Target Heart Rate Zones Calculator: Five Published Maximum-Heart-Rate Equations, Percentage-of-Maximum and Karvonen Side by Side, and the Beats Between Them

Every heart rate zone on every watch and every chart rests on two guesses stacked on top of each other: an equation that predicts your maximum heart rate from your age, and a rule that turns a percentage into a number of beats. This page prints five published maximum equations together — Fox’s 220 − age, Tanaka 2001, Gellish 2007, Nes 2013 and Astrand — and computes every zone BOTH as a percentage of maximum AND by Karvonen’s heart rate reserve, because those two rules routinely put the same zone in windows that do not overlap. The published standard deviation of an age-predicted maximum is 10 to 12 beats a minute, so the spread is printed as an output rather than mentioned in a footnote.

These are estimates from published formulas, not measurements of you, and they assume you are well enough to train. Build up gradually, do not attempt a maximum effort alone or without sound technique, and stop and get advice if you have chest pain, unusual breathlessness, dizziness or palpitations.

Two guesses stacked, and the exact amount by which the two intensity rules disagree

The five age-based equations across the adult range, and the beats between them

One 50-year-old, resting heart rate 60: the same five zones under the two intensity rules

Published agreement between predicted and measured maximum heart rate, nine equations, 99 exercise tests

Where each figure on this page comes from, and what was deliberately left out

Why a zone boundary is a region rather than a line, and why naming the rule matters more than choosing the equation

A heart rate zone is a prediction built on a prediction, and this page is laid out so you can see both of them. The first prediction is your maximum heart rate from your age. The second is the rule that turns a percentage into beats. Neither is a measurement of you, the errors do not cancel, and the second one — which almost nobody thinks about — is usually the larger. That is why the first row under the answer is a spread and not a number.

Start with 220 − age, because it is everywhere and because its reputation and its record do not match. It is attributed to Fox, Naughton and Haskell in 1971, and the attribution is generous: in that paper the line is drawn through data compiled from other studies rather than fitted as a regression, and Robergs and Landwehr traced the history in 2002 and concluded it has no scientific merit as a prediction for an individual. Its published standard deviation across individuals is 10 to 12 beats a minute. Tanaka, Monahan and Seals replaced it in 2001 with 208 − 0.7 × age, from a meta-analysis of 351 studies covering 18,712 people plus a laboratory study of 514 people aged 18 to 81; in that laboratory sample the scatter around the regression line was about 10 beats a minute. Note what that means. The better equation has essentially the same between-person scatter. What Tanaka fixes is the BIAS: 220 − age runs high in young adults, crosses the Tanaka line at exactly age 40, and from there increasingly runs low — about 10 beats low at 70 on the equations alone, and more than 20 beats low for some older individuals once the scatter is added. And when nine equations were tested against 99 graded treadmill tests, the root mean square error of 220 − age was 11.65 beats against 10.71 for Gellish and 10.74 for Tanaka — under one beat of improvement — and 220 − age was the only one of the nine without significant proportional bias. The honest summary is that 220 − age is badly founded, biased by age, and in a general population not measurably much worse than its replacements. All three of those are true at once, and a page that told you only the first would be selling you a different number rather than a better understanding.

Now the part that is bigger and almost never mentioned: percentage of maximum and Karvonen are not interchangeable, and for the lower three zones they often do not overlap at all. Percentage of maximum takes the fraction of the maximum. Karvonen takes the fraction of the reserve — maximum minus resting — and adds resting back. The difference between the two boundaries is exactly resting heart rate multiplied by one minus the fraction, an identity that does not involve the maximum at all: at a resting rate of 60 it is 30 beats at the bottom of zone 1, 18 at the bottom of zone 3 and 6 at the bottom of zone 5. Since a zone is only a tenth of the maximum wide on the percentage rule, that gap can exceed the whole width of the zone. It does so whenever resting heart rate exceeds a tenth of the maximum divided by one minus the fraction — above about a fifth of maximum for zone 1, a quarter for zone 2 and a third for zone 3. For a 50-year-old with a maximum of 173 those thresholds are 35, 43 and 58 beats a minute, which most adults are above. Worked out for that reader at a resting rate of 60, zone 3 is 121 to 138 beats by one rule and 139 to 150 by the other: two people following the same zone label share no heart rate at all. The practical instruction is short. Find out which rule your watch, chart or coach is using before you compare any two zone numbers, and never mix them.

