Heart rate zones: max HR, Karvonen and the fat-burning zone

Where "220 − age" comes from

The most repeated formula in exercise physiology barely has an author. Robergs and Landwehr, in 2002, traced its origin and found that "220 − age" was never published as the result of its own regression: it surfaces around 1971, credited to Fox, Naughton and Haskell, as a line drawn by hand over points compiled from roughly eleven earlier studies, each with different methods, populations and exhaustion criteria. There was no fitted equation, no reported standard error, no validation. The rule caught on because it is easy to do in your head, not because it is accurate.

1. 1957Karvonen defines the reserve

   Karvonen, Kentala and Mustala describe prescription by heart rate reserve in a Finnish longitudinal study.

2. ~1971"220 − age" appears

   Fox, Naughton and Haskell publish the approximate line, with no fitted equation and no reported error.

3. 2001Tanaka revisits HRmax

   A meta-analysis of 351 studies (18,712 people) yields 208 − 0.7 × age.

4. 2010Gulati measures in women

   St. James Women Take Heart: 5,437 women yield 206 − 0.88 × age, specific to women.

The problem is not only philosophical. Maximum heart rate varies widely among people of the same age, and no age-only formula captures that. A recent review comparing the most-used equations found, for "220 − age" (the Fox form), a root-mean-square error of about 11.7 bpm and individual limits of agreement of roughly −23 to +23 bpm. In plain terms: two 40-year-olds with an "estimated HRmax" of 180 can have true maxima of 165 and 195 with nothing wrong at all.

The formulas that replaced it

In 2001, Tanaka, Monahan and Seals did the missing work: a meta-analysis of 351 studies totaling 18,712 people, plus their own laboratory study. The result was HRmax = 208 − 0.7 × age, published in the Journal of the American College of Cardiology. The gap versus 220 − age is systematic, not random: because the intercept is lower (208) and the slope gentler (0.7 instead of 1.0), 220 − age overestimates the maximum in the young and underestimates it in older people. The two lines only cross near age 40, where both give 180.

The third curve matters because 220 − age was built on mostly male data. Gulati and colleagues, in 2010, measured peak heart rate in 5,437 asymptomatic women in the St. James Women Take Heart study and published in Circulation the equation HRmax = 206 − 0.88 × age. The conclusion was blunt: the traditional male-based rule overestimates women’s maximum across nearly the whole age range. None of these formulas is exact for an individual, all carry large scatter, but they miss by less, and with less bias, than the mental-math rule.

What Karvonen actually computes

In 1957, long before 220 − age became folklore, the Finns Karvonen, Kentala and Mustala described a smarter way to prescribe intensity. Instead of taking a fraction of maximum heart rate, they work on the heart rate reserve (HRR): the gap between maximum and resting. The idea is that "0%" effort is not zero beats but your heart at rest, and "100%" is the maximum. A percentage of the reserve is added back onto the resting rate.

The distinction is not cosmetic. A percentage of the reserve (%HRR) maps closely to a percentage of oxygen uptake reserve (%VO₂R), whereas a percentage of maximum heart rate (%HRmax) sits systematically higher. That is why ACSM guidelines treat %HRR and %HRmax as different scales, with different numeric ranges for the same intensity. People with very low resting rates, endurance athletes, feel this difference most, because their reserve is larger.

HRmax

The highest rate the heart reaches at maximal effort. Measured in a test or estimated by formula.

HRrest

Rate at complete rest. It drops with fitness; best measured on waking.

HRR (reserve)

HRmax − HRrest. The heart’s working range, the basis of the Karvonen method.

The five zones (and why the limits are convention)

The five-zone scheme is a useful convention, not a biological constant. The limits below follow the ACSM intensity classification (Garber et al., 2011), which gives separate ranges for %HRmax and %HRR precisely because the two scales do not coincide. Notice how, for the same zone, the %HRR figure is always lower than the %HRmax one, not a mistake, but the consequence of the reserve starting at rest, not at zero.

Other popular tables use round 10% blocks (50–60, 60–70…) over HRmax. There is no single truth: a marathon coach, a cardiologist and a smartwatch app may draw the edges in slightly different places. What does not change is the logic, low zones build base and recover; high zones develop threshold and power. Drop your data in here and watch the ranges come out, with a Karvonen option:

Two ways to compute the same "zone 3"

Here is the part that trips people up most. Take a 40-year-old with a resting rate of 60 bpm. By the classic formula, HRmax = 220 − 40 = 180 bpm (Tanaka agrees: 208 − 0.7 × 40 = 180). The reserve is HRR = 180 − 60 = 120 bpm. Now naively apply the same "70%" on both scales and watch what happens.

1. Example 1, same 70%, two resultsBy %HRmax: 0.70 × 180 = 126 bpm. By Karvonen (%HRR): 60 + 0.70 × 120 = 60 + 84 = 144 bpm. The same "70%" gives 126 and 144 bpm, an 18-beat gap. They are not the same intensity.
2. Example 2, the ACSM zone 3, done rightThe ACSM moderate zone is 64–76% of HRmax OR 40–59% of HRR. By %HRmax: 0.64 × 180 = 115 to 0.76 × 180 = 137 bpm. By %HRR: 60 + 0.40 × 120 = 108 to 60 + 0.59 × 120 = 131 bpm. Now the two ranges nearly coincide (≈ 108–137 bpm), because the percentages were chosen to match.

The lesson: there is no universal "70%". Applying the same number to both scales gives different targets; to hit the same physiological intensity, the %HRR range must be lower than the %HRmax one. The exact conversion depends on your reserve, that is, your resting rate, which is why the Karvonen method individualizes better for people with very high or very low resting rates. To see how this energy expenditure ties into your daily total, read the BMI, TDEE and the limits of calculators guide and estimate yours in the TDEE calculator.

The "fat-burning zone" and the limits of the estimate

The "fat-burning zone" is real as a metabolic phenomenon and misleading as a strategy. At low intensity, a larger fraction of energy comes from fat; as effort rises, the body shifts toward carbohydrate, the so-called crossover point described by Brooks and Mercier in 1994. There is even an intensity at which absolute fat oxidation peaks, FATmax. The mistake is to confuse "higher fat fraction" with "more fat burned" or "more weight lost".