What maximum heart rate is, and what it is not
Maximum heart rate is the highest rate your heart can beat during all-out effort. It is set mainly by the intrinsic rate of the sinoatrial node and by how far the autonomic nervous system can drive it, and it falls with age at somewhere between 0.6 and 1 beat per year depending on which population you look at. It is not a measure of fitness. A sedentary 30-year-old and an Olympic 30-year-old can share the same maximum; what separates them is the amount of blood moved per beat and the amount of oxygen extracted from it.
Because maximum heart rate is the top anchor for every heart rate zone system, an error in it propagates into every training prescription you build on top. That is the entire reason this page exists. If your maximum is really 192 and you train from an estimate of 180, your “threshold” sessions are being run several beats too easy and your easy sessions may be too easy to be worth the time.
Two things it definitely is not: a safety ceiling, and a fixed number. Exceeding an age-predicted maximum during a hard finish is normal for anyone whose true maximum sits above the average for their age — roughly half the population. And your own maximum changes only slowly with age; it is not something you raise by training.
The equations, and why there are so many of them
Each equation is a regression line fitted through a different set of people. That is the whole story of why they disagree.
Fox (220 − age) is the oldest and by far the most quoted. It appeared in a 1971 review by Fox, Naughton and Haskell as a convenient summary of scattered data rather than as an original regression, and it was never presented with the error bars a fitted line would normally carry. Its slope of one beat per year is steeper than most later work supports, which is why it reads high in young adults and low in older ones.
Tanaka (208 − 0.7 × age) came from a 2001 meta-analysis of 351 published studies plus a prospective validation in 514 healthy subjects, and it reported the same line for men and women and for trained and untrained groups. It is the equation most exercise physiology textbooks now default to, and it is the default here.
Gellish (207 − 0.7 × age) came from longitudinal data on adults tracked through a fitness programme — the same slope as Tanaka with an intercept one beat lower, so it sits a single beat below Tanaka at every age.
HUNT (211 − 0.64 × age) came from a large Norwegian population study of healthy adults who were actually tested to maximum. Its shallower slope makes it the highest of the four for anyone over about 25.
Gulati (206 − 0.88 × age) was derived in a women-only cohort and is the one equation on this page that is explicitly sex-specific. Its steeper slope means it falls further below the general equations as age rises.
Because these are all straight lines, they cross at specific ages you can solve for. Fox and Tanaka cross where 220 − a = 208 − 0.7a, that is 0.3a = 12, a = 40 exactly. Fox and HUNT cross where 0.36a = 9, a = 25 exactly. Fox and Gellish cross at 0.3a = 13, a = 43.3. Below those ages Fox reads higher than the equation it is being compared with; above them it reads lower.
Worked example: a 50-year-old woman
Work all five equations at age 50 by hand.
- Fox. 220 − 50 = 170 bpm.
- Tanaka. 0.7 × 50 = 35, so 208 − 35 = 173 bpm.
- Gellish. 207 − 35 = 172 bpm, one beat below Tanaka as always.
- HUNT. 0.64 × 50 = 32, so 211 − 32 = 179 bpm.
- Gulati. 0.88 × 50 = 44, so 206 − 44 = 162 bpm.
- Spread of the four general equations. 179 − 170 = 9 bpm.
- Interval around the automatic choice. For a woman the automatic choice is Gulati, so 162 ± 1.96 × 10 = 162 ± 19.6, giving 142.4 to 181.6 bpm.
Notice the size of that interval relative to the argument about which equation to use. The five equations span 17 bpm at this age; the prediction interval around any one of them spans nearly 40 bpm. Choosing between Tanaka and HUNT is a smaller decision than the uncertainty either one carries, which is the single most useful thing to take away from this page.
Check the Fox-versus-Gulati gap against the identity: (220 − a) − (206 − 0.88a) = 14 − 0.12a. At a = 50 that is 14 − 6 = 8 bpm, and 170 − 162 = 8. It matches, and since 14 − 0.12a stays positive until a = 116.7, Fox reads higher than Gulati at every age this calculator accepts.
How to use the number you get
Treat the headline figure as a starting point for building heart rate zones, and replace it the moment you have real data. The most valuable piece of evidence you already own is your own training history: scroll back through your recorded sessions and find the highest heart rate you have actually reached at the end of a hard effort, ignoring obvious sensor artefacts. If that number exceeds the estimate, your maximum is at least that high.
Sensor artefacts are worth recognising, because they are common enough to mislead. A chest strap that has dried out will occasionally double-count and report a value close to twice your real rate. An optical wrist sensor losing contact often locks onto cadence instead, reporting something close to your step rate. A genuine maximum looks like a plateau at the end of a rising effort, not a spike that appears and vanishes within a few seconds.
