Calories Burned by Heart Rate Calculator: The Keytel Equations

Heart rate is the one effort signal most people can see during a workout, and a widely used way to turn it into calories is a set of equations published by Keytel and colleagues in 2005 in the Journal of Sports Sciences. This heart rate calorie calculator runs them, so it counts calories burned based on heart rate rather than on the activity you did. It has the men's and women's equations without VO2 max and the more accurate pair that adds it.

Many heart rate calorie calculators run the same equations without saying so. This one shows where every coefficient comes from, gives a likely range from the study's own independent check, and flags the inputs the equations were never built for: very low heart rates, ages and weights outside the study, strength training and intervals.

How the calories burned by heart rate calculator works

The Keytel equations predict the energy you spend each minute, EE, in kilojoules, from your average heart rate HR in beats per minute, your weight W in kilograms and your age A in years. Women and men have separate equations, and a second pair adds your VO2 max, the most oxygen your body can use, in milliliters per kilogram per minute.

Without VO2 max

Men: EE = −55.0969 + 0.6309 × HR + 0.1988 × W + 0.2017 × A

Women: EE = −20.4022 + 0.4472 × HR − 0.1263 × W + 0.074 × A

With VO2 max

Men: EE = −95.7735 + 0.634 × HR + 0.394 × W + 0.404 × VO2max + 0.271 × A

Women: EE = −59.3954 + 0.450 × HR + 0.103 × W + 0.380 × VO2max + 0.274 × A

• Kilojoules to calories. A kilocalorie, the calorie on food labels, is 4.184 kilojoules, so divide EE by 4.184 for calories per minute, then multiply by the minutes you exercised.
• Heart rate does most of the work. Each extra beat per minute adds 0.63 kJ (0.15 kcal) a minute in the men's equation and 0.45 kJ (0.11 kcal) in the women's.
• Weight, age and fitness adjust it. At the same heart rate, heavier men, older people and people with a higher VO2 max get a higher estimate. The women's equation without VO2 max is the exception for weight, as the next section explains.
• The result is gross. The study measured all the oxygen used during exercise, so the number includes the calories you would have burned sitting still.

For the default 35-year-old man weighing 81.6 kg at 140 bpm: −55.0969 + 0.6309 × 140 (88.33) + 0.1988 × 81.6 (16.23) + 0.2017 × 35 (7.06) = 56.5 kJ a minute. Divided by 4.184 that is 13.5 kcal a minute, or about 405 calories in 30 minutes.

The 2005 paper itself is not open to read online. The same study, with the same 115 volunteers and the same equations, is the fourth chapter of first author Lara Keytel's 2004 PhD thesis at the University of Cape Town, which is open in the university's repository. We took the coefficients from the thesis (pages 116 and 117, Tables 4.3 and 4.5) and checked them digit for digit against two open papers that reprint them, Jung et al. (2021) and Chiu et al. (2022). The thesis writes the VO2 max pair as one formula with a sex term: −59.3954 for women, and −59.3954 − 36.3781 = −95.7735 for men. The fit figures on this page come from the published abstract.

Calories burned based on heart rate for women and men

Keytel's study fitted separate equations for women and men, so the female and male versions of a heart rate calorie calculator give different answers at the same pulse. The table shows both for a 35-year-old: a 150 lb68.0 kg woman and a 180 lb81.6 kg man, without VO2 max.

At 140 bpm the woman burns about 8.7 calories a minute and the man 13.5. Part of the gap is body size, but most of it is the equations: at the same age, a weight of 150 lb and a heart rate of 140, a man gets 12.9 calories a minute against the woman's 8.7. Each beat simply counts for less in the women's equation, 0.11 kcal a minute against 0.15 for men.

One feature of the women's equation surprises people. Without VO2 max, weight carries a small negative coefficient, −0.1263 kJ a minute per kilogram, and the thesis reports a standard error of 0.1061 for it, almost as large as the coefficient itself, so the study could not tell it apart from zero. In plain terms, once heart rate was known, weight told the study almost nothing about how much a woman burned. The calculator still runs the published equation, so a heavier woman sees a slightly lower number: at 140 bpm for 30 minutes, a 35-year-old woman gets 268 calories at 130 lb59.0 kg and 239 at 200 lb90.7 kg. With a VO2 max of 38 the weight term turns positive, and the same two women get 242 and 265.

Age raises the estimate in every version. At the same heart rate, the men's equation gives a 55-year-old about 11 percent more than a 25-year-old: 434 against 391 calories for 30 minutes at 140 bpm and 180 lb81.6 kg. One likely reason is that maximum heart rate falls by about 0.7 beats per minute for each year of age (Tanaka et al. 2001), so the same pulse is a harder effort for an older heart.

