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 |
|---|
Largely genetic, barely moves with fitness, and can only be measured by going all out. Every formula here is a population average with a spread of about ±10 beats.
220 − age (Fox, 1971) was never properly derived. 208 − 0.7 × age (Tanaka, 2001) comes from 351 studies and 18,712 people. They cross at age 40.
HRmax × p: a share of the ceiling. What most watches use.
HRrest + (HRmax − HRrest) × p (Karvonen): anchors the bottom at your resting rate. What most coaches mean.
Maximum heart rate in bpm. Fox falls a full beat a year where Tanaka falls 0.7, so the two agree only at 40 (180) and the old formula runs too high for the young and too low for the old.
Rate-controlling medication lowers both resting and maximum heart rate, so every formula here overestimates the ceiling and sets every zone too high. Perceived effort is the honest substitute.
At a fixed pace in the heat, heart rate climbs as you dehydrate (cardiac drift). Late in a long session the same zone is a slower pace, which is normal, not lost fitness.
Nothing physiological happens at exactly 70% of anything. Real lactate and ventilatory thresholds sit where they sit and are found by testing; tidy ten-percent bands are a convention for talking about effort.
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.
They start from a heart rate you measured rather than a maximum you estimated. Run 30 minutes alone at the hardest pace you can hold evenly, and your average over the last 20 minutes is your lactate threshold heart rate. Joe Friel’s running zones are percentages of it: zone 2 is 85–89%, zone 4 is 95–99%, and zone 5 begins at threshold. Because the anchor is measured, the ten-beat uncertainty in every maximum formula drops out.
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.
Releases in which this page changed, newest last. Derived from the archived copy of every release, not from notes written afterwards — so it reflects what actually shipped. Site-wide passes are left out; they are in the full changelog.