Enter your age and press "Calculate". If you enter your resting heart rate, the Karvonen formula, which reflects your own fitness, is used (if not, a simple percentage of your maximum heart rate). If you have a maximum heart rate measured in an exercise stress test or similar, you can use it instead of your age.
Enter heart rates as whole numbers in bpm (beats per minute). The results are general guides for healthy adults. If you have heart or blood vessel disease, or take a medicine that affects your heart rate (such as a beta blocker), always talk with your doctor.
Result and graph
Enter your age (and resting heart rate) in the fields on the left and press "Calculate". The result and a graph will appear here.
Table of Contents
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What you can do on this page
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What is this calculation used for?
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How to Use
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Formulas and graphs
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Symbols and terms
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Good to know before you start
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How to calculate it in Excel
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How to calculate it in Google Sheets
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How to calculate it in Python
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How to write it in LaTeX and other math languages (copy and paste)
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How to have ChatGPT do the calculation
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DataChef Features
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Related Features
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NumberChef Calculators List
What you can do on this page
- Enter your age, and you see on the spot your target heart rate zone for exercise (50–85% of your maximum heart rate, the range used by the American Heart Association)
- A table and a graph show your target heart rate for 5 zones from 50% to 100% intensity. They help you choose the right intensity for your goal, such as warming up, burning fat or building endurance
- If you enter your resting heart rate, it uses the Karvonen formula, which reflects your own fitness (if you leave it blank, it uses a simple percentage of your maximum heart rate)
- To estimate your maximum heart rate, you can choose "220 − age" (the standard) or the Tanaka or Nes formula, and if you have a measured value, you can use it as is
- A plain-language explanation of the formulas and copy-and-paste formulas for Excel, Google Sheets and Python are all on this page
Target heart rates are general guides for healthy adults. If you have heart or blood vessel disease, or take a medicine that affects your heart rate (such as a beta blocker), do not use these numbers as they are; always talk with your doctor first.
What is this calculation used for?
Setting the right pace for jogging or walking with numbers
Keeping a pace that is "not too breathless, but still a workout" by feel alone is harder than it sounds. With a target heart rate, you just check your heart rate as you go and adjust your pace objectively.
For example, a 30-year-old with a resting heart rate of 70 bpm who wants to build a base of endurance at 60–70% intensity should aim for 142–154 bpm by the Karvonen formula. You speed up or slow down to stay in that range.
Setting the intensity of cardio for burning fat
Fat is said to be used for energy most easily at a moderate intensity where you can still talk comfortably (around 60–70% of your maximum heart rate). If you push too hard, you cannot keep going for long, and your total calories burned may end up lower.
For example, for a 50-year-old (estimated maximum heart rate 170 bpm), this zone is about 102–119 bpm by the percent of max method. This calculation lets you check with numbers the intensity that "is not hard but still works".
Understanding the heart rate zones on your smartwatch
Many running watches and smartwatches show your heart rate in color-coded zones such as "Zone 1 to 5". The dividing lines behind them come from the same idea as this page, "a percentage of your maximum heart rate".
Once you understand how it works, you can use the display with good reasons, such as "long and easy in Zone 2 today" or "up to Zone 4 in intervals". If you set your own maximum and resting heart rate in the watch settings, the zones also become more accurate.
A safe upper limit when you start exercising after a long break
If you push hard right away after a long break from exercise, you are less likely to stick with it and you put more strain on your body. When you are just starting, the usual advice is to begin at an easy intensity, around the warm-up zone (50–60% of your maximum heart rate).
For example, at 40, the estimated maximum heart rate is 180 bpm, and this zone is about 90–108 bpm. Having an upper limit in numbers, "I will not go above this", works as a safety net when you are tempted to overdo it. If you have a health condition or any health concerns, talk with your doctor before you start.
Managing training for endurance sports such as running and cycling
In endurance sports, athletes commonly use heart rate zones to separate "long, slow days" from "hard days". By not relying on feel to judge intensity, they can build up training that targets the ability they want to improve.