What the Keytel equations were built on

Keytel et al. (2005) tested 115 regularly exercising adults aged 18 to 45, weighing 47 to 120 kg, with VO2 max values from 27 to 81 ml/kg/min, recruited from a fitness center, running clubs and cycle races. Each did a VO2 max test on a treadmill or a cycle ergometer, then three steady stages of 10 minutes on the treadmill or 15 minutes on the bike at about 35, 62 and 80 percent of VO2 max, which the paper reports as about 57, 77 and 90 percent of maximum heart rate. Heart rate came from a Polar heart rate monitor, and energy use from the oxygen used and carbon dioxide produced, measured with a gas analyzer over the last 5 minutes of every stage.

Running and cycling gave the same relationship, so the type of exercise did not enter the equations, and in the thesis's independent check they also matched stationary rowing and stair climbing well. That defines where the calculator works best:

• Steady aerobic exercise with large muscle groups, such as running, cycling, rowing, the elliptical or brisk incline walking.
• An average heart rate between about 57 and 90 percent of your maximum. The calculator estimates your maximum as 208 − 0.7 × age (Tanaka et al. 2001), the formula our max heart rate calculator recommends. At 35 that range is about 105 to 165 bpm.
• Adults aged 18 to 45 weighing 47 to 120 kg (104 to 265 lb), with a VO2 max between 27 and 81 if you enter one.

Outside any of these the calculator still gives a number, and an amber note in the result says which condition you are outside and what it means.

Very low heart rates

Below the easiest stage, the equations are a straight line extended past their data. Near resting heart rate they fall below what a body burns sitting still: for a 30-year-old, 120 lb54.4 kg woman, the women's equation gives 0.4 calories a minute at 60 bpm, less than half of the roughly 1 calorie a minute she burns at rest, and less than zero below about 56 bpm. The calculator refuses a result at zero or below and flags any heart rate under 57 percent of your maximum. Easy walks often sit near that line, and for them our walking calorie calculator, which works from pace, is the steadier choice.

Strength training and intervals

Lifting raises heart rate more than it raises oxygen use. In a circuit of bench presses, rows, curls and squats at 40 to 70 percent of one-rep max, Collins et al. (1991) measured heart rates of 63 to 82 percent of maximum while oxygen uptake was only 33 to 47 percent of VO2 max, a relationship about half as steep as in running or cycling. Kettlebell swings show the same gap. At the same perceived effort and a similar heart rate, about 90 percent of age-predicted maximum, a treadmill run used 25 to 39 percent more oxygen and calories than swings (Hulsey et al. 2012), and 12 minutes of continuous swings held heart rate at 87 percent of maximum with oxygen uptake at 65 percent of VO2 max (Farrar et al. 2010).

Keytel's thesis tested this directly. In a 55-minute gym session that mixed 20 minutes of cardio with 20 minutes of weight training, the steady-exercise equation estimated 39 kJ a minute on average against 30 kJ measured, about 30 percent high. For a 180 lb81.6 kg man doing 45 minutes of dumbbell sets at an average of 120 bpm, this calculator gives about 470 calories, while the 2024 Compendium's value for that kind of session, 3.5 METs, gives about 225.

Intervals cause a different problem. Heart rate takes time to climb at the start of each hard effort and stays up after it, so it trails what your muscles are doing, a lag the thesis's review of earlier studies also describes. Its next chapter built a separate equation for stop-start exercise that adds the previous minute's heart rate, and it explained 78 percent of the variation in measured burn during intermittent gym work against 73 percent for the steady-exercise equation. It needs minute-by-minute heart rate, so this calculator does not run it. Read the result for an interval session as rough.

Heat, dehydration and long sessions

Heart rate can also rise with no extra work. Dehydration and hot weather can strongly change the link between heart rate and oxygen uptake (Achten and Jeukendrup 2003), and in long steady sessions heart rate creeps up while the heart pumps less blood per beat, which Keytel's thesis describes as cardiovascular drift. Both push a heart rate estimate up on hot days and late in long sessions, and neither is in the equations, which were built from stages of 10 to 15 minutes.

Worked examples: calories burned by heart rate for nine workouts

Nine sessions run through the calculator. Each heart rate is shown as a share of the Tanaka maximum for that age.

Three patterns stand out. The men's equation gives more per beat, so the 25-year-old man's 30-minute run at 155 bpm (446 calories) beats the 28-year-old woman's spin class at 150 bpm (296) by half. Adding VO2 max moved both people near the middle of the study's fitness range down a little: a VO2 max of 50 took the man from 405 to 393 calories, and 38 took the woman's elliptical session from 389 to 373, while a fitter man at 60 would get about 422. And time counts as much as effort: the 45-year-old's easy hour on the bike at 125 bpm burns more than any 30-minute session in the table.