Karvonen’s name is attached to the method on thinner grounds than people assume. The 1957 paper by Karvonen, Kentala and Mustala is a longitudinal training study: it looked at what different training intensities did to resting, working and maximum heart rates, and it identified about 60% of heart rate reserve as the threshold above which improvement appeared. It was not a validation of a prescription formula, and the reserve arithmetic that now carries the name is a later convenience. That does not make the method wrong — scaling an intensity to the range a person actually has available is a defensible idea, and arguably more defensible than scaling it to the top end alone — but it does mean neither rule on this page has a strong claim to being the correct one. They are two conventions with different arithmetic, and the honest thing a calculator can do is print both.

The five zones themselves are a convention with no primary source, and the page says so rather than citing an authority it cannot name. The boundaries are round tens of a percentage. Nothing physiological happens at 70% in general: the ventilatory and lactate thresholds that zone schemes are meant to stand in for sit anywhere from roughly 60% to roughly 90% of maximum heart rate in different people, and they move with training within one person — which is exactly the opposite of a fixed percentage. The intensity figures on this page that do come from a named, freely usable source are CDC’s: moderate intensity 64 to 76% of maximum heart rate and vigorous 77 to 93%. Lay those over the deciles and they do not line up, because they were never derived from the same thing. Two figures are also cited from an ACSM position stand for the reserve-based equivalents, moderate 40 to 59% and hard 60 to 84% of heart rate reserve. Worth noticing while reading any of these: CDC’s own published band has itself changed — an earlier version of the same page gave moderate as 50 to 70% and vigorous as 70 to 85% of maximum, which is a different answer from the current 64 to 76% and 77 to 93%. A percentage band is an editorial judgement about where to draw a line on a continuum, and it gets redrawn.

What to do instead of chasing a boundary. Three things that cost nothing and are not downstream of an equation. The talk test: if you can hold a conversation in full sentences you are in the moderate region, if you can manage short phrases you are in the vigorous region, and if you cannot speak you are above both. Rating of perceived exertion, which correlates with intensity well enough to prescribe from and needs no device. And a heart rate you have actually measured at a known effort — the rate you can hold for an hour, for instance — which is a measurement of you rather than a prediction about people your age. If you want a predicted maximum replaced by a measured one, a graded exercise test in a laboratory or clinic gives you that, and gives you a measured VO₂ max at the same time; the VO₂ max page sets out what the field-test alternatives can and cannot do, and the one-rep-max page is the strength-side counterpart to the same problem: an estimate standing in for a maximal effort nobody needs to perform. The energy side of training belongs to the energy requirement page, which compares five predictive equations for resting energy expenditure in the same spirit.

When a heart rate is a reason to stop rather than a number to hit. Chest pain or pressure, unusual or disproportionate breathlessness, dizziness, feeling faint, or a pounding or irregular heartbeat during or shortly after exercise are reasons to stop and get medical advice, and they are reasons regardless of what any zone on this page says. So is a resting heart rate that has changed substantially without explanation. Nothing on this page is screening for anything, and a figure in a zone is not reassurance.