The prediction interval is the part most calculators leave out, and it is the part that changes decisions. With a standard deviation of 10 bpm, the 95% interval is roughly ±20 bpm wide either side of the line, which for a 40-year-old spans about 160 to 200 bpm. Zones built anywhere in that range are internally consistent but may be systematically several beats off for you. This is why measuring, or at least mining your own history, beats arguing about equations.
If you want an intensity anchor that does not depend on maximum heart rate at all, measure something you can observe directly. A 12-minute Cooper test or a 20 m shuttle run gives an aerobic capacity estimate from distance covered, and lactate-threshold pace or functional threshold power give training anchors that sit much closer to the intensities that actually matter.
Predicted HRmax by age under each equation
| Age | Fox 220 − a | Tanaka | Gellish | HUNT | Gulati (women) | Spread of the four general |
|---|---|---|---|---|---|---|
| 20 | 200 | 194.0 | 193.0 | 198.2 | 188.4 | 7.0 |
| 30 | 190 | 187.0 | 186.0 | 191.8 | 179.6 | 5.8 |
| 40 | 180 | 180.0 | 179.0 | 185.4 | 170.8 | 6.4 |
| 50 | 170 | 173.0 | 172.0 | 179.0 | 162.0 | 9.0 |
| 60 | 160 | 166.0 | 165.0 | 172.6 | 153.2 | 12.6 |
| 70 | 150 | 159.0 | 158.0 | 166.2 | 144.4 | 16.2 |
| 80 | 140 | 152.0 | 151.0 | 159.8 | 135.6 | 19.8 |
The spread column covers Fox, Tanaka, Gellish and HUNT only. It is smallest in the mid-twenties to early forties, where the lines cross each other, and widens steadily after that because Fox falls fastest and HUNT falls slowest.
Assumptions and limits worth knowing
- These equations describe healthy people not taking rate-limiting medication. Beta blockers, some calcium channel blockers and rate-controlling drugs for atrial fibrillation reduce maximum heart rate substantially, and no age equation accounts for that. If you take one, heart rate is a poor intensity anchor and perceived exertion or power is better.
- They are fitted lines, not laws. Every one carries residual scatter around it of roughly 10 to 12 bpm in adults, which is wider than the disagreement between the equations themselves at most ages.
- Sport matters. Most athletes record a maximum on the bike a few beats below their running maximum, because cycling recruits less muscle mass. Rowing and swimming maximums differ again.
- Age is a proxy for something else. The decline with age is driven by changes in sinoatrial node function and autonomic responsiveness, not by the calendar. Two people of the same age with different cardiovascular health can differ substantially.
- Children are outside scope. Maximum heart rate is high and nearly flat through childhood, so subtracting age from 220 is meaningless for a 12-year-old.
- A maximal test carries risk for some people. If you have known or suspected cardiovascular disease, are symptomatic on exertion, or have been advised to limit intensity, a supervised clinical test is the appropriate route and a self-administered all-out effort is not.
This is an estimate, not medical advice
The figures on this page are population averages for healthy adults. They are not a diagnostic threshold, not a safe upper limit, and not a substitute for clinical exercise testing. If you have chest pain, unexplained breathlessness, palpitations, a history of cardiac disease, or you have been told to limit exercise intensity, work from a clinician's prescription rather than an age equation. Similarly, if a maximal test is what you need, arrange one with appropriate supervision.
How to measure your maximum instead of estimating it
The reference method is a graded exercise test to volitional exhaustion, run on a treadmill or cycle ergometer with the workload stepped up every minute or two until you cannot continue. The peak heart rate in the final stage is your maximum for that mode of exercise. Done in a clinical or laboratory setting with ECG monitoring, it is also the safest way to reach a true maximum.
A field alternative that gets close for healthy, well-trained people is a hard hill protocol: warm up thoroughly for fifteen minutes, then run or ride a gradient of about 5% at a hard but controlled effort for three minutes, recover for two, and repeat, going all-out on the final repetition and holding it until you have to stop. The highest sustained reading across the set is a good approximation. Wear a chest strap rather than a wrist optical sensor — wrist sensors are least reliable at exactly the intensities you are trying to measure.
Whatever number you end up with, the useful next step is the same: feed it into the heart rate zones calculator to rebuild your bands, or into the Karvonen target heart rate calculator if you have been given a single prescribed intensity to hit. Both use the maximum as their top anchor, so both improve immediately when the estimate is replaced by a measurement.