Max Heart Rate Formulas Compared: 220 Minus Age, Tanaka, Gellish, Nes and Gulati

At age 60, the 220 minus age formula puts maximum heart rate at 160 beats per minute. Tanaka's formula says 166, Gellish's 165, and the Nes formula from Norway's HUNT study says 172.6. The authors of that Norwegian study then reported that real people scatter around their own line with a standard error of 10.8 bpm. The best-supported default for a healthy adult is Tanaka's, 208 minus 0.7 times age: it came from studies covering 18,712 people and was confirmed in a separate lab group of 514. But no age-only formula is accurate to better than about 10 beats for one person. For women, Gulati's 206 minus 0.88 times age was built on 5,437 women and gives the lowest number at every age from 20 to 80.

Two numbers settle most of the 220 minus age vs Tanaka argument. The two formulas give exactly the same answer at 40, 180 bpm. Before 40, 220 minus age is the higher of the two, by 6 bpm at age 20. After 40 it is the lower one, by 6 bpm at 60 and 12 bpm at 80. So the choice barely matters for a 35-year-old and matters quite a lot for a 70-year-old setting training zones.

Max heart rate by age: 20 to 80 under five formulas

Each formula takes age in years and returns a predicted peak heart rate in beats per minute (bpm). They are:

• Fox (1971): HRmax = 220 - age
• Tanaka, Monahan and Seals (2001): HRmax = 208 - 0.7 × age
• Gellish and colleagues (2007): HRmax = 207 - 0.7 × age
• Nes and colleagues (2013): HRmax = 211 - 0.64 × age
• Gulati and colleagues (2010), women: peak HR = 206 - 0.88 × age

Beats per minute. CalculatorVillage ran each formula on October 31, 2026, using the equation exactly as each study's abstract prints it (Fox from the Robergs and Landwehr review). Spread is the highest value in the row minus the lowest.

Slope and intercept explain every row of the grid.

Fox has the steepest slope. It drops a full beat per year of age. Tanaka and Gellish drop 0.7, Nes 0.64. Gulati's women's line drops 0.88. A slope of 1 is why 220 minus age starts high and ends low against the others.

Fox and Tanaka cross at 40. 220 - 40 = 180, and 208 - 0.7 × 40 = 208 - 28 = 180. Fox crosses Gellish at about 43 and Nes at exactly 25, so from age 26 on, Nes gives the highest number in the table.

Gellish is Tanaka minus one. Same slope, intercept one beat lower. For practical purposes they are the same formula derived two different ways, one from a meta-analysis of group averages and one from repeated tests on the same people.

Nes is always above Tanaka. The gap is 3 + 0.06 × age, from 4.2 bpm at 20 to 7.8 bpm at 80. The HUNT authors said in their abstract that earlier equations underestimated measured max in people over 30, and their line sits above the others to match.

Gulati is the lowest line at every age from 20 to 80. It sits 11.6 bpm below Fox at 20 and 4.4 bpm below at 80, and 5.6 below Tanaka at 20 widening to 16.4 below at 80. If you are a woman using a unisex formula, the Gulati column is the one most likely to move your zones down.

The last two columns show how the disagreement grows with age. With Gulati left out, so that the comparison covers only formulas meant for both sexes, the four lines stay within 7 bpm of each other up to 40 and then fan out to almost 20 bpm by 80. Most of that fan is Fox falling away below the other three.

Fox's 1971 line was never fitted

The most used formula has the thinnest pedigree. Robert Robergs and Roberto Landwehr traced 220 minus age back through textbooks in a 2002 commentary in the Journal of Exercise Physiology online. They found it in a 1971 review by Fox, Naughton and Haskell on physical activity and coronary heart disease. In that review, a figure of roughly 35 data points from earlier studies carries a legend saying no single line would represent the data well, and that the formula 220 minus age "defines a line not far from many of the data points." No regression was run.