For example, for a 25-year-old athlete with a resting heart rate of 60 bpm, the anaerobic zone (80–90%) by the Karvonen formula is 168–182 bpm. Coaches use this to plan workouts, such as pushing into this range in interval runs and keeping recovery runs in the lower zones.
Formulas and graphs
Estimating maximum heart rate (220 − age)
Graph
Standard notation
(the usual math form)
\(M\)
\(=\)
\(220\)
\(-\)
\(A\)
In words
(symbols replaced with words)
③
\(M\): maximum heart rate (bpm)
\(=\)
①
constant \(220\)
\(-\)
②
\(A\): age (years)
The formula in words
①
Take the
constant \(220\)
②
subtract your
\(A\): age (years)
③
and you get your
\(M\): maximum heart rate (bpm)
Quick example
For a 30-year-old, the estimated maximum heart rate is
maximum heart rate (bpm)
\(=\)
constant 220
\(-\)
age (30)
\(220 - 30 = 190\ \mathrm{bpm}\)
Key idea
"220 − age" is the most widely used formula for estimating maximum heart rate, and it is the standard in this calculator. The American Heart Association and the CDC also use it in their exercise guides. But a formula only gives a statistical average. For people of the same age, the real maximum heart rate can differ by about ±10 bpm. Only a measurement, such as an exercise stress test at a medical facility, gives the exact value. If you have a measured value, enter it in "Measured max heart rate", and it is used as is instead of the formula.
More accurate formulas (Tanaka and Nes)
Graph
Standard notation
(the usual math form)
\(M\)
\(=\)
\(208\)
\(-\)
\(0.7\)
\(\times\)
\(A\)
\(M\)
\(=\)
\(211\)
\(-\)
\(0.64\)
\(\times\)
\(A\)
In words
(symbols replaced with words)
④
\(M\): max heart rate by Tanaka (bpm)
\(=\)
①
constant \(208\)
\(-\)
②
constant \(0.7\)
\(\times\)
③
\(A\): age (years)
⑧
\(M\): max heart rate by Nes (bpm)
\(=\)
⑤
constant \(211\)
\(-\)
⑥
constant \(0.64\)
\(\times\)
⑦
\(A\): age (years)
The formula in words
①
From the
constant \(208\)
②
subtract the
constant \(0.7\)
③
times your
\(A\): age (years)
④
and you get the
\(M\): max heart rate by Tanaka (bpm)
⑤
From the
constant \(211\)
⑥
subtract the
constant \(0.64\)
⑦
times your
\(A\): age (years)
⑧
and you get the
\(M\): max heart rate by Nes (bpm)
Quick example
For a 40-year-old, the Tanaka formula gives a maximum heart rate of
maximum heart rate (bpm)
\(=\)
constant 208
\(-\)
constant 0.7
\(\times\)
age (40)
\(208 - 0.7 \times 40 = 208 - 28 = 180\ \mathrm{bpm}\)
Key idea
The Tanaka formula (2001) and the Nes formula (2013) are both fairly recent formulas based on large sets of measured data. "220 − age" is known to give values that are too low, especially for middle-aged and older adults, and these formulas were made to fix that. In this calculator, you can choose them from the "Max heart rate formula" menu. All of them are still estimates, so if you are unsure, the standard "220 − age" is good enough.
Percent of max method (without a resting heart rate)
Graph
Standard notation
(the usual math form)
\(T\)
\(=\)
\(M\)
\(\times\)
\(p\)
In words
(symbols replaced with words)
③
\(T\): target heart rate (bpm)
\(=\)
①
\(M\): maximum heart rate (bpm)
\(\times\)
②
\(p\): intensity (% of max)
The formula in words
①
Take your
\(M\): maximum heart rate (bpm)
②
multiply it by the
\(p\): intensity (% of max)
③
and you get your
\(T\): target heart rate (bpm)
Quick example
For a 25-year-old (maximum heart rate 195 bpm) exercising at 60% intensity, the target heart rate is
target heart rate (bpm)
\(=\)
max heart rate (195 bpm)
\(\times\)
intensity (60% = 0.60)
\(195 \times 0.60 = 117\ \mathrm{bpm}\)
Key idea
Do not multiply by "60" as is; first turn the percentage into a decimal (60% → 0.60), then multiply. This method (also written as %HRmax) depends only on your maximum heart rate. It is simple and works well as a guide when you do not know your resting heart rate. The American Heart Association describes moderate exercise as about 50–70% of your maximum heart rate and vigorous exercise as about 70–85%. In this calculator, this method is used automatically when the resting heart rate is left blank.
