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Special Communications: Methods

Heart rate reserve is equivalent to%˙VO2Reserve, not to%˙VO2max


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Medicine & Science in Sports & Exercise: March 1997 - Volume 29 - Issue 3 - p 410-414
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For exercise prescription purposes, the American College of Sports Medicine (ACSM) assumes that a percentage of the difference between maximal and resting heart rate, i.e.,% heart rate reserve (%HRR), provides the same intensity as the equivalent percentage of maximal oxygen consumption(%˙VO2max) (1). The use of this prescription method dates back to the seminal work of Karvonen (4). However, Karvonen did not claim that the heart rate reserve method provided an equivalency to%˙VO2max (in fact, ˙VO2 was not measured in that study), and such a relationship has not been established in subsequent literature.

A person at rest has a nonzero heart rate and a nonzero ˙VO2. Thus, if one compares the range of heart rates from rest to maximum with a range of ˙VO2 from zero to maximum, an error is introduced. When expressing these ranges as percentages of their maxima, the magnitude of the error will depend on the absolute value of ˙VO2max. For example, an individual with a 10 MET capacity is at 10% of ˙VO2max at rest (1 MET/10 METs), and at 0% of HRR (by definition). Thus, a 10% discrepancy is introduced at the resting end of the%HRR:%˙VO2max relationship. A highly fit individual with a 20 MET capacity will have a 5% discrepancy (1 MET/20 METs), while a deconditioned individual with a 5 MET capacity will have a 20% discrepancy (1 MET/5 METs).

To eliminate this error, one should compare the range of resting to maximal heart rate with the range of resting to maximal ˙VO2 (i.e.,˙VO2Reserve). Theoretically,%HRR should be equivalent to%˙VO2Reserve (%˙VO2R).

The purpose of this study was to test the hypothesis that%HRR is equivalent to%˙VO2R, not to%˙VO2max. A second hypothesis was that the discrepancy between%HRR and%˙VO2max would be inversely related to fitness level.


Subjects. All subjects were between 18 and 40 yr old and were apparently healthy as defined by the American College of Sports Medicine(1). All subjects provided informed consent in accordance with institutional guidelines for research with human subjects. A total of 63 subjects participated in the study (33 males, 30 females). A summary of their physical characteristics is presented in Table 1. Physiological characteristics recorded during testing are presented inTable 2.

Protocol. Each subject's height, weight, and skinfold measurements (the latter to estimate percent fat (7)) were recorded. Subjects were fitted with a mouthpiece (Hans Rudolph, Kansas City, MO), and ECG electrodes were placed in a lead II configuration. Each subject performed an incremental exercise test on an electrically braked and calibrated bicycle ergometer (SensorMedics model 800, Yorba Linda, CA) at 80 rpm. The seat was adjusted to provide a slight bend (approximately 5°) in the knee at full extension. Pedal straps were used. Ambient temperature during testing was 21.8 ± 0.1°C. Subjects were asked to abstain from alcohol, caffeine, and other drugs for 24 h and not to eat for at least 1 h prior to testing.

After approximately 5 min of seated rest, the incremental exercise test was performed in 3-min stages. Most subjects began at a power output of 40 W, which was then increased by 40 W per stage. Subjects with significant cycling experience performed a modified protocol to reduce the total duration of their tests. They began at 80 W for the first stage, proceeded to 160 W for the second stage, and then had 40 W per stage increments thereafter. This allowed them to complete a similar number of stages as the other subjects(approximately 5, on average). All subjects exercised until they reached exhaustion and under their own volition decided to stop or until they were no longer able to maintain the prescribed cadence. This was followed by 2-3 min of active cooldown.

Data collection and analysis. Heart rate was measured continuously on an automated ECG system (SensorMedics Max-1). Expired gases were collected continuously and analyzed for the determination of ventilation(˙VE), oxygen consumption (˙VO2), and carbon dioxide production (˙VCO2) using a metabolic cart (SensorMedics 2900c), whose O2 and CO2 analyzers were calibrated prior to each test against known gas concentrations and whose flowmeter was calibrated at least once per day against a 3.0-1 syringe. Maximal oxygen consumption was defined as the highest ˙VO2 obtained over any continuous 60-s time period provided that respiratory exchange ratio (RER) was ≥ 1.10. Maximal heart rate was similarly defined as the highest value recorded over any continuous 60-s period during exercise.

The lowest values of heart rate and ˙VO2 recorded over any continuous 60 s during the rest period were considered to be the resting values. The heart rate and ˙VO2 obtained during the last 60 s of each stage were recorded and expressed as percentages of their respective ranges, i.e.,%HRR, and%˙VO2R. Furthermore, the end-of-stage˙VO2 was expressed as a percentage of the maxima, i.e.,%˙VO2max.

