Comparisons of Age-Predicted Maximum Heart Rate Equations in College-Aged Subjects : The Journal of Strength & Conditioning Research

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Comparisons of Age-Predicted Maximum Heart Rate Equations in College-Aged Subjects

Cleary, Michelle A; Hetzler, Ronald K; Wages, Jennifer J; Lentz, Melissa A; Stickley, Christopher D; Kimura, Iris F

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Journal of Strength and Conditioning Research 25(9):p 2591-2597, September 2011. | DOI: 10.1519/JSC.0b013e3182001832
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Using heart rate as an accurate indicator of the intensity of work is fundamental for developing exercise prescription programs for cardiovascular training and allows for quantification of intensity and effort during exercise (4). The techniques for developing exercise prescriptions, often taught in university physical education and health and wellness classes, are typically based on estimates of heart rate maximum (HRmax) using a common equation originally developed by Fox et al. (HRmax = 220 − age) (8) combined with the Karvonen equation (15). Exercise prescriptions are most accurate when HRmax is actually determined rather than estimated. However, estimation of HRmax using prediction equations is the method of choice in most settings. The most commonly used Fox equation (8) has been reported to have an SD between 10 and 12 b·min−1 (1). Thus, when estimating HRmax using the Fox equation, approximately 66% of the population should fall within ±10 beats of the actual HRmax, but for the remaining population, the actual HRmax could differ by as much as 12-20 b·min−1 or more. Recently, it has been reported that the Fox equation significantly overestimates HRmax in younger adults and underestimates it in older individuals (10,22). This systematic error or bias has led to the development of new equations for estimation of HRmax in an attempt to more accurately predict HRmax in large, heterogeneous populations (7,8,10,13,22). It is unknown as to how well these equations work in a college-age population, which constitutes a relatively homogenous age group and tends to be more physically active than other segments of the population.

Questions remain as to the accuracy of prediction equations when applied to a relatively homogeneous age group. Age has been established as the best predictor of HRmax using large groups of heterogeneous subjects, and HRmax has been demonstrated to decrease with age (7,8,10,22). College-age individuals are generally in good health and of similar age (18-25 years); therefore, the use of age-predicted maximum HR equations tends to result in nearly identical exercise prescriptions for these individuals. A limitation of the Fox equation is the systematic bias of overpredicting HRmax in younger individuals and underpredicting HRmax in older individuals (10). The systematic overprediction of HRmax in young adults will result in systematic errors when developing exercise prescriptions. Using this approach, many individuals will be prescribed an exercise intensity, which is higher than what may be needed to improve cardiovascular fitness. Reducing the error of estimating HRmax would improve the accuracy of exercise prescription.

Determining actual HRmax using graded exercise testing (GXT) is a common laboratory technique. However, the GXT requires trained personnel to conduct tests that are usually 10-20 minutes for each subject, with expensive laboratory equipment and is impractical when dealing with large groups. Physical educators, personal trainers, and coaches would benefit from the knowledge and ability to use a shorter duration anaerobic capacity test, which may allow for determination of HRmax quickly and accurately using palpation of pulse or an HR monitor. Our hypotheses were that (a) a short-duration, anaerobic field test elicits an accurate HRmax and (b) recent age-predicted HRmax equations are more accurate in predicting actual HRmax among college-aged individuals than the Fox equation. Therefore, the purposes of this study were to establish efficacy of short-duration anaerobic capacity tests to determine the actual HRmax and to determine the accuracy of age-predicted equations to predict HRmax in a college-age sample.


Experimental Approach to the Problem

This study used a test-retest design to establish a criterion HRmax (CHRmax) assessed by completing a 30-second Wingate anaerobic test (WAnT) and 2 200-m sprint trials and with each test separated by at least 3 days. A subgroup of the sample (n = 25) volunteered to perform a GXT on a motor driven treadmill using the Bruce Protocol (1) to confirm that CHRmax obtained from the anaerobic tests were representative of actual HRmax. The CHRmax was compared to the HRmax predicted by the Fox equation and 6 other recently developed age-predicted HR equations (Gellish1, Gellish2, Gellish3, Tanaka, Fairbarn, and Hossack).


Participants in this study consisted of a cross-sectional sample of 96 healthy volunteers aged 18-33 years recruited from health and physical education classes from the university, which tends to be a physically active group. Anthropometric data are presented in Table 1.

Table 1:
Participant physical characteristics (mean ± SD) (n = 96).