Most people count exercise calories because they are trying to lose weight, and the calories a workout burns are the hardest part of that sum to measure. Two or three strength sessions a week help you keep muscle while you lose fat, and our comparison of the best workout apps for weight loss looks at which apps build that strength work into the plan.

Why a heart rate estimate and a MET estimate differ for the same session

FitCraft's calories burned calculator uses METs, multiples of resting metabolism measured for each activity and listed in the 2024 Adult Compendium of Physical Activities (Herrmann et al. 2024). It asks what you did and scales by your weight; this page asks how hard your heart worked. Both give gross calories, so the numbers compare directly. Here are the same sessions run through both.

• Fitness. A MET value is the same for every runner of the same weight at the same pace, but a fitter heart beats slower at that pace. For the 30-minute run at 6 mph, the heart rate estimate runs from 383 calories at 135 bpm to 518 at 165, while the MET estimate stays at 399. Adding VO2 max narrows that spread to 385 against 463, which is why the VO2 max equations fit the study better.
• Sex. The women's equation counts fewer calories per beat, so for the 150 lb68.0 kg woman's 5 mph run the heart rate estimate lands within about 10 percent of the MET figure at 145 to 160 bpm.
• Session type. For dumbbell sets, heart rate overstates the work, and the heart rate estimate comes out about twice the Compendium's.

Use the MET calculator when you know the activity and the pace, and this one for steady sessions that are hard to describe by pace, such as a hilly ride or a session on the elliptical. When the two disagree by a lot, look for something that raises heart rate without raising the work: heat, dehydration, a long session or lifting. If you want to aim a session rather than count it, the heart rate zone calculator turns your maximum heart rate into training zones.

How accurate is a calories burned by heart rate calculator?

The calculator runs Keytel's equations exactly, so the real question is how close the equations come to measured energy use. In the study's 115 adults, the equation with VO2 max explained 83 percent of the variation in measured burn (r = 0.913) and the equation without it 73 percent (r = 0.857). Those figures describe the people the equations were fitted on. The thesis also tested both on 17 new exercisers, 9 men and 8 women aged 21 to 53, during a 20-minute cardio session of their choice on gym equipment, measured with a portable gas analyzer.

In that check both equations read high on average, and 95 percent of the errors fell between about 3 calories a minute too low and 6 too high. The result card applies that window to your session as the likely range: for the default 30-minute session at 13.5 calories a minute, it runs from about 225 to 496 calories. The low end never drops below the resting rate of 1 MET. Treat the window as approximate, since it comes from 17 people over 20 minutes.

How accurate are calorie calculators and wrist devices?

For one person on one day, none of the common methods is precise. Shcherbina et al. (2017) tested seven wrist devices against lab gas analysis in 60 volunteers sitting, walking, running and cycling. Heart rate was measured well, with median errors of about 2 to 7 percent by device, but no device estimated energy expenditure within 20 percent, and the median errors ran from 27 to 93 percent. A review of 158 studies by Fuller et al. (2020) found that in controlled settings only 9 percent of energy expenditure comparisons fell within 3 percent of the measured value, while 54 percent read low and 37 percent read high. A meta-analysis of 60 studies found that accuracy depended on the activity and that devices combining heart rate with motion sensing had smaller errors in most activities (O'Driscoll et al. 2020).

MET calculators have their own errors, mostly from assuming the same resting burn and the same economy for everyone, which our calories burned calculator explains. Read any of these numbers as a way to compare your own sessions, and plan meals around the likely range rather than the single number.

When to ignore this calculator

The equations were built on healthy adults who exercise regularly. In these cases, skip the number or ask a clinician first.

• Heart rate medicines, a pacemaker or an irregular rhythm. Beta blockers and some other medicines slow the heart at every effort, and a pacemaker or a rhythm problem such as atrial fibrillation breaks the link between pulse and work. Ask your doctor or cardiac rehab team how to judge effort instead.
• Pregnancy. Heart rate, blood volume and weight change through pregnancy, and the equations were not built for it. Ask your obstetric care team about exercise intensity.
• Heart, lung or circulation conditions. See a doctor before training by heart rate if exercise brings on chest pain, faintness or breathlessness out of proportion to the effort.
• Eating disorders or recent recovery. Counting exercise calories can feed a harmful cycle. A clinician or registered dietitian who treats eating disorders is the right guide.
• Teenagers and children. The equations come from adults aged 18 to 45, so young people need separate advice.
• Hot weather and long sessions. Heat and dehydration raise heart rate without raising the work. The sweat rate calculator estimates how much fluid you lose per hour from a before-and-after weigh-in.