Karvonen formula (with a resting heart rate)
Graph
Standard notation
(the usual math form)
\(T\)
\(=\)
\(R\)
\(+\)
\(p\)
\(\times\)
\((\)
\(M\)
\(-\)
\(R\)
\()\)
In words
(symbols replaced with words)
⑤
\(T\): target heart rate (bpm)
\(=\)
④
\(R\): resting heart rate (bpm)
\(+\)
③
\(p\): intensity (% of max)
\(\times\)
\((\)
①
\(M\): maximum heart rate (bpm)
\(-\)
②
\(R\): resting heart rate (bpm)
\()\)
The formula in words
①
From your
\(M\): maximum heart rate (bpm)
②
subtract your
\(R\): resting heart rate (bpm)
to get the heart rate reserve
③
multiply it by the
\(p\): intensity (% of max)
④
add back your
\(R\): resting heart rate (bpm)
⑤
and you get your
\(T\): target heart rate (bpm)
Quick example
For a 30-year-old (maximum heart rate 190 bpm) with a resting heart rate of 70 bpm, exercising at 50% intensity, the target heart rate is
target heart rate (bpm)
\(=\)
resting heart rate (70 bpm)
\(+\)
intensity (50% = 0.50)
\(\times\)
\((\)
max heart rate (190 bpm)
\(-\)
resting heart rate (70 bpm)
\()\)
\(70 + 0.50 \times (190 - 70) = 70 + 60 = 130\ \mathrm{bpm}\)
Key idea
The Karvonen formula looks at the range your heart rate can move through, from resting to maximum (the heart rate reserve, \(M - R\)). As you get fitter and your resting heart rate drops, the target for the same intensity changes, so it reflects your own fitness better. It is widely used by fitness professionals and in cardiac rehabilitation, and the American College of Sports Medicine also uses the heart rate reserve to set exercise intensity. In this calculator, it is used automatically when you enter a resting heart rate.
The basic rule for a target heart rate is "maximum heart rate (estimated with 220 − age or similar) × intensity". If you know your resting heart rate, the Karvonen formula, which multiplies the heart rate reserve (max − resting) by the intensity and then adds back the resting heart rate, gives a target that better reflects your own fitness.
Symbols and terms
Symbols
| \(T\) | The target heart rate you want to find (bpm). From the first letter of "target". |
| \(M\) | Maximum heart rate (bpm), the highest heart rate you can reach during all-out exercise. From the first letter of "maximum". |
| \(A\) | Age in years. From the first letter of "age". |
| \(R\) | Resting heart rate (bpm). From the first letter of "rest". |
| \(p\) | Intensity, how hard you exercise as a share of the maximum, written as a decimal (0.50 for 50%). From "percent". |
| \(M - R\) | Heart rate reserve (maximum heart rate − resting heart rate). It is the room your heart rate has to rise during exercise, and it is the base of the Karvonen formula. |
Terms
| heart rate | How many times your heart beats in 1 minute. The unit is bpm (beats per minute). You can also measure it by counting your pulse at the wrist for 15 seconds and multiplying by 4. |
| maximum heart rate | The highest heart rate you can reach during all-out exercise. It tends to go down with age and is estimated with formulas such as "220 − age" (people of the same age can differ by about ±10 bpm). |
| resting heart rate | Your heart rate when you are calm and at rest. For adults it is usually about 60 to 100 bpm, and people who do regular endurance exercise often have lower rates. It is best measured right after you wake up in the morning. |
| heart rate reserve (HRR) | Maximum heart rate minus resting heart rate. It is the room your heart rate has to rise during exercise, and it is the base of the Karvonen formula. |
| Karvonen formula | A common method for target heart rate that multiplies the heart rate reserve by the intensity and adds back the resting heart rate. It was proposed by the Finnish physiologist Martti Karvonen and is widely used by fitness professionals. |
| target heart rate (THR) | The heart rate to aim for during exercise so that you stay at the right intensity for your goal. It is the value this page finds. |
| intensity | How hard the exercise is. On this page it is written as a percentage of your maximum heart rate (or of your heart rate reserve). |
| bpm | Short for beats per minute, the unit of heart rate. |
| beta blocker | A medicine that slows the heart rate, used to treat high blood pressure and heart disease. When you take one, your heart rate rises less during exercise, so the numbers on this page do not apply. Ask your doctor how hard you should exercise. |
Good to know before you start
Here is what helps you use the calculation on this page with real understanding, not just by pressing the button.