Robergs and Landwehr rebuilt that figure from the plotted points and fitted a line to it. They got HRmax = 215.4 - 0.9147 × age, with r = 0.51 and a standard error of estimate (Sxy) of 21 bpm. On Fox's own data, then, the best straight line is not 220 minus age, and the scatter around it is about twice what later, larger studies report.

They also asked the two researchers whose names most often get attached to the formula. M. J. Karvonen told them in 2000 that he had never published original research on it; his work was on heart rate reserve, not maximum heart rate. P.-O. Åstrand said he had not published data deriving it either. Of the 18 exercise physiology textbooks listed in their Table 2, 13 printed the formula with no citation at all.

None of this makes 220 minus age useless. It makes it a rule of thumb that happens to land near the better-fitted lines for people in their 30s and 40s, and drifts away from them on both sides.

Four regressions that replaced it

Each of the other four formulas came from a regression on measured peak heart rates, but the samples differ in ways that explain why their lines differ.

Tanaka (2001) worked in two stages. First, a meta-analysis collected group mean max heart rates from 351 published studies, covering 492 groups and 18,712 people, and found HRmax strongly related to age (r = -0.90) along 208 - 0.7 × age. Then the team measured max heart rate in 514 healthy people in their own lab and got 209 - 0.7 × age, which the abstract calls virtually identical. The line did not differ between men and women, or between people with very different activity levels. The authors concluded that the 220 formula underestimates max heart rate in older adults.

Gellish (2007) used one fitness center's records instead of many studies' averages. A university health-assessment program had tested 132 members repeatedly between 1978 and 2003, for 908 maximal graded exercise tests in all. A linear mixed model, which follows the same individuals as they age, produced 207 - 0.7 × age. The authors noted that this longitudinal result confirmed the cross-sectional findings.

Nes (2013) came from the HUNT Fitness Study in Norway, run in 2007 and 2008: 3,320 healthy men and women, included only if a maximal effort could be verified. Age alone explained HRmax as 211 - 0.64 × age, with a standard error of estimate of 10.8 bpm. Sex, physical activity, VO2max level and body mass index did not change the relationship in any meaningful way.

Gulati (2010) comes from cardiology rather than exercise science. The St. James Women Take Heart Project gave symptom-limited maximal stress tests to 5,437 women without symptoms in 1992, mean age 52 (standard deviation 11), then followed them for deaths to the end of 2008. Mean peak heart rate fell with age along 206 - 0.88 × age. The authors concluded that the traditional calculation, built mostly on men, overestimates peak heart rate for age in women.

The samples explain a lot. Tanaka averaged groups, which smooths out individual scatter. Gellish followed the same people, which removes differences between people from the slope. Nes tested a large general population and counted only verified maximal efforts. Gulati tested women only, in a clinical stress-test setting. Four reasonable methods, four lines within a few beats of each other for men and women in middle age, and further apart at the ends.

The error band your calculator leaves out

A prediction formula gives the middle of a cloud of real values. The standard error of estimate (SEE, sometimes written Sxy) is the typical distance between a person's measured max and the line. Of the four regression papers, only Nes states one in its abstract, so the bands below are limited to figures actually printed:

So the Nes band is the only one that can be drawn from a primary statement. Here is what ±10.8 bpm looks like around the Nes line:

Computed by CalculatorVillage, October 31, 2026. The ±2 SEE column assumes errors roughly follow a bell curve, under which about 95% of people would fall inside it; the Nes abstract reports only the single SEE.

Compare the bands with the first table. At age 60, the five formulas run from 153.2 to 172.6, a 19.4 bpm spread. The Nes ±1 SEE band at 60 alone is 21.6 bpm wide. Choosing the right formula moves you around inside the cloud; it does not shrink the cloud. Robergs and Landwehr made the same point in 2002, after collecting 43 published equations: the best general one they found, Inbar's 205.8 - 0.685 × age, still had an Sxy of 6.4 bpm, which they called unacceptably large.

