Three formulas for your maximum heart rate, and why all of them are wrong

Your maximum heart rate sets the boundaries of every training zone. Get it wrong and every zone beneath it moves. The effort you think is zone 3 may really be zone 2, and you haven't been pushing yourself as hard as you thought.

Three age-based estimates are widely used, but treat any of them as a starting point only. For most people, each one is wrong. Enter your age below to see the estimates from the three most commonly used methods.

The one equation whose paper publishes a standard error puts it at 10.8 beats per minute, and that figure describes the spread of real people around the line rather than any uncertainty in the line itself. Roughly two thirds of people sit within 10.8 beats of the answer their formula gives them. About one in twenty is more than twenty-one beats out, high or low. Treat the number as a starting estimate and replace it with a measurement.

Fox, 1971

Where 220 − age actually came from

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 It came from a figure of roughly 35 data points compiled from about eleven sources, some of them unpublished, with no regression analysis performed on them at all.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, 2001

The one built from the most studies

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, nor was it shifted by wide variation in habitual physical activity. Being fit does not raise your ceiling. And they found that 220 − age underestimates maximum heart rate in older adults, so the traditional formula becomes less accurate as you age.2

Nes, 2013

The one that measured the most people

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 That is a maximum falling by 0.64 beats a year, a little less than Tanaka's 0.7 and well short of the full beat a year in 220 − age. By 70, Nes puts the typical maximum at 166, against 159 for Tanaka and 150 for 220 − age.

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.

That standard error is the number to carry away from this page. It is more than half a training zone in either direction, from the equation that measured the most people and was most honest about the result.

Because Nes published that spread, it can also be run the other way. If you have measured your maximum, put it in below with your age to see where it sits among people your age.

A high or low percentile says nothing about fitness. Nes found no link between maximum heart rate and VO₂max or physical activity, so it only tells you how far the formulas were off for you.3

So which one, and why ZonePoints uses the most basic one

If you want a single answer on the science: Nes, for men and women alike. It is the newest, it measured maximums directly rather than pooling other studies, and it tells you how far off it can be.

ZonePoints uses 220 − age anyway. The choice between the three matters less than it looks: across them, a 40-year-old gets 180, 180 and 185. That spread of five beats is far 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 — and the large one is that none of these is your number.

Given that, ZonePoints chose 220 − age for reasons other than accuracy. It is the most widely used formula, so you may already be using it in other apps, and your zones will line up with theirs. It moves exactly one beat per year, so a single age control sets a whole-number maximum with no fractional beats to explain. And it is the formula you are most likely to be able to check in your head.

None of that makes it right. It makes it a placeholder for a number you are meant to replace.

Measuring it instead

The estimate is a placeholder for a measurement, and the measurement is not difficult, only uncomfortable. The problem is that finding your 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 — find your nearest event and turn up. Running with other people motivates you to push harder than you might alone. Warm up properly, run the 5 km, and finish with a flat-out sprint or a hard drive up the last hill. If you truly could not have pushed any harder, the highest reading your monitor records at the finish is your maximum heart rate.

However you test, you need three things. 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 a finish that is genuinely all-out, not one that merely feels hard.

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 still have to push, but not in a dedicated test

The effort is the test. What you can skip is the rigid protocol around it — the booked slot, the lab, the deliberate all-out session with nothing else in it.

ZonePoints keeps the highest heart rate it has ever recorded for you. It offers to adopt this when it exceeds your configured maximum, so the hard sessions you were going to do anyway converge on your real number. You still have to reach it: you only record your maximum when you genuinely empty the tank, and no amount of measuring finds a number you never produced. 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