Statistics. For each subject two linear regressions were performed: one on the values of%HRR versus%˙VO2max, and one on the values of%HRR versus%˙VO2R. In each case, data obtained at rest, at each completed stage of exercise, and at maximum were entered into the regressions. (Group regressions, in which data from separate subjects are analyzed together, were not performed, as this would statistically obscure the individual relationships.) The mean (± SE) values for intercepts, slopes, and Pearson r correlations were determined for the two sets of regressions. Student t-tests were used to determine if the mean intercepts and slopes differed from 0 and 1, respectively (i.e., if they differed from the line of identity).

To test the relationship between fitness level and the discrepancy between%HRR and%˙VO2max, a regression was performed on each subject's intercept (from his%HRR vs% ˙VO2max regression) versus his ˙VO2max expressed in ml·min-1·kg-1.


The regressions for%HRR versus%˙VO2max did not coincide with the line of identity (Fig. 1). The mean value for the intercept (-11.6 ± 1.0%HRR units) was significantly different from zero(P < 0.001). The mean value for the slope (1.12 ± 0.01) was significantly different from 1 (P < 0.001). The mean correlation coefficient was 0.990 ± 0.001.

The regressions for%HRR versus%˙VO2R were not distinguishable from the line of identity (Fig. 2). There were no significant differences between the mean intercept (-0.1 ± 0.6%HRR units) and 0 or between the mean slope (1.00 ± 0.01) and 1. The mean correlation coefficient was 0.991 ± 0.001.

There was a significant inverse relationship between fitness level(˙VO2max) and the intercept of the%HRR versus%˙VO2max regressions (r = 0.53, P < 0.01). To illustrate this fitness effect, the%HRR versus% ˙VO2max data for high fit subjects(˙VO2max > 50 ml·min-1·kg-1;N = 11) was plotted along with the data for low fit subjects(˙VO2max < 30 ml·min-1·kg-1;N = 14) in Figure 3. The low fit subjects demonstrate a significantly greater deviation from zero for their intercepts than do the high fit subjects.

The high fit subjects in Figure 3 were all males, while the low fit subjects were mostly females (12 of the 14). To determine if the difference was a result of gender or fitness, the subjects with˙VO2max values between 30 and 50 ml·min-1·kg-1 were analyzed. Within this group there were 20 males and 18 females, whose mean ˙VO2max values did not differ (39.6 ± 1.2 and 38.3 ± 1.4 ml·min-1·kg-1, respectively). There were also no differences in their mean intercepts (- 12.3 ± 1.1 and - 12.7 ± 2.0, respectively) or mean slopes (1.13 ± 0.01 and 1.14 ± 0.02, respectively).


It is well established that%HRmax is not equivalent to%˙VO2max(8). Individuals who prescribe exercise by heart rate take this fact into consideration either by employing a higher percentage of maximum HR than the desired percentage of maximum˙VO2, or by employing the heart rate reserve method, in which it is generally assumed that values of%HRR are equivalent to values of%˙VO2max. This study demonstrates that%HRR is not equivalent to%˙VO2max but is instead equivalent to%˙VO2R. The exercise community has embraced the supposed equivalency of%HRR and%˙VO2max without justification. The universally cited work establishing the heart rate reserve method of exercise prescription was published by Karvonen et al. (4). This study examined heart rate responses of six young adult males to exercise training. Exercise heart rates were expressed as a percentage of the difference between rest and maximum, hence the current use of the term “Karvonen heart rate” for heart rate reserve. However, oxygen consumption was not measured, and thus no conclusions regarding the relationship between%HRR and%˙VO2max can be drawn from the study.

A review of the literature revealed no studies after 1957 that established an equivalency between%HRR and%˙VO2max. However, one study supports the equivalency of%HRR and%˙VO2R(3), two studies provide an indirect comparision of%HRR and%˙VO2max with mixed results (9,10), and two studies provide direct support for the lack of equivalency of%HRR and%˙VO2max(2,6).

Davis and Convertino (3) studied nine highly fit, young adult males during treadmill running and determined that%HRR was equivalent to a percentage of the net ˙VO2 (referred to in the current study as ˙VO2R) at four steady-state workloads ranging from approximately 30 to 80% of maximal capacity. While they did not evaluate%HRR relative to%˙VO2max, their finding agrees with the current study regarding%HRR and%˙VO2R. Weltman et al. performed two studies that evaluated the intensity of treadmill exercise necessary to elicit the lactate threshold in a majority of subjects. The lactate threshold was attained by a majority of female subjects at 55% of either HRR or ˙VO2max(10), while a majority of male subjects attained the lactate threshold at 85% of HRR and at 90% of ˙VO2max(9). The study in men supports the current findings, while that in women does not. However, in both cases the authors were not attempting to compare HR to ˙VO2, and a comparison of their data with that of the current study through the subjects' lactate responses is indirect at best. Of greater relevance to this study, two studies have evaluated%HRR and%˙VO2max during treadmill exercise by the elderly(2,6). Both found that at any given exercise intensity the values for%HRR were lower than the values for%˙VO2max in support of the current findings.

