Max heart rate calculator: three formulas, side by side

Estimated maximum heart rate at age 40worked example

180 bpm

Fox 1971 (220 - age): 180 bpmnever validated as a regression
Tanaka 2001 (208 - 0.7 x age): 180 bpm351 studies, 18,712 subjects
Gulati 2010 (206 - 0.88 x age): 171 bpmderived in 5,437 women
How far apart they are: 9 bpmthe gap is the honest answer

This page shows Tanaka (208 - 0.7 x age) as its headline figure because Tanaka 2001 pooled 351 studies and concluded that 220 - age underestimates maximum heart rate in older adults; its authors recommend 208 - 0.7 x age for healthy adults. The other two are printed above rather than hidden, because they disagree by 9 bpm at your age and no calculator can tell you which one your own heart follows.

Realistic range

170 bpm to 190 bpm

This is the spread of measured maximum heart rates around an age-based prediction in study populations. It is not a confidence interval for one person: your own maximum can sit outside the band, and only a supervised maximal test measures it.

Your ageAll three equations take age and nothing else.

Sex

Only used to pick between the Gulati and Tanaka equations.

Resting heart rate (optional)Adds the Karvonen target, which is not the same as a percent of maximum.

Maximum heart rate by age, from all three published equations
Age	Fox (220 - age)	Tanaka	Gulati (women)	Widest gap
20	200	194	188	12 bpm
30	190	187	180	10 bpm
40	180	180	171	9 bpm
50	170	173	162	11 bpm
60	160	166	153	13 bpm
70	150	159	144	15 bpm
80	140	152	136	16 bpm

Notice the crossover: at 20 the Fox figure is the highest of the three, and by 60 it is the lowest. That is the effect Tanaka 2001 was written to report, and it is why the same reader can find two charts that disagree by nine beats and both look authoritative.

Where 220 minus age actually came from

Robergs and Landwehr went looking for the derivation in 2002 and found there is not one. The equation traces to Fox, Naughton and Haskell in 1971, who drew a line by observation through raw and mean data compiled from roughly eleven sources, and who did not claim it was a regression. It is printed on cardio equipment worldwide anyway. Tanaka 2001 later pooled 351 studies and found that 220 minus age underestimates maximum heart rate in older adults; Gulati 2010 found the male-derived equations overestimate it in women. This calculator computes all three because readers arrive holding the first one.

A maximum heart rate calculator estimates the fastest your heart beats at all-out effort. This one runs three published equations at once: Fox 220 minus age, Tanaka 208 minus 0.7 times age, and Gulati 206 minus 0.88 times age for women. It shows the gap between them and states that 220 minus age was never a validated regression.

Maximum heart rate (Fox, 220 - age)convention — HRmax (bpm) = 220 - age. Verified 2026-07-30 against Fox, Naughton & Haskell 1971, as documented by Robergs & Landwehr, JEPonline 2002 (There is no published regression behind this equation. Robergs and Landwehr traced it to a line drawn by observation through raw and mean data compiled from roughly eleven sources in 1971, and report a standard error of estimate of 7-11 bpm across two decades of HRmax prediction research. It also underestimates maximum heart rate in older adults, which is the finding Tanaka 2001 was written to report.)
Maximum heart rate (Tanaka, 208 - 0.7 x age) — HRmax (bpm) = 208 - 0.7 x age. Verified 2026-07-30 against Tanaka, Monahan & Seals, J Am Coll Cardiol 2001 (Derived by meta-analysis of 351 studies (492 groups, 18,712 subjects, r = -0.90 with age) and cross-validated in 514 more; sex and physical activity level did not shift the regression line. It remains a population regression: individual maximum heart rates at any given age scatter around it, and prediction error for age-based equations is reported at 7-11 bpm. This site therefore renders every predicted HRmax inside a +/-10 bpm band.)
Maximum heart rate in women (Gulati, 206 - 0.88 x age) — HRmax (bpm) = 206 - 0.88 x age. Verified 2026-07-30 against Gulati et al., Circulation 2010 (St James Women Take Heart Project) (Derived in 5,437 asymptomatic women (mean age 52 +/- 11) followed for a mean of 15.9 years, with a reported standard error of about 9 bpm. The paper's central finding for this purpose is that the male-derived equations overestimate peak heart rate for women of the same age.)
Prediction error of age-based HRmax equations — standard error of estimate = 7 to 11 bpm; this site renders +/-10 bpm. Verified 2026-07-30 against Robergs & Landwehr, Journal of Exercise Physiology Online 2002 (This is the spread of measured maximum heart rates around an age-based prediction in study populations. It is not a confidence interval for one person: your own maximum can sit outside the band, and only a supervised maximal test measures it.)
Target heart rate (Karvonen, heart-rate reserve) — THR (bpm) = (HRmax - HRrest) x intensity + HRrest. Verified 2026-07-30 against Karvonen, Kentala & Mustala 1957 (Inherits every bit of uncertainty in the HRmax estimate it is built on, plus the accuracy of the resting rate you measured. A resting heart rate taken after coffee or on waking from a bad night can move the answer by several beats.)

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Frequently asked questions

What is the formula for maximum heart rate?

There are three in common use. Fox 1971 gives 220 minus your age. Tanaka 2001 gives 208 minus 0.7 times your age. Gulati 2010, derived in women, gives 206 minus 0.88 times your age. At age 50 those are 170, 173 and 162 bpm.

Is 220 minus age accurate?

It was never validated as a regression. Robergs and Landwehr traced it to a line drawn by observation through data compiled from about eleven sources in 1971, with no published derivation. Tanaka 2001 found it underestimates maximum heart rate in older adults, which is why this page shows the alternatives beside it.

Which formula should women use?

Gulati 2010 was derived in 5,437 asymptomatic women and its authors reported that the male-derived equations overestimate peak heart rate for women of the same age. This tool uses it when you state female, and still shows the other two so you can see the difference.

How accurate is any age-based estimate?

Prediction error is reported at roughly 7 to 11 beats per minute across two decades of research, and Gulati 2010 reports about 9 bpm for its own equation. This tool therefore shows every prediction inside a 10 bpm band. Only a supervised maximal test measures your actual maximum.

What is the Karvonen formula?

Target heart rate equals your heart-rate reserve, which is maximum minus resting, times the intensity you want, plus your resting rate back on. At a maximum of 190 and a resting rate of 60, 70% Karvonen is 151 bpm, while 70% of maximum is 133 bpm. They are not the same number.

Does a higher maximum heart rate mean better fitness?

No. Maximum heart rate falls with age and varies widely between people at the same age and fitness level, and training does not raise it. The numbers that do move with training are your resting rate and how fast your heart recovers after effort.

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The next number

No body metric means much on its own. Here is what this one feeds into.

Heart rate zone calculatorYour maximum is only the ceiling. The zones built on it are what you actually train in, and they inherit its 10 bpm of uncertainty.Calories burned calculatorEffort measured in heart rate and effort measured in METs are two views of the same session.

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Every formula on this page is listed with its source on the methodology page, and changes to any reference value are logged in the data changelog. Canonical URL: https://myhealthmywellness.com/max-heart-rate-calculator