Heart-rate zones on cardio equipment and in apps usually rest on an estimate of maximum heart rate, and the most familiar estimate is 220 minus age. Research has tested this and several alternative equations against measured maximum heart rate. This article summarises four studies, the equations they support and the size of the error they report. It concerns general exercise physiology in healthy people and is not medical advice; anyone with a heart or health condition should follow their clinician’s guidance on exercise intensity.
The equations in circulation
The equations named in the studies below include:
- 220 minus age, the most commonly used;
- 208 minus 0.7 times age, from a 2001 meta-analysis by Tanaka and colleagues;
- 211 minus 0.64 times age, from the Norwegian HUNT Fitness Study of 2013;
- 209.3 minus 0.72 times age, from a US registry analysis of 4,796 people.
Worked through for a 40-year-old, 220 minus age gives 180 beats per minute, the Tanaka equation gives 180, the HUNT equation gives about 185 and the registry equation about 181. For a 55-year-old the same equations give 165, about 170, about 176 and about 170. The equations differ most at older ages, which is where the studies report the largest disagreement.
The 2001 meta-analysis
Tanaka, Monahan and Seals gathered group mean values from 351 studies covering 492 groups and 18,712 subjects. Maximum heart rate was strongly related to age (r = -0.90), and the regression equation was 208 minus 0.7 times age. A laboratory study of 514 healthy subjects gave a virtually identical equation, and the line did not differ between men and women or with habitual physical activity. The authors concluded that the then-current 220 minus age formula underestimates maximum heart rate in older adults.
The HUNT Fitness Study
Nes and colleagues measured maximum heart rate in 3,320 healthy men and women where a maximal effort was verified. Age alone explained the result with the formula 211 minus 0.64 times age, and there was no evidence of interaction with gender, physical activity, fitness level or body mass index. They found that the earlier equations underestimated measured maximum heart rate in subjects older than 30. Importantly, they report a standard error of the estimate of 10.8 beats per minute and say it must be taken into account, meaning even the better equation leaves a wide range around any individual.
The registry analysis
A study using the FRIEND Registry analysed 4,796 apparently healthy people who reached maximal effort on a treadmill test. The fitted equation was 209.3 minus 0.72 times age, with a correlation of 0.61 and a standard error of estimate of 11.35 beats per minute. The mean difference between measured and predicted maximum heart rate was not significantly different from zero, but the limits of agreement were about plus or minus 25 beats per minute and there was a significant proportional bias. The authors advise against using age-predicted maximum heart rate as a measure of whether a person has made a maximal effort.
Comparing nine equations in a general sample
Shookster and colleagues (2020) compared nine equations, including those named by Fox, Tanaka, Nes and Gellish, against 99 graded treadmill exercise tests that ended at volitional fatigue with a respiratory exchange ratio above 1.10. Significant differences from measured values were found for the Gulati, Astrand, Nes and Fairbarn (male) equations, and Bland-Altman plots showed wide limits of agreement for all nine, meaning poor agreement between predicted and measured maximum heart rate. Proportional bias meant equations tended to underestimate at lower measured values and overestimate at higher ones, with the exception of the Fox equation (220 minus age), which the authors suggest may be the best option for a general population because it is less likely to under- or overestimate. They advise individuals to use data from a graded exercise test to determine maximum heart rate when possible.
What the disagreement means in practice
The studies point in different directions on which equation is best, which is itself informative: none is reliable for an individual. A rough illustration: a person predicted at 180 beats per minute could, with an error of about 25 beats either way, have a true maximum anywhere from about 155 to 205. Seventy per cent of those two figures is around 109 and 144 beats per minute, so a zone set from the formula could feel very different in practice from what the label suggests. Any zone programme, whether on a machine, a watch or an app, that begins from an age-based estimate inherits this uncertainty.
Practical points when using zones
- Treat zones as approximate ranges, not targets to the beat.
- Use perceived effort alongside heart rate. A related guide on this site covers rating of perceived exertion for strength work, and the same principle of checking a number against how hard the effort feels applies to cardio.
- Where accuracy matters, a supervised maximal test is the route the studies point to, rather than another formula.
- Different tools may use different equations, so a change of device can change the zones without any change in fitness.
Frequently asked questions
Is 220 minus age wrong?
It is approximate. The 2001 meta-analysis and the HUNT study found it underestimates in older adults, while a later sample of 99 tests found it less prone to bias than several alternatives. Every study reports wide individual error.
Which equation is most accurate?
The studies do not agree on one, and the standard errors reported (10.8 and 11.35 beats per minute) show a wide range around any prediction.
The bottom line
Age-based equations give a reasonable population average but a poor individual answer, with errors of roughly 10 to 11 beats per minute for one standard deviation and about 25 for the limits of agreement in the largest registry sample. Heart-rate zones set from them should be treated as a rough guide, checked against perceived effort and, where precision matters, against a supervised maximal test.
Sources
- Tanaka H, Monahan KD, Seals DR, “Age-predicted maximal heart rate revisited”, Journal of the American College of Cardiology, 2001
- Nes BM et al., “Age-predicted maximal heart rate in healthy subjects: The HUNT fitness study”, Scandinavian Journal of Medicine & Science in Sports, 2013
- “Revisiting age-predicted maximal heart rate: Can it be used as a valid measure of effort?” (FRIEND Registry), 2016
- Shookster D et al., “Accuracy of Commonly Used Age-Predicted Maximal Heart Rate Equations”, International Journal of Exercise Science, 2020