Frequently asked questions

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References

1. Fox SM 3rd, Naughton JP, Haskell WL. Physical activity and the prevention of coronary heart disease. Ann Clin Res 1971;3:404–32 — the origin of 220 − age. NOTE on what this citation does and does not support: the equation appears here as a line through compiled data rather than as a regression the authors fitted and reported with error terms, which is the substance of the criticism in the next reference. The primary article was not read in full for this page; its role as the source of the equation is taken from Robergs & Landwehr and from Shookster et al., both of which cite it as such.
2. Robergs RA, Landwehr R. The surprising history of the “HRmax = 220 − age” equation. J Exerc Physiol Online 2002;5(2):1–10. The review that traced the equation to Fox 1971 and concluded it has no scientific merit for predicting an individual’s maximum heart rate. WHAT COULD NOT BE ESTABLISHED: the full text was not reachable from here, so no figure is quoted directly from it on this page. The ±10 to 12 beats a minute standard deviation attributed to 220 − age on this page is taken from Shookster et al. 2020, which states it explicitly, and is consistent with the roughly 10 beats a minute scatter Tanaka et al. report around their own regression and the 10.8 beats a minute standard error Nes et al. report around theirs.
3. Tanaka H, Monahan KD, Seals DR. Age-predicted maximal heart rate revisited. J Am Coll Cardiol 2001;37(1):153–6. Source of 208 − 0.7 × age, this page’s default. Two datasets: a meta-analysis of 351 studies covering 492 subject groups (161 female, 331 male) and 18,712 subjects, in which age alone accounted for about 80% of the between-person variance in maximum heart rate (r = −0.90); and a laboratory study of 514 healthy subjects aged 18 to 81, in which the standard deviation around the regression line was approximately 10 beats a minute. Also the source of the statement on this page that 220 − age overestimates maximum heart rate in young adults, intersects the new equation at age 40, and then increasingly underestimates it — by about 10 beats a minute at age 70 on the equations alone, and by more than 20 beats for some older adults once the between-person scatter is included.
4. Gellish RL, Goslin BR, Olson RE, McDonald A, Russi GD, Moudgil VK. Longitudinal modeling of the relationship between age and maximal heart rate. Med Sci Sports Exerc 2007;39(5):822–9. Source of 207 − 0.7 × age, from 908 graded exercise tests in 132 individuals followed over 25 years — the only longitudinal design among the equations here, which matters because a cross-sectional fit and a within-person decline are different quantities. WHAT COULD NOT BE ESTABLISHED: no standard error of estimate was available in the abstract consulted, so none is quoted.
5. Nes BM, Janszky I, Wisløff U, Støylen A, Karlsen T. Age-predicted maximal heart rate in healthy subjects: the HUNT Fitness Study. Scand J Med Sci Sports 2013;23(6):697–704. Source of 211 − 0.64 × age, from 3,320 healthy subjects, with a standard error of estimate of 10.8 beats a minute that the authors explicitly say must be taken into account. Also the source of the finding that previously suggested prediction equations underestimated measured maximum heart rate in subjects older than 30, and that no interaction was found with sex, physical activity, VO₂ max level or body mass index group — which is why four of the five equations on this page have no sex term.
6. Gulati M, Shaw LJ, Thisted RA, Black HR, Bairey Merz CN, Arnsdorf MF. Heart rate response to exercise stress testing in asymptomatic women: the St James Women Take Heart Project. Circulation 2010;122(2):130–7. Source of 206 − 0.88 × age for women. PROVENANCE NOTE: the primary article was not reachable from here; the equation and its female-only population are taken from Shookster et al. 2020, which tests it and reports it in that form, and the page says so rather than implying the original was read.
7. Shookster D, Lindsey B, Cortes N, Martin J. Accuracy of 5 common age-predicted maximal heart rate equations. Int J Exerc Sci 2020;13(7):1242–50. Source of the nine-equation agreement table on this page: 99 graded treadmill tests to volitional fatigue in a general population, included only where the respiratory exchange ratio exceeded 1.10. Bias, limits of agreement and root mean square error per equation are reproduced as published. Also the source of the ±10 to 12 beats a minute standard deviation quoted for 220 − age, of the Astrand (216.6 − 0.84 × age), Arena (209.3 − 0.72 × age) and Fairbarn (208 − 0.8 and 201 − 0.63 × age) coefficients used here, and of the authors’ conclusion that all nine equations agree poorly with measured maximum heart rate and that 220 − age was the only one without significant proportional bias. CAVEAT stated on the page as well as here: n = 99 is a small sample on which to rank nine equations, and the ranking should not be treated as settled.
8. Karvonen MJ, Kentala E, Mustala O. The effects of training on heart rate: a longitudinal study. Ann Med Exp Biol Fenn 1957;35(3):307–15. The paper the heart rate reserve method is named after. What it actually did: examined the effect of different training intensities on resting, working and maximum heart rates, and identified about 60% of heart rate reserve as the threshold above which improvement was seen. WHAT COULD NOT BE ESTABLISHED: the sample size and design details of the 1957 study could not be confirmed from any source reachable here, and the page therefore makes no claim about them beyond the 60% threshold, which is reported in a historical review of Karvonen’s work in the BC Medical Journal. The reserve arithmetic now universally called the Karvonen formula is a later convenience rather than something that paper validated, and the page says so.