No attempt was made to document or control for training (aerobic or resistance) status of the participants or menstrual phase of the women. Before testing, all participants completed a medical history questionnaire and physical activity self-assessments developed in accordance with the American College of Sports Medicine (ACSM) guidelines for participation in exercise (1). Inclusion criteria for all participants included classification as low risk (ACSM Risk Stratification Categories) for exercise testing and absence of cardiovascular, coronary artery, pulmonary, or metabolic diseases (1). Preparticipation forms were reviewed to exclude those unable to participate in maximal effort testing, and 9 potential participants were excluded for not meeting inclusion criteria. All data were collected during the Spring semester. Before testing, all participants provided informed consent to participate in the study by reading and signing informed consent forms. This study was approved by the University Institutional Review Board, Committee on Human Subjects.


Wingate Anaerobic Test

The WAnT is a maximal effort 30-second cycling test against frictional resistance (2). A cycle ergometer designed specifically for use with the WAnT protocol (Monark Ergomedic 834 E, Monark Exercise AB, Vansbro, Sweden) was used following standard procedures (2,14). Data were collected using specialized software (SMI Power, Sports Medicine Industries, Inc., St Cloud, MN, USA), which uses an optical sensor to count flywheel revolutions and corrects the data for flywheel inertia. The optical sensor position was calibrated before each test (2,14). The reliability of the WAnT was not tested in this study but has been reported to range from r = 0.89 to 0.98 (3) with r = 0.96 (p < 0.05) when testing active young adults (6). Validity of the WAnT was established through correlation to various other field and laboratory tests (r = 0.75) (2).

Two Hundred-meter Sprint Trial

The 200-m sprint was performed on a standard 400-m track (Super X Performance, Mondo USA, Grapevine, TX, USA). The 200-m distance is optimal to evaluate HRmax in approximately 30 seconds for healthy physically active people (17,19-21). A test period of 30 seconds corresponds to a sufficient duration to extensively tax the phosphagen and glycolytic anaerobic energy systems (19). The highest HRmax of the 2 sprint trials was used for data analyses.

A portable wireless timing system (Wireless Sprint System, Brower Timing Systems, Draper, UT, USA) was used to collect sprint times during the trials. This system included an electronic timer triggered start as participants ran through infrared beams and results were displayed on a hand held monitor. Electronic timing gates were used to record 200-m run times for each participant. The infrared beams have a reported range of 260 m and an accuracy of 0.001 seconds (5). Participants completed the test on a timed course set up in a similar fashion to the 200-m event as performed during competition. Participants were read a standardized set of instructions to exert maximal effort by running as fast as possible without pacing themselves or saving their energy for a burst of speed at the finish. Before entering the timed portion of the 200-m sprint, participants were instructed to begin with a running start by accelerating to near maximal speed over a 15-m distance before the starting line. A 225-m timing gate was placed at the end of the timed distance to encourage participants to sprint through the entire 200-m timing course but was not activated or used in the subsequent analysis.

Graded Exercise Test

The Bruce treadmill protocol (1) was used to elicit maximum physiologic responses to exercise in a subgroup of participants. Data from the GXT including lactate, ratings of perceived exertion, respiratory exchange ratio, and maximum oxygen consumption are presented in Table 2.

Table 2:
HRmax descriptives (mean ± SD) for subsample (n = 25).*

Heart Rate Analysis

Heart rate data were used to confirm achievement of maximal effort throughout each trial. A standard heart rate monitor with telemetry system (Polar Electro Inc., Woodbury, NY, USA) was used to measure heart rate. The heart rate monitor was fitted to each participant's chest and worn during all exercise tests. The HRmax during exercise was displayed on a monitor and used for data analysis. Commercially available heart rate monitors have been compared to standard electrocardiograms to establish validity and reliability (16,23) resulting in a high correlation between the 2 devices (r = 0.93-0.98) (16).

Lactate Analysis

Blood lactate concentrations were analyzed using the YSI 1500 Sport-L Lactate Analyzer (Yellow Springs Instrument Co., Inc., Yellow Springs, OH, USA). Before blood sample analysis, the lactate analyzer was calibrated using commercial standards according to the company's user manual. Blood samples were obtained from a free flowing digit puncture and handled according to guidelines set forth by the Occupational Safety and Health Administration. Samples were lysed and stored on ice and analyzed at the completion of each data collection session. Lactate analysis has been reported to be a valid and reliable measure of anaerobic capacity (23). Blood lactate production from 200-m sprints has been previously reported to correlate highly to run times (r = 0.78, p < 0.001) (9,11).

Ratings of Perceived Exertion

Ratings of perceived exertion (RPEs) were assessed using Borg's RPE (6-20) scale (4) to determine the attainment of maximal effort from participants throughout all exercise tests. Participants were read standard instructions as suggested by Pandolf (18) to rate the amount of work (feelings and sensations felt during work) according to the scale upon completion of the sprint trial.

