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Formula comparison

Tanaka vs Karvonen vs 220-Age

The 220 − age formula everyone learned is reliably wrong by ±10–12 bpm. Tanaka 2001 cut that error by 25%. Karvonen adds individualisation via resting heart rate. Here\'s when each is the right choice for setting training zones.

The 60-second summary

220 − age = Fox, Naughton, Haskell 1971. The pop-culture default. ±10–12 bpm error. Acceptable for young adults; increasingly inaccurate with age.

Tanaka 2001 = 208 − 0.7 × age. Validated in 18,712 subjects across 351 studies. Cuts prediction error by ~25% vs 220-age, especially for adults 30–70.

Karvonen 1957 = uses Heart Rate Reserve (HRmax − RHR) for individualised zones. Requires resting heart rate measurement. Best when you have RHR data.

Practical recommendation: Tanaka for HRmax estimate, then Karvonen for zone calculation if you have RHR. Skip 220-age entirely.

The three formulas

220 − age (Fox, Naughton, Haskell, 1971): Derived from a small dataset of 35 references with limited methodological standardisation. Published as a rough teaching tool, never intended as a precise predictor. Has standard error of ±10–12 bpm — meaning two people of the same age can have a true HRmax 24 bpm apart.

Tanaka (208 − 0.7 × age, 2001): Tanaka, Monahan, and Seals published their meta-analysis in the Journal of the American College of Cardiology after pooling 351 studies covering 18,712 subjects across a wide age range. The Tanaka formula reduces prediction error by approximately 25% vs 220-age and is particularly more accurate for adults aged 30–70. It\'s the current evidence-based standard for HRmax estimation in the absence of direct measurement.

Karvonen (1957): Uses Heart Rate Reserve (HRR = HRmax − RHR) rather than HRmax alone. Target HR = RHR + (intensity% × HRR). This individualises zones based on cardiac efficiency — well-trained athletes with low resting heart rates get appropriately lower target HRs at the same percentage intensity. Karvonen is the most accurate formula for zone calculation when RHR is known and reliable.

Head-to-head comparison

Dimension220 − ageTanakaKarvonen
Year197120011957
Validation N~35 references18,712 subjectsn/a (uses RHR)
Inputs neededAgeAgeAge + RHR
HRmax error±10–12 bpm±8–10 bpmUses externally estimated HRmax
Best forQuick approximationHRmax in absence of RHRZone calculation with RHR
Used by Garmin / Apple defaultsYes (frequently)Some watchesOptional in most apps
Accuracy at age 30AcceptableBetterBest (with RHR)
Accuracy at age 60PoorAcceptableGood (with RHR)

Why 220-age is so wrong

The 220 − age formula came from a 1971 paper by Fox, Naughton, and Haskell — a teaching review, not an original research study. It was derived as a rough approximation from ~35 prior references with limited methodological standardisation. Even Fox himself acknowledged the formula was a "best estimate" with substantial error.

Standard error of ±10–12 bpm. For a 35-year-old, the formula predicts HRmax of 185, but the actual lab-measured value for two different 35-year-olds can range from 173 to 197 — a 24 bpm spread. Setting Zone 2 (60–70% HRmax) becomes meaningless when the underlying HRmax estimate is that imprecise. The formula remains in use mostly because the equipment industry hasn\'t updated defaults — but evidence-based practice should use Tanaka instead.

When Tanaka is the right choice

Tanaka 2001 is the default formula when you don\'t have a reliable resting heart rate measurement or a lab-measured HRmax. It\'s a population-level estimate, but a better population-level estimate than 220-age across most adult age ranges. Use it for:

When Karvonen is the right choice

Karvonen requires a reliable resting heart rate measurement. RHR is best measured first thing in the morning before getting out of bed, averaged across multiple days. A typical adult RHR is 60–80 bpm; trained endurance athletes can have RHR in the 40s; elite endurance athletes (Tour de France cyclists, world-class runners) can have RHR in the 30s.

Karvonen formula: Target HR = RHR + (intensity% × HRR), where HRR = HRmax − RHR. Example: A 35-year-old with HRmax 188 (via Tanaka) and RHR 60 has HRR of 128. Zone 2 at 60–70% intensity = 60 + (0.60 to 0.70 × 128) = 137 to 150 bpm. This is more individualised than calculating 60–70% of HRmax directly (113 to 132 bpm), which would understate the target for a fit individual.

Use Karvonen when you have reliable RHR data and want personalised zones — especially as RHR drops with training, the same intensity percentage produces a different (correctly higher) target HR, automatically scaling zones to improving fitness.

What about lab measurement?

The gold standard for HRmax is a graded maximal exercise test (treadmill or bike) under controlled conditions, ideally in a sports lab. Cost: $100–300 in most cities, often bundled with VO₂ max testing. Worth it for: competitive athletes setting precise training zones, anyone training seriously with HR-based programming, anyone whose Tanaka or Karvonen-calculated zones produce results that "feel wrong" (too hard or too easy at target HR). For recreational fitness, formula-based zones are adequate and the lab test isn\'t necessary.

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FAQ

Why is 220 minus age still used if Tanaka is more accurate?
Inertia. The 220 − age formula was published by Fox, Naughton, and Haskell in 1971 as a rough approximation derived from a small dataset, and despite being repeatedly shown to have ±10–12 bpm prediction error it became the industry standard for fitness equipment, watches, and pop guidance. Even Apple Watch defaults to 220 − age unless you explicitly customise. The Tanaka et al. 2001 paper in the Journal of the American College of Cardiology analysed 351 studies covering 18,712 subjects and showed (208 − 0.7 × age) reduces prediction error by ~25%, but the older formula remains in widespread use simply because changing defaults requires effort.
Which formula should I actually use?
For setting heart rate training zones: Tanaka (208 − 0.7 × age) if you don't have a resting heart rate measurement; Karvonen (Heart Rate Reserve method) if you do. Karvonen is the most personalised because it accounts for individual cardiac efficiency via RHR. The 220 − age formula is acceptable for young adults (under 30) but increasingly inaccurate with age — by 60, it can be 10+ bpm off from a treadmill-measured true HRmax. None of the field formulas match the accuracy of a graded exercise test in a lab, where actual HRmax can be 10–15 bpm above or below any formula prediction.
What's "Zone 2" and why does everyone talk about it now?
Zone 2 is the second of five heart rate zones, typically defined as 60–70% of HRmax. It corresponds to the first lactate threshold — the highest intensity you can sustain with primary reliance on fat oxidation and aerobic metabolism. Zone 2 training has become popular because it builds mitochondrial density and fat-burning capacity without producing the recovery cost of higher-intensity work. The 2006 Seiler & Kjerland study of elite endurance athletes showed they spend ~80% of training time below lactate threshold — primarily Zone 2 — and only 20% at high intensity. This "polarised" 80/20 distribution produces superior VO₂ max gains and lower injury rates than threshold-heavy training.
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