Age-predicted heart rate formulas have long been used in the athletic and fitness communities as a way to measure and safely prescribe exercise intensity, but little research exists about how those equations were derived. And there are numerous discrepancies surrounding these formulas which are considered commonplace.

Further research is needed to determine more valid and reliable methods to measure maximum heart rate for all age groups, genders, and fitness levels within practical resource means.

Developing a standardized approach to achieve more valid and reliable methods to measure maximum heart rate has been an ongoing challenge to scientists, especially considering the number of variables that can affect testing protocol.

These same variables can greatly affect the implementation of heart rate training on a daily basis. This potentially renders it less than adequate for prescribing specific intensities during a session with the intent to achieve a particular adaptation.

The most commonly used and well-known formula is 220 minus an individual’s age, which gives the age-predicted heart rate maximum value (Robergs & Landwehr, 2002). Unfortunately, this formula, nor any other derivative of age-predicted heart rate max, has accurately predicted maximum heart rate on a consistent and individualized basis within a reasonably narrow window of standard deviation.

In fact, this formula was never derived from original scientific evidence, but rather, from observation and compilation from other invalidated research sources (Robergs & Landwehr, 2002). There are numerous variables unaccounted for by these formulas. These include training experience, stress level, efficiency, adaptation level, hemoglobin content of the blood (oxygen carrying capacity), training phase, recovery status, health status, pre-existing health conditions, medications, and more. All of these can drastically affect heart rate and perceived exertion at a given exercise intensity each day.

Physiologically, to compete with the demand for oxygen delivery to the muscles and blood distribution requirements, the natural cardiac response to physical exertion is to increase the heart’s contractility and stroke volume to supply this demand. The two variables that directly play into cardiac output (CO) are stroke volume (SV) and heart rate (HR) such that CO = SV x HR. Therefore, if either one or both of these is amplified or diminished, CO is proportionally affected.

Heart rate max generally decreases with age and diminishing fitness levels and is also influenced by gender (Esco et al., 2015). The most accurate way to determine this value is by maximum exercise testing. Because this is not always practical or feasible for the general population, a heavy reliance on age-predictive formulas has ensued.

Daniels (2014) discusses the correlation between heart rate, velocity at VO2 max (vVO2 max) and blood lactate relating to training adaptation over time. The notion is that with advancement in training, the measured heart rate and blood lactate values associated with an improved VO2 max and vVO2 max were once the values representing lower levels of fitness and speed at a given intensity (Daniels, 2014). Essentially this means that, if a runner can perform at a faster speed with the same heart rate and blood lactate production levels as he or she has done at slower speeds in the past, they have adapted to a given training stimulus and become more efficient as a result.

In this respect, heart rate can be utilized to measure and record training adaptations over time. Relatively speaking, a given starting heart rate per intensity can be compared to the measured heart rate at the same intensity over time.

Typically exercise intensity is prescribed as a percent of the heart rate maximum, which is initially predicted with the infamous age-adjusted calculators, or sometimes through a graded exercise test.

The question remains, if the starting maximum heart rate is predicted incorrectly, does this affect the derived percentage intensities? Or is it all relative regardless of how inaccurate the initial starting number? Or, if the max heart rate is off by 10%, then the subsequent percent heart rates also will be 10% off. This is equivalent to all of them being 100% accurate, right? Let’s test this theory:

According to Daniels (2014), the associated heart rate intensities for a given running pace are distributed as follows:

- Easy/Long Run Pace: 65-79% of Max HR
- Marathon Pace: 80-85% of Max HR
- Threshold Pace: 82-88% of Max HR
- Interval Pace: 90-100% of Max HR
- Repetition Pace: 97+% of Max HR

So if we have John Doe, age 45, with a Predicted Max HR of (220-45 = 175), his respective heart rate measured in beats per minute (bpm) would be as follows:

- Easy/Long Run Pace: 65-79% of Max HR – 114 to 138 bpm
- Marathon Pace: 80-85% of Max HR – 140 to 149 bpm
- Threshold Pace: 82-88% of Max HR – 144 to 154 bpm
- Interval Pace: 90-100% of Max HR – 158 to 175 bpm
- Repetition Pace: 97+% of Max HR – 170+ bpm

Now if John Doe’s actual heart rate were measured at 186 bpm by a graded exercise test, representing a 6.3% difference in maximum heart rate, the values would be as follows:

- Easy/Long Run Pace: 65-79% of Max HR – 120 to 147 bpm
- Marathon Pace: 80-85% of Max HR – 149 to 158 bpm
- Threshold Pace: 82-88% of Max HR – 153 to 164 bpm
- Interval Pace: 90-100% of Max HR – 167 to 186 bpm
- Repetition Pace: 97+% of Max HR – 180+ bpm

As we can see from comparing the actual versus the predicted numbers, the actual appropriate intensities for John are staggered by nearly an entire pace level up, which represents a 6 bpm to 10 bpm difference from the predicted values. Since there is not an even distribution across all intensities, it isn’t safe to assume that all adaptations to training are relative to the initial measurements. Clearly the values are not directly proportional to one another.

