are statistical in nature and driven by the sample size differences between Black and White subjects in HERITAGE. However, subsequent sub-analyses performed (e.g., within ethnic group by sex; within offspring only by ethnic group, etc.) showed that the differences in SEE between Blacks and Whites remained even when the sample sizes were similar between ethnic groups. Therefore, although sample size plays a role in the calculation of SEE, we do not believe it is the major contributing factor to the apparent differences in SEE between ethnic groups observed in the present study. A biological explanation for the observed ethnic differences in SEE is genetic differences between Blacks and Whites. Here we report that the maximal heritability estimates for measured HRmax in HERITAGE are 39% for Blacks and 44% for Whites. Although the genetic component is similar between Blacks and Whites, the genetic factors contributing to the HRmax phenotype may not be the same between ethnic groups and thus may contribute differently to the variation in HRmax and accuracy of the prediction formulas. If biological factors are involved in ethnic differences of HRmax, the autonomic nervous system (ANS) would be a viable candidate to consider, as the ANS is known to play a role in heart rate regulation, including HRmax and heart rate variability (HRV). Previous studies have shown evidence of ethnic differences in HRV, with Blacks generally having higher HRV compared to Whites (Choi et al., 2006; Liao et al., 1995; Wang et al., 2005; Zion et al., 2003). Furthermore, it has been hypothesized that young Blacks may experience premature “aging” in their autonomic nervous system activity, specifically a decline in parasympathetic activity, compared to similarly aged Whites (Choi et al., 2006). Although we do not have substantive data to support the role of biological and genetic factors in HRmax and the accuracy of HRmax prediction formulas between ethnic groups, it is a hypothesis that cannot be excluded. Targeted biological studies are needed that investigate ethnic differences in HRmax, including examining the factors underlying the heterogeneity in predicted HRmax found in Blacks compared to Whites. Furthermore, given the differences in measured HRmax and the accuracy of HRmax predictions between ethnic groups, it appears that the already fairly large error in prediction equations is exacerbated further by not considering ethnic differences. Thus, there is a need for clinicians and researchers to take ethnicity into account when developing exercise prescriptions and prediction formulas. These results have many implications for exercise programs based on age-predicted HRmax target heart rate prescriptions and for the estimation of aerobic fitness levels. It is not uncommon for exercise stress tests to be terminated at 85% of age-predicted HRmax (i.e., FoxHRmax). Accordingly, corresponding diagnostic criteria surrounding these tests may prove sub-optimal should a patient’s target heart rate fall outside the mean estimates used for HRmax prediction (Lauer et al., 2005). In exercise programs based on age-predicted HRmax target heart rate prescriptions; this could result in target heart rates above or below the intended intensity, which could affect both the health benefits and safety of the participant. Similarly, these results could lead to either an over- or under-estimation of aerobic fitness levels (i.e., maximal aerobic power), which in turn may also affect exercise prescriptions. For example, in a cohort of subjects with a positive exercise ECG, patients had significantly fewer positive ECGs and less ST-segment depression at 85% of age-predicted HRmax than at peak exercise (Jain et al., 2011). Maximum workload was similar between patients that stopped exercise before reaching 85% of age-predicted HRmax and those achieving 85% of age-predicted HRmax. The authors postulate that these results indicate maximal exercise effort is more important for diagnostic testing than attaining an arbitrarily chosen target heart rate (Jain et al., 2011). The current evidence suggests the inability of existing and most likely future prediction formulas to capture physiologic HRmax through tests based only on submaximal efforts. A true maximal exercise test is the gold standard measure of maximal aerobic power compared with symptom-limited and submaximal/predictive tests. The Fox-HRmax formula was based on data from 35 studies that appear to have true maximal exercise tests, although the Fox-HRmax formula was not based on regression analysis and may have included subjects with cardiovascular disease who smoked or were taking cardiac-related drugs, conditions that influence HRmax regardless of age. The Tanaka-HRmax formula was based on a meta-analysis of 351 studies (18,712 healthy subjects) with cycle or treadmill