When one assumes that%HRR is equivalent to%˙VO2max, the magnitude of the error is influenced by two factors, the fitness level of the subject and the intensity of exercise. According to the results of this study, it is not influenced by gender. By a simple mathematical transposition, the fitness level of a subject will determine the percentage of ˙VO2max for the subject when at rest. An average subject with a 10 MET capacity will be at 1 MET/10 MET, or 10% of ˙VO2max at rest. Thus, there will be an error of 10 units between%HRR and%˙VO2max at rest. As described earlier, a subject with a 20 MET capacity would have a 5 percentage point error, while a subject with a 5 MET capacity would have a 20 percentage point error. Similar errors are clearly illustrated in Figure 3. The high fit and low fit subjects have average ˙VO2max values of 15.9 METs and 7.4 METs, for expected%˙VO2max errors of 1/15.9 and 1/7.4, or 6.3% and 13.6%, respectively. The actual mean errors in%˙VO2max at rest (i.e., the x-intercepts) are 3.9% and 13.4%, respectively.

While these are the errors at rest, the errors within a typical range of exercise intensities will be lower. As seen in Figures 1 and 3, the discrepancy between%HRR and%˙VO2max becomes smaller as maximal exercise is reached and both values attain 100%.

This finding is supported by Belman and Gaesser, who performed a training study on 17 elderly subjects (2). Eight of the subjects were placed at a high intensity, 75% of HRR, which was reported to be approximately 82% of their ˙VO2max. The 9 remaining subjects were placed at a low intensity, 35% of HRR, which was approximately 53% of˙VO2max. In the current study, 75% of HRR corresponded to 77% of˙VO2max on average, and 35% of HRR corresponded to 42% of˙VO2max on average. The greater discrepancies in the Belman and Gaesser study are likely a result of the lower fitness level of their elderly subjects, which averaged 7.1 METs.

In terms of exercise prescription, it must be pointed out that a relatively small discrepancy between%HRR and%˙VO2max results in a greater error in exercise intensity. For example, the 7 percentage point difference in the 35% HRR versus 42% ˙VO2max cited above translates to a 7/35 = 20% error in exercise intensity.

To avoid such errors, exercise intensity should be prescribed in units of%˙VO2R, not%˙VO2max. This would be especially important for very deconditioned subjects (such as the frail elderly, cardiac, renal failure and pulmonary patients, and the obese), provided future research confirms this relationship in such populations. An exercise prescription at 40-50% of ˙VO2max has little meaning if the subject is already at 20-30% of ˙VO2max when at rest. Instead, the difference between rest and maximal ˙VO2 should be considered in determining an appropriate intensity. Once such an intensity is assigned using%˙VO2R units, it can accurately be translated to a heart rate based on the equivalency of%HRR and%˙VO2R.

Another source of error in exercise prescriptions is lack of knowledge of a client's true maximal heart rate. While most practitioners realize that the estimate of 220-age provides only a rough estimate of HRmax, fewer realize that HRmax during cycling exercise is consistently less than this value. In the current study, subjects with an average age of 28 yr had an average HRmax of only 180 bpm, i.e., 12 bpm less than the estimated value. A comprehensive review by Londeree and Moeschberger developed generalized equations for HRmax that yield an estimated HRmax for 28-yr olds performing cycle ergometry of 182 bpm (5). They concluded that the 95% confidence interval for HRmax (regardless of age, gender, or mode of exercise) is about 22 bpm above and below the mean value. Obviously, ascertaining true HRmax should be done whenever practical if accurate heart rate prescriptions are desired.


Percentage of HRR is equivalent to%˙VO2R, not to%˙VO2max. The discrepancy between%HRR and%˙VO2max is inversely proportional to exercise intensity, being a sizable error during low intensity exercise. The discrepancy between%HRR and%˙VO2max is inversely proportional to fitness level, being of greater significance for low fit subjects. Based on these findings, we recommend that the equivalency of%HRR to%˙VO2R should be employed in the design of exercise prescriptions. The findings of the current study apply to young, apparently healthy adults performing cycling exercise. Similar findings by Davis and Convertino (3) on young males performing treadmill exercise, related literature using elderly subjects(2,6), as well as the strong theoretical basis of these findings, support their generalization. However, further confirming studies are needed.

Figure 1-Scatter plot of the%HRR vs%˙VO2max data from all 63 subjects. The regression equation is the average of 63 individual regressions.
Figure 1-Scatter plot of the%HRR vs%˙VO2max data from all 63 subjects. The regression equation is the average of 63 individual regressions.
Figure 2-Scatter plot of the%HRR vs%˙VO2R data for all 63 subjects. The regression equation is the average of 63 individual regressions.
Figure 2-Scatter plot of the%HRR vs%˙VO2R data for all 63 subjects. The regression equation is the average of 63 individual regressions.
Figure 3-Scatter plot of the%HRR vs%˙VO2max data for 11 high fit subjects and 14 low fit subjects. The two regression equations are the average for each group.
Figure 3-Scatter plot of the%HRR vs%˙VO2max data for 11 high fit subjects and 14 low fit subjects. The two regression equations are the average for each group.


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©1997The American College of Sports Medicine