Max heart rate and heart rate reserve: how to calculate them

By PounceFit Team · Updated on 2026-10-06

Technical content for health and fitness professionals. It reproduces formulas and protocols published in the scientific literature, with the sources at the end of the page. It is not a recommendation and does not replace the judgment of the professional who runs the assessment.

Max heart rate (HRmax) is calculated from age: the classic formula is 220 - age, and the Tanaka formula (208 - 0.7 × age) is more accurate in older people (Tanaka, Monahan and Seals, 2001). Heart rate reserve (HRR) is HRmax minus resting heart rate, and the Karvonen method uses that reserve to calculate training heart rate: resting HR plus a percentage of the reserve (Karvonen, Kentala and Mustala, 1957).

Any age-based estimate has an error of about 10 beats per minute for an individual (Robergs and Landwehr, 2002; Nes et al., 2013). PounceFit, body assessment software for personal trainers, calculates HRmax with 220 - age and shows heart rate reserve when resting heart rate is entered.

The formulas in full

Age in years, heart rates in beats per minute (bpm).

Max heart rate, classic formula (attributed to Fox, Naughton and Haskell, 1971):

HRmax = 220 - age

Max heart rate, Tanaka (Tanaka, Monahan and Seals, 2001):

HRmax = 208 - 0.7 × age

Max heart rate, Gellish (Gellish et al., 2007):

HRmax = 207 - 0.7 × age

Heart rate reserve:

HRR = HRmax - resting HR

Training heart rate, Karvonen method (Karvonen, Kentala and Mustala, 1957):

Training HR = resting HR + intensity × HRR

Intensity goes in as a fraction: 60% becomes 0.60.

Where the formulas come from

220 - age did not come from a regression study. Robergs and Landwehr (2002) traced its history: it came from eyeballing data from about 11 references, gathered in a 1971 review article (Fox, Naughton and Haskell, 1971), and spread through textbooks without ever coming from original research. The standard error of age-based HRmax estimates ranges from 7 to 11 bpm (Robergs and Landwehr, 2002).

Tanaka, Monahan and Seals (2001) pooled 351 studies with 18,712 people and arrived at 208 - 0.7 × age. The equation was confirmed in a laboratory study of 514 healthy adults and did not differ between men and women or with physical activity level. Gellish et al. (2007) followed 132 people with repeated tests over 25 years and arrived at 207 - 0.7 × age, almost the same line. In the Norwegian HUNT study, with 3,320 healthy adults, the best equation was 211 - 0.64 × age, with a standard error of 10.8 bpm (Nes et al., 2013).

Intensity zones by reserve

ACSM classifies aerobic exercise intensity by percentage of heart rate reserve (Garber et al., 2011, Table 5):

Worked example

A 50-year-old woman with a resting HR of 70 bpm wants to train at 60% and 80% of her reserve.

1. HRmax by 220 - age: 220 - 50 = 170 bpm.
2. HRmax by Tanaka: 208 - 0.7 × 50 = 208 - 35 = 173 bpm.
3. Heart rate reserve (with 220 - age): 170 - 70 = 100 bpm.
4. Training at 60%: 70 + 0.60 × 100 = 130 bpm.
5. Training at 80%: 70 + 0.80 × 100 = 150 bpm.

With Tanaka, the reserve would be 173 - 70 = 103 bpm, and the 60 to 80% range would run from 131.8 to 152.4 bpm (round to 132 to 152). For this client, the choice of formula shifts the zone by 2 bpm. At age 70, the gap between the two HRmax values grows to 9 bpm (150 vs 159).

In PounceFit, this client would see "170 / 100 bpm": HRmax by 220 - age and heart rate reserve. You calculate the Karvonen training zone from those two numbers.

Why use the reserve and not only the max

Two 50-year-old clients have the same estimated HRmax, 170 bpm. One has a resting HR of 55 bpm, the other 80 bpm. At 70% of HRmax, both would train at 119 bpm. With the Karvonen method at 60% of reserve, the first would train at 124 bpm (55 + 0.6 × 115) and the second at 134 bpm (80 + 0.6 × 90). The reserve accounts for each person's starting point. Following this reasoning, Karvonen, Kentala and Mustala (1957) saw a training effect from about 60% of reserve.

Limits

• Individual error. A standard error of 10 bpm means that for about a third of people, true HRmax is more than 10 bpm above or below the estimate. If the training zone feels too easy or too hard, adjust by perceived exertion.
• Medication. Beta-blockers and other drugs that change heart rate make the formulas useless for that client (ACSM, 2021).
• Maximal test. HRmax measured in a maximal exercise test always beats any formula. When the client has a recent exercise stress test, use that value.
• Poorly measured resting HR. A resting HR taken right after the client climbs the stairs changes the reserve and the whole training zone. Measure it calmly and repeat.
• Follow-up. Resting HR usually drops with aerobic training. Record it at every reassessment, always under the same conditions.

To estimate aerobic fitness itself, see the Cooper and Rockport VO₂max field tests.