Anthropometric Measurements

Demographics were recorded for participants cleared for data collection. Height was determined using a wall-mounted stadiometer (67032 Seca Telescopic Stadiometer, Fitness Mart, Country Technology Inc., Gays Mills, WI, USA), and data were recorded to the nearest 0.5 cm. Body mass was measured using an eye-level triple beam scale (442 Certifier, Detecto, Cardinal Scale Manufacturing Co., Webb City, MO, USA), and data were recorded to the nearest 0.01 kg. Body composition was determined by measurements from skinfold calipers (Lange Skinfold Caliper, Cambridge Scientific Industries, Cambridge, MA, USA). Gender-specific body density was estimated using the Jackson and Pollock (1) 3 site equations and converted to percent body fat. Men were assessed through thigh, chest, and abdomen skinfolds, whereas women had their thigh, triceps, and suprailium skinfold sites measured. Participants' sites were located and marked, and skinfolds were obtained as described by Jackson and Pollock. All measurements were taken on participants' dominant side, each site was measured twice and if values differed by >1 mm, a third measurement was taken. Skinfold data were averaged, and these data were used to estimate body composition (1).

Data Collection Procedures

Familiarization Session

During a familiarization session (before exercise trial 1), potential participants read and signed a medical history form, a physical fitness readiness questionnaire, and the informed consent form. Forms were reviewed to exclude those unable to participate in maximal effort testing. Data for the sprint trials were collected on 3 separate days, each separated by at least 72 hours. Participants were instructed to maintain activities of daily living between exercise trials and refrain from overexertion through participation in any strenuous activities. Exercise modes were randomly assigned before the first trial and counterbalanced for the second and third trial sessions to control for an order effect. Additionally, 25 subjects volunteered to complete a Bruce protocol GXT.

Exercise Tests

Participants were instructed to report to the University of Hawaii Human Performance Laboratory dressed in appropriate athletic attire. Upon arrival, participants were fitted with a heart rate monitor to wear throughout the duration of the session. Participants' resting heart rate and RPE were recorded, and pretest blood samples were obtained for blood lactate analysis. Immediately after completion of each test, RPE values were recorded, and maximal heart rate was assessed. Seven minutes after completion of the exercise test, participants' posttest blood samples were collected. Maximal effort was confirmed by a blood lactate concentration of at least 7.0 mmol·L−1 and an overall RPE of ≥17 (1).

Statistical Analyses

Descriptive data were calculated and reported in Table 1 for the entire sample (n = 96) and the subsample (n = 25). The first hypothesis (i.e., a short-duration, anaerobic field test elicits an accurate CHRmax) required an examination of the following: (a) analyzing differences in HRmax from the 2 sprint trials using dependent 2-tailed t-tests, (b) determining the reliability of HRmax obtained during the 2 sprint trials using intraclass correlation coefficients (ICC[(2,1]) and SEM, both calculated as described by Weir (24), and (c) determining differences in CHRmax from the Wingate sprint trials and the GXT in a subsample (n = 25) using analysis of variance (ANOVA) for repeated measures. A retrospective power analysis was performed to compare the CHRmax from the 2 sprint trials and the graded exercise test (n = 25).

The second hypothesis (recently developed age-predicted HRmax equations are more accurate in predicting actual HRmax among college-aged individuals than the Fox equation) was tested by comparing CHRmax from the sprint trials to 7 age-predicted HRmax equations: the equation from Fox et al., 3 equations from Gellish et al., Tanaka et al., and gender-specific equations from Fairbarn et al., and Hossack et al. For each equation, descriptive statistics and standard errors of estimate (SEEs) were calculated. One-way ANOVA was used to assess differences between the CHRmax and age-predicted HRmax. Statistical analyses were conducted using a standard statistics software package (SPSS version 16.0, Chicago, IL, USA). Significance was set a p ≤ 0.05 for all analyses.


In the subsample (n = 25), the HRmax from the GXT (190.0 ± 7.4 b·min−1) compared to the sprint trials HRmax (190.1 ± 7.9 b·min−1) were nearly identical and differences were not significant (p = 0.710), although the relationship was not perfect (mean absolute error = 5.8 b·min−1). Of the participants completing the GXT, 13 of 25 (52%) had higher HRmax during the GXT than during the sprint trials. The Wingate test resulted in significantly lower mean HRmax than the sprint trials (−10.6 b·min−1, p < 0.001) and the GXT (−10.6 b·min−1, p < 0.001). Therefore, the highest HR obtained from the sprint trials was used to represent CHRmax as a criterion measure for the entire sample population. Mean lactate values for each exercise test were all >8.4 ± 1.0 mmol·L−1, and mean RPE vales were all >16.5 ± 1.5. Data for the subsample exercise trials are presented in Table 2.