That review also pooled 30 equations from healthy samples into one line, 208.754 - 0.734 × age, with Sxy 7.2 bpm. They noted it lands very close to Tanaka's. Two separate routes to the "average of the literature" ending up at about 208 minus 0.7 times age is part of why Tanaka is the usual default now.

Evidence table: what the papers themselves report

Blog posts often attach claims to these formulas that the studies do not make. The table below keeps to what each abstract, or the open-access full text, states. Where a study tested several formulas against measured values, the result is given as the authors put it.

Two results in that table pull against the usual advice and are worth a closer look.

Shookster and colleagues found that every equation they tested, Tanaka included, showed proportional bias except Fox. The others underestimated max in people whose measured max was low and overestimated it in people whose max was high. On a 99-test sample, Fox came out as the least biased. That does not overturn Tanaka's 18,712-person meta-analysis; it is one small sample. But it is a reminder that "Tanaka is more accurate" is a statement about groups and especially about older groups, not a guarantee for one person.

Esco and colleagues tested young female athletes, the group where the formulas disagree least by age but most by sex. Fox overshot their measured max by about 12.6 bpm on average and Tanaka by about 7.1. Gulati was within about 1.2 bpm. All five equations had nearly the same SEE, between 5.0 and 5.4 bpm; what separated them was the bias, the average miss, which Gulati nearly removed for this group.

Tanaka or 220 minus age at your age

With the grid and the evidence side by side, the choice by age group comes out like this. It applies to healthy adults; people with heart disease, and anyone taking medication that changes heart rate, should get their zones from the clinician who knows their case.

For a 65-year-old man, the difference is concrete. 220 - 65 = 155. Tanaka gives 208 - 45.5 = 162.5. Training at "75% of max" means 116 bpm on the first and 122 on the second. That is a 6 bpm difference in the target, at the age where Tanaka's paper says the old formula falls short.

One runner, two zone systems

Take a hypothetical runner: a 45-year-old woman with a resting heart rate of 52 bpm, measured on waking. Her predicted max under each formula is 175 (Fox), 176.5 (Tanaka), 175.5 (Gellish), 182.2 (Nes) and 166.4 (Gulati). There are two common ways to turn a max into zones.

Percentage of max (%HRmax): target = max × percentage. Resting heart rate plays no part.

Karvonen, or heart rate reserve (%HRR): target = resting + percentage × (max - resting). Max minus resting is the heart rate reserve. Robergs and Landwehr credit the reserve concept to Karvonen's 1957 study of training and heart rate.

Here are her five zones both ways, using 220 minus age (175) as the max:

bpm, computed by CalculatorVillage, October 31, 2026, rounded to the nearest beat.

The last column follows a clean rule: the Karvonen target minus the %HRmax target equals (1 - percentage) × resting heart rate. At 70%, that is 0.3 × 52 = 15.6, which shows as 15 after each target is rounded. At 50% it is 26. So "70% intensity" can mean 123 bpm or 138 bpm for the same woman depending on which system the plan was written in. The labels are the same, but the numbers are 15 beats apart.

The two systems were never meant to share percentages. Swain and colleagues, testing 162 young adults in 1994, found that 40%, 60%, 80% and 85% of VO2max corresponded on average to 63%, 76%, 89% and 92% of max heart rate. Robergs and Landwehr's Table 1, adapted from that work, treats percentage of heart rate reserve as roughly equal to percentage of VO2max. Put together: 60% of reserve sits near 76% of max, not 60% of max. For our runner, 60% of reserve is 126 bpm and 76% of max is 133 bpm. They are close, not equal: Swain's figures are group averages, and how a percentage of reserve translates into a percentage of max depends on each person's resting rate relative to max.

Now change the formula, keeping Karvonen:

bpm, computed by CalculatorVillage, October 31, 2026; Karvonen with a resting rate of 52.