Coaches take a large risk prescribing exercise based on predicted percentage of heart rate values. Share on XCoaches take a large risk when prescribing exercise based on predicted values. There is some overlap at the lower intensities of training, so having John keep his heart rate at an average of 132 bpm for an ‘easy run’ would satisfy both the predicted and actual ranges. However, if John performs his intervals at 160 bpm, in reality, only satisfies the threshold category of training. This which means John would achieve a drastically different outcome from that training session.

Daniels (2014) does note that these generic formulas may be useful for estimating heart rate for a large group of people. On an individual basis, however, there are more accurate ways to prescribe intensity that involve actual performance-based values and account for an athlete’s specific physiology and training background.

Nikolaidis (2014) compared the use of three separate heart rate max equations against a measured maximum in an age group-distributed sample of sport athletes under 18 years-old. Two of these equations are widely used, and one has recently been developed, respectively:

- Fox-HRmax = 220-age
- Tanaka-HRmax = 208 – (0.7 x age)
- Nikolaidis-HRmax = 223 – (1.44 x age) (Nikolaidis, 2014)

To physically measure heart rate max, all of the athletes participated in a graded exercise field assessment involving the 20m shuttle run endurance test (Nikolaidis, 2014). A total 147 athletes across a wide variety of sports (soccer, futsal, basketball, and water polo) were assessed for both a predictive and actual measurement. The values were then compared for data analysis.

This study found that none of the predictive heart rate equations provide accurate values of heart rate max in the sample of young athletes. The Tanaka-HRmax equation underestimated the actual max, and Fox-HRmax and Nikolaidis-HRmax overestimated the actual max across the whole sample.

Equations that overestimate this value can lead to athletes working at a higher intensity than desired and those that underestimate can lead to a lack of stimulus for adaptation. The equations could not be validated in this study. If, however, they are the limiting factor in developing an exercise program, the Tanaka-HRmax equation can be used when coaches want to avoid overtraining. The Fox-HRmax and Nikolaidis-HRmax equations can ensure that adequate intensity stimulus is provided (Nikolaidis, 2014).

In a similar study involving female collegiate athletes from 19 to 25 years-old, three general equations, and two female-specific equations were compared for accuracy against a treadmill-based graded exercise test using the Bruce protocol (3-minute stages with consecutive increases in speed and grade) (Esco et al., 2015). With this protocol, expired gas fractions are monitored by a metabolic cart to assess the respiratory exchange ratio of oxygen to carbon dioxide.

This gives insight as to how the individual is handling the increasing work rate and shows when they pass through the aerobic-anaerobic threshold and the VO2 max is approaching (as indicated by a plateau in oxygen consumption). The highest recorded value of VO2 is then matched with the corresponding heart to determine the maximum heart rate value of an individual athlete (Esco et al., 2015).

The three general predictive formulas used were:

- Fox-HRmax = 220-age
- Tanaka-HRmax = 208 – (0.7 x age)
- Astrand-HRmax = 216.6 – (0.84 x age)

The two female-specific formulas were:

- Fairburn-HRmax = 201 – (0.63 x age)
- Gulati-HRmax = 206 – (0.88 x age) (Esco et al., 2015)

All of the equations resulted in large limits of agreement, ranging 10 bpm above and below the mean error, which is not a promising indication that any of these formulas provide a veritable function in exercise assessment (Esco et al., 2015).

The two female-specific formulas were “more accurate” than the three general equations. However, they still tended to over-predict when compared to the actual measured value. When graded exercise testing is not feasible due to a lack of availability of resources, other exercise-based protocols can be implemented, such as the 20m shuttle test mentioned earlier, 2 x 200m sprint trials, and similar assessments (Esco et al., 2015).

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## References

- Daniels, J. T. (2014).
*Daniels’ Running Formula (3rd ed.),*. Champaign, IL: Human Kinetics. - Esco, M. R., Chamberlain, N., Flatt, A. A., Snarr, R. L., Bishop, P. A., & Williford, H. N. (2015). Cross-Validation of Age-Predicted Maximal Heart Rate Equations Among Female Collegiate Athletes.
*Journal of Strength & and Conditioning Research,*29(11), 3053-3059. doi: 10.1519/JSC.0000000000000978. - Nikolaidis, P. T. (2014). Age-predicted vs. measured maximal heart rate in young team sport athletes.
*Nigerian Medical Journal,*55(4), 314-320. doi: 10.4103/0300-1652.137192 - Robergs, R. A., & Landwehr, R. (2002). The surprising history of the “Hrmax=220-age” equation.
*Journal of Exercise Physiology (online),*5(2), 1-10.

Good to see this article. I often hear “that’s too high” or” your monitor is off” when traing at higher rates than 220-age formula. Just started using a hr monitor again after 10 years not using and realized I was not traing hard enough. Much better now.