maximal exercise tests and a laboratory-based study of 514 healthy subjects with maximal treadmill tests. The heterogeneity between studies used to derive the Fox-HRmax and Tanaka-HRmax formulas is not an issue in the present study. HERITAGE subjects completed two true maximal exercise tests using the same cycle ergometers in the same laboratory. Furthermore, as described in more detail in the Methods section, measured HRmax was shown to be highly reproducible in HERITAGE (Skinner et al., 1999). A limitation of the present study is that for 70 subjects who achieved the age-predicted HR criteria, we could not distinguish whether they also achieved the VO2 plateau criteria. If the exercise tests of these subjects were deemed maximal solely through reaching the age-predicted HRmax criterion, this would represent an obvious issue for the analyses of the associations between measured HRmax and age-predicted HRmax. Thus, we chose to exclude these 70 subjects. However, our results and interpretation did not differ in analyses including all subjects with valid maximal exercise tests (N = 832). Lastly, the present study is based on data from cycle ergometer maximal exercise tests. Maximal values for some physiological variables (e.g., VO2max) obtained on a cycle ergometer may differ from values obtained on a treadmill or other exercise modalities. However, well-controlled laboratory studies of healthy adults that performed an individualized ramp exercise protocol on a bicycle ergometer and a treadmill in random order, showed that although peak VO2 values were different between the two modes of exercise, HRmax and maximum RER did not differ (Bouchard et al., 1979; Maeder et al., 2005). Despite the known limitations of age-based prediction formulas, their clinical and societal use is still wide-spread. Considering the doubtful validity of predicted HRmax values, as illustrated in the present study by the large SEE values, there is a need to develop alternative cardiorespiratory fitness standards and exercise prescription practices that do not require predicting HRmax. For instance, oxygen consumption and rating of perceived exertion (RPE) can be monitored during submaximal exercise testing, and subsequent exercise sessions can be prescribed using the power output corresponding to a certain VO2, RPE, or energy expenditure. Nonheart rate, intensity based exercise prescriptions would be especially appropriate for those individuals who are unable to raise heart rate or have trouble with heart rate monitoring. In conclusion, our results fail to validate the effectiveness of either of the two most widely used age-based HRmax prediction equations in sedentary, healthy adults. These results suggest that it may be very difficult, perhaps even impossible, to predict with a low SEE HRmax from age. They stress the importance of finding and validating other measures to be used in exercise prescriptions for the determination of intensity of exercise, the estimation of fitness levels, and as a criterion for achieving maximal exertion. ACKNOWLEDGMENTSThanks are expressed to Jack Wilmore for his contributions to the study. Contract grant sponsor: National Heart, Lung, and Blood Institute; Contract grant numbers: HL-45670, HL-47323, HL-47317, HL-47327, and HL-47321; Contract grant sponsor: John W. Barton Sr. Chair and Henry L. Taylor Professorship. LITERATURE CITED
What does the formula 220 your age tell you Apex?Just about anyone who has been on a treadmill, elliptical, or used a heart rate monitor has seen the chart that tells you to take 220 and subtract your age to get your maximum heart rate. This gives you a percentage of that maximum which puts you in a “weight loss zone”, an “aerobic zone”, or an “anaerobic zone”.
Why is Max heart rate 220 minus age?For many years, the typical formula for calculating your maximum heart rate was 220 minus age. Eventually, experts realized there's a big problem with that particular formula, as it doesn't reflect the way heart rate changes with age. MHR actually decreases as we age.
What is 220 in Karvonen formula?The Karvonen formula is your heart rate reserve multiplied by the percentage of intensity plus your resting heart rate. For example, a 50-year-old with a resting heart rate of 65 would calculate as follows: 220 - 50 = 170 for HRmax. 170 - 65 = 105 for RHR.
Is 220 age accurate for everyone as a Max HR predictor?The traditional formula for determining HRmax is "220 minus age", but can underestimate HRmax by up to 40 beats per minute in seniors. In fact, the method is inaccurate already at an age of 30–40 years, and gets more inaccurate the older you are.
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The formula 220 minus age is commonly used to estimate what cardiorespiratory information?
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