Fox and Tanaka agree within 2 bpm at her age, as the crossover at 40 predicts. Gulati moves her top two zones down by about 6 to 9 bpm against Fox. Nes moves them up by 6 to 7. A run she would log as "Aerobic" at 145 bpm under Fox is "Anaerobic" under Gulati and still "Aerobic" under Nes. Nothing about her body changed; only the formula did.

Making this site's calculator use a different max

The target heart rate calculator on CalculatorVillage takes two inputs, age and resting heart rate, and fixes max heart rate at 220 minus age. It then applies Karvonen to draw five zones at 50, 60, 70, 80 and 90% of heart rate reserve, with the top of the fifth zone set to the estimated max. Ages and resting rates are read as whole numbers. There is no formula switch.

You can still make it use any max you like, Tanaka's, Gulati's or a value you measured, by entering a substitute age:

Substitute age = 220 - the max you want.

The calculator then computes 220 - (220 - max) = your max, and every Karvonen zone follows from it. For our runner with resting rate 52:

Results replicate the calculator's own rounding (each boundary rounded to the nearest beat), checked by CalculatorVillage on October 31, 2026.

Because the age box takes whole numbers, a non-integer max like Tanaka's 176.5 has to be rounded to 176 or 177. That moves each boundary by at most one beat. The Gulati row differs by a beat in two places from the earlier table for the same reason: the calculator works from a max of 166 rather than 166.4.

If you would rather adjust by hand, there is a quick rule. When the max changes by some number of beats, each Karvonen boundary moves by that change times its percentage. Going from Fox (175) to Nes (182.2) is +7.2 bpm, so the 80% boundary moves up 0.8 × 7.2 = 5.8 bpm, from 150 to about 156, matching the table. The resting heart rate box works normally either way; the substitute age changes only the max.

The calculator's page also notes, in its own FAQ, that it uses 220 minus age and that past 40 its zones run lower than Tanaka would give. The substitute-age entry is the fix for that.

How a 10 bpm miss moves each zone

If the true max is 10.8 bpm away from the formula's answer, one Nes standard error, every zone boundary in either system moves by the percentage times 10.8:

For our runner, each Karvonen zone is 10% of a 123 bpm reserve, about 12.3 bpm wide. A one-SEE miss shifts the 80% line by 8.6 bpm, about 70% of a zone width. If errors follow a bell curve, about a third of people have a true max more than one SEE from the line, which is why two runners of the same age, using the same formula, can feel completely different at the same "Zone 3" number.

Robergs and Landwehr worked the same sum for a 25-year-old with a true max of 192 and resting rate 50. The 60 to 80% reserve range is 135 to 164 bpm. If the formula underestimates max by 8 bpm, it becomes 130 to 157. They judged errors of 8 bpm or less acceptable for setting training ranges, and argued that much tighter accuracy, under 3 bpm, is needed when max heart rate feeds a VO2max estimate. On that test, an age formula with a 10.8 bpm standard error is borderline for training zones and not good enough for fitness estimates that lean on max heart rate.

The shift in beats is the same in both systems, but the zones are not the same width. In %HRmax, a 10-point zone for our runner is 10% of 175, or 17.5 bpm, so an 8.6 bpm miss is about half a zone. In Karvonen the zone is 12.3 bpm, so the same miss is about 70% of one. Karvonen's narrower zones are more sensitive to a wrong max, which is a reason to pin the max down before relying on them.

Getting a measured max: lab test or field effort

The studies that set formulas against measured values point the same way. Shookster and colleagues advised using graded exercise test data to set max heart rate when it is available, and Esco and colleagues said age-predicted values should be used only with caution because of their wide limits of agreement. Robergs and Landwehr wrote that a properly measured max is accurate to within about 2 bpm if the person truly reaches maximal effort, against 7 to 11 bpm for the formula.

For a healthy runner, the practical options are a supervised graded exercise test or the highest reading recorded on a monitor at the end of a hard, all-out race or repeated hill effort after a full warm-up. A field reading is a floor rather than a ceiling: you may not have reached your true max, so the highest figure you see over several hard efforts is a better guide than any single one. This is general fitness information, not medical advice. Anyone with heart disease, symptoms on exertion, or medication that changes heart rate should test only under clinical supervision, if at all.