When examining the reliability of the 2 sprint trials (n = 96), no significant differences were found between the 2 trials (mean HRmax trial 1 = 185.7 ± 8.6 b·min−1 and trial 2 = 184.8 ± 9.6 b·min−1) (p = 0.388, power = 0.138). However, because the ICC(2,1) was 0.43, and the SEM was 6.9, 2 sprint trials were necessary to establish HRmax. Table 3 presents the means, SD, and SEE for the CHRmax from the sprint trials and the prediction equations.

Table 3:
Prediction equation comparisons to CHRmax (mean ± SD) (n = 96).*

Predicted HRmax from Fox, Gellish1, Gellish3, Tanaka, and Hossack were all significantly different (p ≤ 0.001) from CHRmax (Table 3). The most commonly used prediction equation (Fox) resulted in 88.5% of the cases where HRmax was overpredicted compared to the CHRmax by a mean overestimation of 12 ± 7 b·min−1 and a range of 1-37 b·min−1. The CHRmax when compared to the age-predicted HRmax resulted in the following percentages of the CHRmax: Fox equation = 104.8%, Gellish1 = 95.2%, Gellish2 = 99.6%, Gellish3 = 101.8%, Tanaka = 102.0%, Fairbarn = 100.1%, and Hossack = 105.2% of CHRmax.


The most important finding of this study was that the best performing prediction equations were the Gellish2 and the Fairbarn equations, which both arrived at reasonable estimates that did not differ significantly from the CHRmax. In addition, based on GXT results from the subsample, HRmax may be determined by performing 2 200-m sprint trials and the sprint trials provided better estimates of HRmax than the WAnT. Mean HRmax, lactate, and RPE values for the exercise tests were in the expected range for maximum effort (Table 2). A limitation of this study was that HRmax was not assessed using GXT for all subjects.

Recognizing the limitations of the Fox et al. age-predicted HRmax formula (8), several recent studies (7,10,22) have challenged the utility of the equation for exercise prescription. Because maximal exercise testing is not feasible in many settings, HRmax is often estimated using the Fox et al. age-predicted equation of 220 − age. However, the validity of this equation has been called into question, primarily because it was originally developed based on the HRmax derived from a meta-analysis of research articles on coronary heart disease patients (8). When healthy, sedentary men and women are included, a gender difference in the age-related decline of HRmax is found with a more rapid decline with age in men than in women (13). Age-related decreases in HRmax within the range of 0.5-1.6 of a beat per year have been reported (12,13) suggesting that the Fox equation (which corresponds to a decline of an even 1 beat per year) may be inaccurate for many individuals.

Because of the importance of being able to accurately estimate HRmax, a number of studies have been conducted examining modified age-predicted HRmax equations. Fairbarn (7) developed prediction equations based on data from 231 healthy men and women equally divided within decades between 20 and 80 years (N = 20-30 subjects per decade) and found that the accuracy of predicting the HRmax for women was highest with a single equation for the women as 1 age group, whereas for the men, the equation was more accurate when divided into a younger group and a group >70 years. Gellish et al. examined the relationship between age and HRmax and compared their equations to the Fox equation using HRmax values obtained through maximal exercise testing (10). This retrospective study examined previously collected data on 4,666 individuals from 25 years of research and identified a longitudinal relationship between age and HRmax during graded exercise testing. The Fox equation (8) was found to be inaccurate in determining HRmax as the age − heart rate relationship was nonlinear. Therefore, Gellish et al. proposed 3 new equations, one of which was reported to be the most accurate (192 − 0.007·age2) for predicting HRmax based on age (10). Data from this study supported the findings of Gellish that the Fox equation significantly overpredicted HRmax in the college-age population. Additionally, the Gellish2 and the Fairbarn gender-specific equations were the most accurate prediction models.