Related reading

References

1. Keytel LR, Goedecke JH, Noakes TD, Hiiloskorpi H, Laukkanen R, van der Merwe L, Lambert EV. "Prediction of energy expenditure from heart rate monitoring during submaximal exercise." J Sports Sci. 2005;23(3):289-297. doi:10.1080/02640410470001730089, PubMed 15966347. Study conditions and fit figures from the abstract; coefficients as printed in reference 2.
2. Keytel L. "Application and development of indirect measures of free-living energy expenditure." PhD thesis, Department of Human Biology, University of Cape Town; 2004. hdl.handle.net/11427/19142, OpenUCT record. Chapter 4: equations (pp. 116-117, Tables 4.3 and 4.5) and independent check (Table 4.7). Chapter 5: gym session with weights (Table 5.7).
3. Jung WS, Park HY, Kim SW, Kim J, Hwang H, Lim K. "Estimating excess post-exercise oxygen consumption using multiple linear regression in healthy Korean adults: a pilot study." Phys Act Nutr. 2021;25(1):35-41. doi:10.20463/pan.2021.0006, PMC8076581. Reprints both Keytel equations.
4. Chiu YW, Clemente FM, Bezerra P, Pagaduan JC, Chen YS. "Day-to-day variation of the heart rate, heart rate variability, and energy expenditure during FIFA 11+ and dynamic warm-up exercises." J Hum Kinet. 2022;81:73-84. doi:10.2478/hukin-2022-0007, PMC8884869. Reprints the equations without VO2 max.
5. Tanaka H, Monahan KD, Seals DR. "Age-predicted maximal heart rate revisited." J Am Coll Cardiol. 2001;37(1):153-156. doi:10.1016/S0735-1097(00)01054-8, PubMed 11153730
6. Herrmann SD, Willis EA, Ainsworth BE, et al. "2024 Adult Compendium of Physical Activities: a third update of the energy costs of human activities." J Sport Health Sci. 2024;13(1):6-12. doi:10.1016/j.jshs.2023.10.010, PMC10818145. Codes: running, conditioning exercise
7. Collins MA, Cureton KJ, Hill DW, Ray CA. "Relationship of heart rate to oxygen uptake during weight lifting exercise." Med Sci Sports Exerc. 1991;23(5):636-640. doi:10.1249/00005768-199105000-00018, PubMed 2072844
8. Hulsey CR, Soto DT, Koch AJ, Mayhew JL. "Comparison of kettlebell swings and treadmill running at equivalent rating of perceived exertion values." J Strength Cond Res. 2012;26(5):1203-1207. doi:10.1519/JSC.0b013e3182510629, PubMed 22395274
9. Farrar RE, Mayhew JL, Koch AJ. "Oxygen cost of kettlebell swings." J Strength Cond Res. 2010;24(4):1034-1036. doi:10.1519/JSC.0b013e3181d15516, PubMed 20300022
10. Achten J, Jeukendrup AE. "Heart rate monitoring: applications and limitations." Sports Med. 2003;33(7):517-538. doi:10.2165/00007256-200333070-00004, PubMed 12762827
11. Shcherbina A, Mattsson CM, Waggott D, et al. "Accuracy in wrist-worn, sensor-based measurements of heart rate and energy expenditure in a diverse cohort." J Pers Med. 2017;7(2):3. doi:10.3390/jpm7020003, PMC5491979
12. Fuller D, Colwell E, Low J, et al. "Reliability and validity of commercially available wearable devices for measuring steps, energy expenditure, and heart rate: systematic review." JMIR Mhealth Uhealth. 2020;8(9):e18694. doi:10.2196/18694, PMC7509623
13. O'Driscoll R, Turicchi J, Beaulieu K, et al. "How well do activity monitors estimate energy expenditure? A systematic review and meta-analysis of the validity of current technologies." Br J Sports Med. 2020;54(6):332-340. doi:10.1136/bjsports-2018-099643, PubMed 30194221. Cited from the abstract.

How this calculator differs from typical heart rate calorie calculators

Most online calorie calculators that work from heart rate run the Keytel equations without saying where the coefficients come from, and give one number with no range. Few mention that the equations were built on steady running and cycling in adults aged 18 to 45, so they return confident numbers for a resting heart rate, a weight session or a 70-year-old.

This calculator takes its coefficients from the open thesis that contains the study and checks them against two open papers that reprint them. It runs both the equations without VO2 max and the more accurate pair with it, shows a likely range from the study's own independent check, and flags inputs outside the conditions the equations were built under: heart rates below 57 or above 90 percent of your age-predicted maximum, ages outside 18 to 45, and weights or VO2 max values beyond the study's range. It explains why strength training and intervals read high or rough, compares the result with the MET method for the same session, and refuses a result when the equation drops to zero or below.