The Karvonen Formula (Heart Rate Reserve Method)

Target heart rate is not simply your maximum heart rate times a percentage. That method ignores your resting heart rate, which means two people of the same age get the same target even if one is an endurance athlete and the other has never exercised. The Karvonen formula, also called the heart rate reserve (HRR) method, fixes that by subtracting your resting heart rate from your max, taking a percentage of what is left, and adding your resting rate back. The result is a target heart rate that reflects your current fitness level, not a population average.

The formula is Target HR = ((Max HR − Resting HR) × Intensity %) + Resting HR. Max HR is your highest possible heart rate during maximal exertion. Resting HR is your heart rate when fully awake but at complete rest, measured first thing in the morning before you get out of bed. Heart rate reserve (HRR) is Max HR minus Resting HR; it represents the range your heart has to increase during exercise. Intensity % is your desired effort as a decimal, so 70% becomes 0.70. The original paper describing this method was published by Karvonen, Kentala and Mustala in 1957, not the 1970s as some sources claim.

You need three numbers: your age, your resting heart rate, and your desired exercise intensity. You also need to choose a max HR formula, because the original method did not specify one.

Step 1: Estimate Your Max HR

For men, the traditional estimate is 220 minus age. For women, the only female-derived formula with published data is the Gulati formula: 206 − (0.88 × age), from Gulati et al. Circulation 2010. For anyone over 40, the Tanaka formula, 208 − (0.7 × age), is more accurate than 220 minus age and has a lower standard deviation. The standard deviation of the 220 minus age formula is about 12 bpm, meaning two people of the same age can have true max HRs that differ by 20 bpm or more.

Step 2: Measure Your Resting Heart Rate

Measure it first thing in the morning, before you sit up, after a full night of sleep, and before caffeine. Take it for 60 seconds. Average three mornings for a reliable baseline. A single measurement can be off by 10 bpm due to hydration, sleep quality, or illness.

Step 3: Calculate HRR and Target HR

Subtract your resting HR from your max HR to get your heart rate reserve. Multiply the reserve by your intensity percentage as a decimal. Add your resting HR back. That is your target heart rate for that intensity.

Take a 30-year-old person with a resting heart rate of 70 bpm who wants to exercise at 60%, 70%, and 80% intensity. Use the Tanaka formula for max HR: 208 − (0.7 × 30) = 187 bpm. HRR = 187 − 70 = 117 bpm.The moderate intensity range per ACSM Guidelines 11th edition is 40-59% of HRR, which corresponds to 64-76% of max HR. Vigorous intensity is 60-84% of HRR. So for this person, 140 bpm (60% HRR) is at the low end of vigorous, 152 bpm (70% HRR) is solidly vigorous, and 164 bpm (80% HRR) is near the top of the vigorous zone.

Here is a second worked example: a 45-year-old woman using the Gulati formula.Resting HR = 65 bpm. HRR = 166 − 65 = 101 bpm.Notice that the max HR estimate (166 bpm) is much lower than the 220 minus age estimate of 175 bpm, which would produce targets about 5-7 bpm higher across the board. Using an unsourced 226 minus age formula would give an even higher estimate of 181 bpm, moving targets by another 9-10 bpm.

The ACSM Guidelines 11th edition state that %HRR is equivalent to %VO2R (VO2 reserve) within plus or minus 5% for steady-state exercise at 40-85% of VO2max. VO2R is the difference between your VO2max and your resting oxygen consumption. This equivalence means that when you exercise at 70% of your heart rate reserve, you are also exercising at roughly 70% of your usable oxygen capacity. The simpler percent of max HR method does not have this property. Two people of the same age but different resting HRs will have the same %MHR target but different relative oxygen demands. The Karvonen method adjusts for that by accounting for resting HR, which correlates with resting oxygen consumption. For a person with a low resting HR, the HRR is larger, so a given %HRR represents a larger absolute increase in heart rate and oxygen demand than for someone with a high resting HR. That is not a flaw; it is the point. The method matches the physiological concept of reserve capacity.

The conversion formula from ACSM is %HRR = 0.64 × %VO2max + 37 for moderate intensity, but in practice the direct equivalence is good enough for zone setting. Moderate intensity is 40-59% HRR (64-76% HRmax), vigorous is 60-84% HRR (77-93% HRmax), and near-maximal is 85% or more HRR (94% or more HRmax).

The Karvonen formula itself does not specify which max HR formula to use. You need to pick one. The 220 minus age formula is historically entrenched but scientifically unsupported; its standard deviation of 12 bpm means it can be off by 20 bpm for many people. For anyone over 40, the Tanaka formula (208 − 0.7 × age) is more accurate. For women, the Gulati formula (206 − 0.88 × age) is the only female-derived formula with published data. If you have access to a maximal exercise test with ECG or a verified field test (e.g., a ramp test on a bike or treadmill to volitional failure), use that measured number instead of any formula. The Karvonen method is still valid with a measured max HR; the formula does not care where the max HR number came from.

Resting heart rate varies with hydration, sleep, caffeine, and illness. Do not rely on a single measurement. Average three mornings.

Martti Karvonen, Eino Kentala, and O. Mustala published "The effects of training on heart rate; a longitudinal study" in Annales Medicinae Experimentalis et Biologiae Fenniae in 1957. They studied the relationship between heart rate and exercise intensity and proposed using the difference between max and resting heart rate as a better measure of relative workload. The paper is foundational in exercise physiology. The method is still recommended by the American College of Sports Medicine (ACSM) for prescribing exercise intensity, specifically in the ACSM Guidelines 11th edition (2021). Karvonen published in 1957, not in the 1950s or 1970s.