Every line below claims to give the same thing. 220 − age falls fastest, so it reads high when you are young and low when you are old — it crosses Tanaka at exactly age 40, which is the one age where the famous formula and the best-evidenced one agree.
This is the one that quietly ruins training plans. A percentage of your max and the same
percentage of your reserve are different heart rates, and the gap is
resting × (1 − percentage) — so it is largest in the easy zones, exactly
where getting it wrong matters most.
| Zone | % of max | % of reserve | Difference |
|---|
Everything here rests on a single number you almost certainly do not know: your true maximum heart rate. It is largely genetic, barely moves with fitness, and can only be measured by going all out. Every formula on this page is a population average, and a population average has a spread.
220 − age (Fox, 1971) was never properly derived — it came from a rough
line through a few dozen mixed data points. 208 − 0.7 × age (Tanaka,
2001) comes from a meta-analysis of 351 studies and 18,712 people, and is the usual
recommendation. Because Fox falls at 1.0 beats per year and Tanaka at 0.7, they cross at
age 40 and diverge in both directions.
% of max is simply HRmax × p. % of reserve is
HRrest + (HRmax − HRrest) × p — Karvonen’s method, which
anchors the bottom of the range at your resting heart rate instead of at zero. Subtract one from
the other and the difference is exactly HRrest × (1 − p).
A 35-year-old with a resting heart rate of 60 gets a Tanaka maximum of 183.5 bpm, shown as 184. The bottom of zone 2 is 110 bpm as a percentage of max, but 134 bpm as a percentage of reserve — a 24-beat difference from the same zone label. An easy run at one is a tempo run at the other.
Tanaka, if you have to pick one — it rests on far more data than the others. But the honest answer is that a formula is a starting point: the spread between the four here is around 11 bpm at 25 and over 20 bpm by 70, and your own value could sit outside all of them. A hard race or a supervised test beats every formula on this page.
Because it is easy to remember and it was in print first. Its own co-author later said it was never meant as a precise formula. It happens to be close to the better-evidenced curve around age 40, which is roughly the middle of the population using it — so it looks reasonable on average while being wrong at both ends.
Almost always because one is using a percentage of maximum and the other a percentage of
reserve. The difference is resting × (1 − percentage), which for a
resting rate of 60 is 24 beats at the bottom of zone 2. Neither is wrong; they are
different definitions, and the fix is agreeing which one you mean.
Broadly, within one person over time — endurance training does lower it. Between two people it says much less, because the range in healthy adults is wide and largely inherited. It is most useful as your own baseline: a resting rate several beats above your normal often means you are under-recovered, ill, or short of sleep.
Then none of this applies. Rate-controlling medication lowers both resting and maximum heart rate, often substantially, so every formula here will overestimate your ceiling and every zone will be set too high. Train to perceived effort or ask the clinician who prescribed it.
A healthy adult with no rate-controlling medication and no cardiac condition. Formula values are population averages with real scatter, not predictions for an individual. Zone boundaries are the common five-zone convention and are not physiological thresholds — genuine lactate or ventilatory thresholds are found by testing, not arithmetic, and sit wherever they sit regardless of these percentages.