Within the limitations of this study, prediction of HRmax in a college-age population was best accomplished using the Gellish2 (10) equation or the Fairbarn (7) gender-specific equations, because they were not significantly different from the criterion measure (p > 0.05). Both resulted in mean values that were nearly identical to the CHRmax measure (Table 3). The mean absolute difference between the CHRmax and the Gellish2 equation was 6.5 b·min−1 and the Fairbarn equation was 9.2 b·min−1, respectively, indicating that the Gellish2 equation may be a better choice in this population. Additionally, the SEEs for these 2 equations were similar and were the lowest of those examined in this investigation (SEE = 8.3 and 8.5 b·min−1, respectively). All the other prediction equations resulted in mean HRmax values, which were significantly different from the CHRmax (p < 0.001). In our sample, the Fox equation and the Gellish1 equation (proposed for general use by Gellish) had SEE of 12.2 and 12.7 b·min−1, respectively, precluding the utility of these equation for estimating HRmax in college-age individuals. Gellish et al. reported that the Gellish2 equation was their most accurate equation (but these researchers stated that it was “… less desirable from a usability point of view…” because of its nonlinear form). Although the Gellish study (10) derived their equations from an older subject population (where the youngest man was 27 years, and the youngest woman was 28 years), our findings support the use of the Gellish2 equation when estimating HRmax in a college-age sample, which tends to be more physically active than other segments of the population.

In situations where a CHRmax is a variable of interest, the results of the present investigation support the use of sprint tests as a reasonable alternative to GXT to determine HRmax in a class or group setting. These data indicated that the 200-m sprint trials provided better estimates of HRmax than the WAnT in the college-aged sample. However, because the absolute difference between the CHRmax from the 2 sprint trails was a mean of 7.0 b·min−1 and the reliability between trials was only moderate (ICC[2,1] = 0.43; SEM = 6.9 b·min−1), 2 sprint trials should be performed, and the highest value used to represent HRmax for exercise prescription. The low ICC (n = 96) for the 2 sprint trials was expected because of the homogenous nature of the subjects' age. Weir reported that if subjects differ little from each other the ICCs are expected to be low even when the trial-to-trial variability is small (24). The HRmax (n = 25) achieved in the sprint trials trials (mean HRmax = 190.1 ± 7.9 b·min−1) favorably compared to the CHRmax from the GXT (mean HRmax = 190.0 ± 7.5 b·min−1) as the means were not significantly different.

Data from this study suggest that a GXT or 2- 200-m sprints should be used when practical to determine HRmax instead of age-related prediction equations. However, when exercise testing is impractical, the best performing age-predicated HRmax equations (Gellish2 or Fairbarn) should be used. When using age-predicted HRmax to calculate training HR range with the Karvonen equation, the Fox equation resulted in a significantly higher training HR range (60-80% training HR range = 147.3-172.6 b·min−1) than obtained using the CHRmax (60-80% of training HR range = 141.7-165.2 b·min−1, p < 0.001). Compared to the CHRmax, the Fox equation predicted a training HR range that was about 5.6 beats higher on the low end and about 7.5 beats higher on the high end of the prescription range. Alternatively, the Gellish2 equation more accurately predicted training HR range (60-80% of training range = 141.3-164.7 b·min−1), which was only 0.4 b·min−1 lower on the low end and 0.5 b·min−1 lower on the high end of the prescription range as determined by the CHRmax. The overprediction of training HR range by the Fox equation may not be safe for all college-age individuals. It was concluded that, if using an equation is necessary for exercise prescription, the Gellish2 equation most accurately predicted training HR range when using the Karvonen equation compared to the CHRmax. Further, when prescribing training HR ranges, the Gellish2 or Fairbarn equations both provided accurate results that were within 1 b·min−1 of the training HR range established using the CHRmax.

Practical Applications

Physical educators, personal trainers, and coaches should be aware that when prescribing exercise for young adults, a GXT or 2 200-m sprint trials (with the highest values used as the HRmax), should be used when possible to accurately determine HRmax. However, when the use of a GXT or 2- 200-m sprint trials is impractical, the Gellish2 or the Fairbarn equations should be used to determine aerobic exercise prescriptions using the Karvonen equation in a college-age population. The findings of this study determined that the Fox equation was not the best age-predicted HR equation to use and other population-specific equations are more appropriate. Although the Fox equation (HRmax = 220 - age) has traditionally been taught and used in a variety of health and fitness settings the Gellish2 and Fairbarn equations were the most accurate of the age-predicted HRmax equations tested in a college-age population. The Gellish2 marginally outperformed the Fairbarn equation; nonetheless, both equations were determined to increase the accuracy of exercise prescription.


Funding sources were provided by the University of Hawaii, Manoa, Department of Kinesiology and Rehabilitation Science. No companies, manufacturers, or outside organizations provided financial, technical, or equipment support. There are no professional relationships with companies or manufacturers who will benefit from the results of this study. The results of this study do not constitute endorsement by the National Strength and Conditioning Association.


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maximum exercise testing; exercise prescription; heart rate prediction; Wingate anaerobic test; 200-m sprint

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