| Percents (Grade 6) |
|
| Order of operations (Grades 5–6) |
|
| Rounding (Grades 4–5) |
|
| Evaluating expressions (Grades 6–7) |
|
How to calculate it in Excel
Copy the whole table below and paste it into cell A1 in Excel. It works as is.
Table to find the maximum heart rate (220 − age)
| Age A (years) | 30 |
| Maximum heart rate M (bpm) | =220-B1 |
Table to find the maximum heart rate by the Tanaka and Nes formulas
| Age A (years) | 40 |
| Max heart rate by Tanaka (bpm) | =ROUND(208-0.7*B1,0) |
| Max heart rate by Nes (bpm) | =ROUND(211-0.64*B1,0) |
Table to find the target heart rate by the percent of max method
| Maximum heart rate M (bpm) | 195 |
| Intensity p (for 60%, enter 0.6) | 0.6 |
| Target heart rate T (bpm) | =ROUND(B1*B2,0) |
Table to find the target heart rate by the Karvonen formula
| Maximum heart rate M (bpm) | 190 |
| Resting heart rate R (bpm) | 70 |
| Intensity p (for 50%, enter 0.5) | 0.5 |
| Target heart rate T (bpm) | =ROUND(B2+B3*(B1-B2),0) |
After pasting, the upper rows are your inputs and the formula rows are calculated automatically.
"ROUND(value,0)" rounds to a whole number. With the example numbers, the first table shows 190, the second 180 and 185, the third 117 and the fourth 130. Just replace the age and heart rates with your own.
"ROUND(value,0)" rounds to a whole number. With the example numbers, the first table shows 190, the second 180 and 185, the third 117 and the fourth 130. Just replace the age and heart rates with your own.
How to calculate it in Google Sheets
Copy the whole table below and paste it into cell A1 in Google Sheets. It works as is.
Table to find the maximum heart rate (220 − age)
| Age A (years) | 30 |
| Maximum heart rate M (bpm) | =220-B1 |
Table to find the maximum heart rate by the Tanaka and Nes formulas
| Age A (years) | 40 |
| Max heart rate by Tanaka (bpm) | =ROUND(208-0.7*B1,0) |
| Max heart rate by Nes (bpm) | =ROUND(211-0.64*B1,0) |
Table to find the target heart rate by the percent of max method
| Maximum heart rate M (bpm) | 195 |
| Intensity p (for 60%, enter 0.6) | 0.6 |
| Target heart rate T (bpm) | =ROUND(B1*B2,0) |
Table to find the target heart rate by the Karvonen formula
| Maximum heart rate M (bpm) | 190 |
| Resting heart rate R (bpm) | 70 |
| Intensity p (for 50%, enter 0.5) | 0.5 |
| Target heart rate T (bpm) | =ROUND(B2+B3*(B1-B2),0) |
The same formulas as in Excel work as is. Copy the whole table, paste it into cell A1, and replace the age and heart rates with your own.