9. Centers for Disease Control and Prevention. Target Heart Rate and Estimated Maximum Heart Rate. Source of the only intensity bands on this page taken from a named, freely usable authority: estimate maximum heart rate as 220 − age; moderate-intensity physical activity is 64 to 76% of that maximum and vigorous-intensity is 77 to 93%. This page’s engine reproduces both of CDC’s worked examples to the beat. A 50-year-old at moderate intensity: 170 × 0.64 = 108.8 and 170 × 0.76 = 129.2, which round to CDC’s printed 109 and 129. A 35-year-old at vigorous intensity: 185 × 0.77 = 142.45 and 185 × 0.93 = 172.05, which round to CDC’s printed 142 and 172. The secondary rows here print one decimal place instead of rounding to a whole beat, so a reader checking them against CDC’s page will see 108.8 where CDC says 109. PROVENANCE NOTE, and it matters: cdc.gov was not reachable from the environment this page was written in, so the figures were taken from two independent republications of the page and cross-checked against a third (a US Department of Defense human performance resource that cites CDC 2020 for the same 64–76% and 77–93% bands). A fourth republication, of an earlier version of the same CDC page, gives moderate as 50 to 70% and vigorous as 70 to 85% — so CDC’s own published band has changed, which is recorded on the page because it shows what kind of figure a percentage band is.
10. American College of Sports Medicine position stand, The recommended quantity and quality of exercise for developing and maintaining cardiorespiratory and muscular fitness, and flexibility in healthy adults. Med Sci Sports Exerc 1998;30(6). Four figures only are cited from it — moderate intensity 40 to 59% of heart rate reserve and hard 60 to 84% — and no ACSM table or text is reproduced anywhere on this page, in line with this site’s standing position on guideline bodies. WHAT COULD NOT BE ESTABLISHED: the corresponding figures in the current position stand (Garber CE et al., Med Sci Sports Exerc 2011;43(7):1334–59) could not be verified from a source reachable here. A vigorous band of 60 to 89% of heart rate reserve is widely quoted for the later guidance and is NOT stated on this page, because it could not be traced to the document itself.
11. LICENSING POSITION taken for this page, recorded because it determined what the page contains. Every maximum-heart-rate equation here is a two-coefficient linear relation published in a journal article: an arithmetic statement, not a protected expression, and used freely. The Bland–Altman biases, limits of agreement and root mean square errors in the agreement table are measurements, reproduced with full attribution to Shookster et al. 2020, which appeared in a diamond open-access journal. The intensity bands are treated differently: CDC is a United States Government work and its bands are reproduced and computed; ACSM’s are cited as four bare figures with no table, no criteria list and no recommendation text. No guidance from the UK national institute is used anywhere, because its open content licence is United Kingdom-only and forbids display of the licensed information beside advertising, and this site carries advertising; and no World Health Organization material is used or reached through a republisher, because WHO publications are licensed non-commercially. The five-zone decile scheme is presented as a convention precisely because the named schemes in circulation are commercial coaching and consumer-device products: this page uses only round tenths of a percentage, which is arithmetic, and reproduces no vendor’s zone table, zone names or training prescriptions.
12. Derivations and checks performed for this page rather than taken from a source, recorded so they can be checked. (1) The spread between the five age-based equations, in bpm: 7.0 at age 20, 5.8 at 30 (the narrowest), 6.4 at 40, 9.0 at 50, 12.6 at 60, 16.2 at 70, 19.8 at 80 and 23.4 at 90. The widening is a slope effect, not noise. (2) Fox minus Tanaka is the exact identity 12 − 0.3 × age, so the two cross at exactly age 40, are 6.6 beats apart at 18 and 15 beats apart at 90. (3) The Karvonen boundary minus the matching percentage-of-maximum boundary is the exact identity HR_rest(1 − f), independent of the maximum: 30, 24, 18, 12 and 6 beats at the bottoms of zones 1 to 5 for a resting rate of 60. (4) The two rules’ windows for one zone are disjoint when HR_rest > 0.1 HR_max/(1 − f), which at a maximum of 180 is a resting rate above 36, 45, 60 and 90 bpm for zones 1 to 4, and is impossible for zone 5. (5) An error of δ beats in the maximum arrives at a zone edge as δf beats, so the ±10 beat standard deviation becomes a 14 beat window at the bottom of zone 3 and an 18 beat window at the bottom of zone 5. (6) Every figure in this page’s worked example and in both of its computed tables was produced by the same engine that answers the calculator, and CDC’s two published worked examples were reproduced to the beat as a check on the percentage arithmetic.

CalcEngines health calculators are for education and for checking arithmetic that has already been decided elsewhere. They are not medical advice, they do not decide what to give, and they do not replace the judgement of a doctor, nurse, midwife or dietitian who knows the person in front of them. Every figure depends on the values you enter and on the assumptions stated on the page — check it against the prescription, the product label and your local policy before acting on it.