Your max heart rate, four ways, and how wrong each one is

Your maximum heart rate sets the boundaries of every training zone you have. Get it wrong by ten beats and every zone beneath it moves, which means the effort you think is zone 3 is really zone 2, all year.

So here is the number, four ways. Then the part the calculators leave out: where each formula came from, and how far off it can be for you personally.

220 − age was never research

The formula everyone knows is the one with the least behind it. In their commentary "The surprising history of the 'HRmax=220-age' equation," Robergs and Landwehr traced it back to a 1971 report by Fox, Naughton and Haskell and found, in their words, that "there is no published record of research for this equation."1 It was not derived from a study. It came from a figure of roughly 35 data points compiled from about eleven sources, some of them unpublished, with no regression analysis performed on them at all.

The detail that ought to have ended it: the authors of that 1971 figure said in their own legend that "no single line will adequately represent the data on the apparent decline of maximal heart rate with age."1 The line was drawn anyway, and it became the most repeated number in fitness.

Robergs and Landwehr put the standard deviation of the estimate at 7 to 11 beats per minute and concluded that the formula "has no scientific merit for use in exercise physiology and related fields."1 It survives because it is easy to do in your head.

Tanaka: the one most apps actually use

In "Age-predicted maximal heart rate revisited," Tanaka, Monahan and Seals pooled group mean values from 351 studies covering 492 groups and 18,712 subjects, derived 208 − 0.7 × age, then cross-validated it in a laboratory study of 514 healthy subjects, where the measured relationship came out at 209 − 0.7 × age.2

Two findings from that paper matter more than the equation. The regression line did not differ between men and women, and it was not shifted by wide variation in habitual physical activity, so being fit does not raise your ceiling. And they found that 220 − age underestimates maximum heart rate in older adults, which means the traditional formula does not merely add noise, it is biased with age.2

Nes: the one that publishes its error

The HUNT Fitness Study measured maximum heart rate directly in 3,320 healthy adults across a wide age range, and Nes, Janszky, Wisløff, Støylen and Karlsen reported 211 − 0.64 × age.3

This is the equation to use if you want to know how much to trust the answer, because its authors say so plainly: a standard error of estimate of 10.8 beats per minute, which they write "must be taken into account."3 They also found no interaction with sex, body mass index, physical activity status or VO₂max, and that previously suggested equations underestimated measured maximum heart rate in subjects over 30.

Ten point eight beats is the number to carry away from this page. It is roughly a third of a training zone in either direction, from the equation that measured the most people and was most honest about the result.

Gulati: for women, and derived from women

Every formula above was built mostly on men. In the St. James Women Take Heart Project, Gulati, Shaw, Thisted, Black, Bairey Merz and Arnsdorf gave symptom-limited maximal stress tests to 5,437 asymptomatic women and found mean peak heart rate fell with age as 206 − 0.88 × age.4 Their conclusion was that "the traditional male-based calculation overestimates the maximum HR for age in women."4

One honest caveat, because it changes what the number means. That study was about prognosis, not training: it was measuring chronotropic response and its link to mortality over sixteen years of follow-up, and the heart rates were peaks reached on a treadmill stress test that stops at symptoms. A peak on a clinical test is not necessarily the highest number you would ever reach in a race. It is the best female-derived estimate available, and it is not the same object as an all-out athletic maximum.

So which one

If you want a single answer: Tanaka if you are estimating, Nes if you want to know the error, Gulati if you are a woman and want an equation derived from women. Not 220 − age, which is the only one here that no study produced.

But the honest answer is that the choice between them matters less than it looks. Across the four, a 40-year-old gets 180, 180, 185 and 171. That spread of fourteen beats is smaller than the ±10.8 beat error inside any one of them. Picking the best formula is tuning the small term while the large one goes unexamined.

Measuring it instead

The estimate is a placeholder for a measurement, and the measurement is not difficult, only uncomfortable. The problem is that a true maximum requires a genuinely all-out effort, which is very hard to produce alone.

That is why a weekly 5 km parkrun works well, and it is free and worldwide. The people around you supply the effort you would not squeeze out of yourself. Warm up properly, run the 5 km, and finish with a flat-out sprint or a hard drive up the last hill. The highest reading your monitor records over the line is your real maximum, or within a beat or two of it.

Whatever protocol you use, the requirements are the same: a chest strap rather than a wrist sensor, because optical sensors are least reliable exactly when the effort is hardest; a proper warm-up; and an ending you have to be dragged through rather than one you choose.

Get medical clearance first. A maximal effort is a genuine cardiovascular stress and is not appropriate for everyone. If you have any cardiac history, any risk factors, or you are returning to exercise after a long gap, ask a doctor before doing this, and ask about a supervised test instead.

You may not need to test at all

ZonePoints keeps the highest heart rate it has ever recorded for you and offers to adopt it when it exceeds your configured maximum, so ordinary hard sessions converge on your real number without a dedicated test. Because it is a high-water mark it only moves up, so a strap glitch sticks: if a reading is recorded that you know you did not reach, reset it so a true one can take its place.

For what your maximum then does to your zones, and why it is not a fitness metric, see what is my max heart rate.

1. Robergs RA, Landwehr R. "The Surprising History of the 'HRmax=220-age' Equation." Journal of Exercise Physiology online. 2002;5(2):1–10. asep.org (PDF)
2. Tanaka H, Monahan KD, Seals DR. "Age-predicted maximal heart rate revisited." Journal of the American College of Cardiology. 2001;37(1):153–156. PubMed
3. Nes BM, Janszky I, Wisløff U, Støylen A, Karlsen T. "Age-predicted maximal heart rate in healthy subjects: The HUNT Fitness Study." Scandinavian Journal of Medicine & Science in Sports. 2013;23(6):697–704. PubMed
4. Gulati M, Shaw LJ, Thisted RA, Black HR, Bairey Merz CN, Arnsdorf MF. "Heart rate response to exercise stress testing in asymptomatic women: the St. James Women Take Heart Project." Circulation. 2010;122(2):130–137. PubMed