Once you have a measured max, the substitute-age entry above turns it into zones in the heart rate calculator. A measured max also improves the other numbers that depend on heart rate. The Rockport walk test in the VO2 max calculator uses your heart rate at the end of a timed one-mile walk, and the running pace calculator turns a distance and a time into pace, so you can record which pace holds you inside a given zone. For energy rather than effort, the BMR and TDEE equations comparison shows a similar gap between formulas and measurement, and the one rep max formulas comparison does the same for strength. More training tools are collected in the fitness hub.

If you train by heart rate after 50 and have only ever used 220 minus age, put your age into the Tanaka line once (208 minus 0.7 times age) and compare. If the gap is 6 bpm or more, your hardest sessions have probably been labelled one zone too high, and entering 220 minus the Tanaka figure as your age in the calculator will show you where the lines should sit.

Sources

• Tanaka H, Monahan KD, Seals DR. Age-predicted maximal heart rate revisited. Journal of the American College of Cardiology 2001;37(1):153-156. PubMed abstract, checked October 31, 2026.
• Gellish RL, Goslin BR, Olson RE, et al. Longitudinal modeling of the relationship between age and maximal heart rate. Medicine and Science in Sports and Exercise 2007;39(5):822-829. PubMed abstract, checked October 31, 2026.
• Nes BM, Janszky I, Wisløff U, Støylen A, Karlsen T. Age-predicted maximal heart rate in healthy subjects: The HUNT fitness study. Scandinavian Journal of Medicine and Science in Sports 2013;23(6):697-704. PubMed abstract, checked October 31, 2026.
• Gulati M, Shaw LJ, Thisted RA, et al. Heart rate response to exercise stress testing in asymptomatic women: the St. James Women Take Heart Project. Circulation 2010;122(2):130-137. PubMed abstract, checked October 31, 2026.
• Robergs RA, Landwehr R. The surprising history of the "HRmax=220-age" equation. Journal of Exercise Physiology online 2002;5(2):1-10. Full text (PDF) from the American Society of Exercise Physiologists, checked October 31, 2026. Source for the Fox 1971 figure legend, the refit of Fox's data, Tables 1, 3 and 5, and the Karvonen and Åstrand correspondence.
• Shookster D, Lindsey B, Cortes N, Martin JR. Accuracy of commonly used age-predicted maximal heart rate equations. International Journal of Exercise Science 2020;13(7):1242-1250. PubMed abstract, checked October 31, 2026.
• Esco MR, Chamberlain N, Flatt AA, et al. Cross-validation of age-predicted maximal heart rate equations among female collegiate athletes. Journal of Strength and Conditioning Research 2015;29(11):3053-3059. PubMed abstract, checked October 31, 2026.
• Cicone ZS, Holmes CJ, Fedewa MV, et al. Age-based prediction of maximal heart rate in children and adolescents: a systematic review and meta-analysis. Research Quarterly for Exercise and Sport 2019;90(3):417-428. PubMed abstract, checked October 31, 2026.
• Swain DP, Abernathy KS, Smith CS, et al. Target heart rates for the development of cardiorespiratory fitness. Medicine and Science in Sports and Exercise 1994;26(1):112-116. PubMed abstract, checked October 31, 2026.
• Karvonen MJ, Kentala E, Mustala O. The effects of training on heart rate; a longitudinal study. Annales Medicinae Experimentalis et Biologiae Fenniae 1957;35(3):307-315. PubMed record (no abstract), checked October 31, 2026; cited for the origin of the heart rate reserve method as described by Robergs and Landwehr.
• CalculatorVillage target heart rate calculator source (calculateHeartRate in the site's health math library), read October 31, 2026, for the 220 minus age max, the Karvonen zones and the rounding replicated above.