How to calculate it in Python
age = 30 # age (years)
resting_hr = 70 # resting heart rate (bpm). Set to None if unknown
measured_max_hr = None # measured maximum heart rate (bpm). Enter a number if you have one
# Maximum heart rate (use the measured value if there is one; otherwise estimate with 220 - age)
if measured_max_hr is not None:
max_hr = measured_max_hr
else:
max_hr = 220 - age
def round_half_up(x):
# Round half up by adding 0.5 and cutting off the decimals (Python's round() rounds 0.5 to even, so it is not used)
return int(x + 0.5)
def target_hr(intensity_percent):
# Karvonen formula if there is a resting heart rate; otherwise the percent of max method
if resting_hr is not None:
return round_half_up(resting_hr + intensity_percent / 100 * (max_hr - resting_hr))
return round_half_up(max_hr * intensity_percent / 100)
print(f"Maximum heart rate: {round_half_up(max_hr)} bpm")
print(f"Target heart rate (50-85% intensity): {target_hr(50)}-{target_hr(85)} bpm")
for lower, upper in [(50, 60), (60, 70), (70, 80), (80, 90), (90, 100)]:
print(f"Intensity {lower}-{upper}%: {target_hr(lower)}-{target_hr(upper)} bpm")
Runs with the standard library only. Change the age and resting heart rate at the top to your own and run it. If you set the resting heart rate to None, it uses a simple percentage of your maximum heart rate (the percent of max method).
How to write it in LaTeX and other math languages (copy and paste)
Estimating maximum heart rate (220 − age)
M = 220 − A
M = 220 - A
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>M</mi>
<mo>=</mo>
<mn>220</mn>
<mo>−</mo>
<mi>A</mi>
</mrow>
</math>
M = 220 - A
220 - A
M := 220 - A;
M = 220 - A;
M = 220 - A
More accurate formulas (Tanaka and Nes)
M = 208 − 0.7 × A, M = 211 − 0.64 × A
M = 208 - 0.7A, \quad M = 211 - 0.64A
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>M</mi>
<mo>=</mo>
<mn>208</mn>
<mo>−</mo>
<mn>0.7</mn>
<mi>A</mi>
<mo>,</mo>
<mi>M</mi>
<mo>=</mo>
<mn>211</mn>
<mo>−</mo>
<mn>0.64</mn>
<mi>A</mi>
</mrow>
</math>
M = 208 - 0.7A, M = 211 - 0.64A
{208 - 0.7*A, 211 - 0.64*A}
M1 := 208 - 0.7*A; M2 := 211 - 0.64*A;
M1 = 208 - 0.7*A; M2 = 211 - 0.64*A;
M = 208 - 0.7A, M = 211 - 0.64A
Percent of max method (without a resting heart rate)
T = M × p
T = M \times p
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>T</mi>
<mo>=</mo>
<mi>M</mi>
<mo>×</mo>
<mi>p</mi>
</mrow>
</math>
T = M p
M*p
T := M*p;
T = M*p;
T = M p
Karvonen formula (with a resting heart rate)
T = R + p × (M − R)
T = R + p \times (M - R)
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>T</mi>
<mo>=</mo>
<mi>R</mi>
<mo>+</mo>
<mi>p</mi>
<mo>×</mo>
<mrow>
<mo>(</mo>
<mi>M</mi>
<mo>−</mo>
<mi>R</mi>
<mo>)</mo>
</mrow>
</mrow>
</math>
T = R + p xx (M - R)
R + p*(M - R)
T := R + p*(M - R);
T = R + p*(M - R);
T = R + p(M - R)
How to have ChatGPT do the calculation
You are a calculation assistant for exercise physiology. Do the following calculation by actually running Python code, and base your answer only on the numbers from the execution result (do not answer by mental math or guessing). Find the target heart rate for a 30-year-old with a resting heart rate of 70 bpm. 1. Estimate the maximum heart rate with "220 − age". 2. With the Karvonen formula, T = resting heart rate + intensity × (maximum heart rate − resting heart rate), list the target heart rate at 50%, 60%, 70%, 80%, 90% and 100% intensity. 3. Round each heart rate to a whole number of bpm (round 0.5 up). Show the formulas you used and the numbers from the execution result. Also add a note that these are general guides for healthy adults, and that people with heart disease or who take medicine that affects heart rate should talk with their doctor.
How to Use
-
1Enter your numbersType the numbers you want to calculate with into the input fields
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2CalculatePress the "Calculate" button
-
3Check the resultThe result appears on the spot. The same page also explains the idea behind the calculation and the formula
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