In 5069 endurance athletes (abstract; 5311 in the Results and Table 1, corrected 2026-10-12, full text) tested to exhaustion, 9 of 13 age-based HRmax formulas differed significantly from the measured value
And even the four that agreed on average were wrong by about 10 bpm on the individual (RMSE 9.1-10.5)
Participants
n=5069 endurance athletes: 4043 runners (age 33.6 ± 8.1 y, 83.5% male, BMI 23.7 ± 2.5) and 1026 cyclists (age 36.9 ± 9.0 y, 89.7% male, BMI 24.0 ± 2.7), all completing maximal CPET (abstract figures).
The Results and Table 1 instead report a cohort of 5311 with 1268 cycling CPETs (1137 men, 89.67%), so the paper is internally inconsistent on the cycling sample (corrected 2026-10-12, full text). Measured HRmax: 184.6 ± 9.8 bpm running, 182.7 ± 10.3 bpm cycling (p=0.001 between modes).
Protocol
Maximal cardiopulmonary exercise test (running or cycling); eight running and five cycling HRmax equations validated externally against the measured value with Student t-test, mean absolute percentage error (MAPE) and root mean square error (RMSE)
Key Findings
9 of 13 model-mode combinations (69.2%) differed significantly (p=0.001) from measured HRmax. HRmax was overestimated by 8 formulae (61.5%) and underestimated by 5 (38.5%); overestimation reached 4.9 bpm and underestimation was in the range up to 4.9 bpm. The abstract also states that "HRmax was more often underestimated than overestimated" — the two sentences of the abstract do not agree; the per-model direction is in the full-text table below.
RMSE across all models: 9.1-10.5 bpm. MAPE up to 4.7%. The group-level bias is small; the individual error is not.
Per-model results (full text, checked 2026-09-27):
Running (predicted HRmax, mean difference, MAPE, RMSE, p):
Fox 220−age: 184.4, −0.18 bpm, 4.25%, 9.79, p=0.38 (not significant)
Arena 209.3−0.72·age: 183.7, −0.91, 3.95%, 9.13, p<0.001
Tanaka 208−0.7·age: 183.1, −1.50, 3.96%, 9.18, p<0.001
Gellish 207−0.7·age: 182.1, −2.50, 4.03%, 9.40, p<0.001
Inbar 205.8−0.685·age: 181.4, −3.17, 4.10%, 9.58, p<0.001
Londeree 206.3−0.711·age: 181.0, −3.59, 4.17%, 9.76, p<0.001
Nes 211−0.64·age: 188.2, +3.63, 4.31%, 9.69, p<0.001
Machado 218−0.8·age: 189.5, +4.94, 4.69%, 10.47, p<0.001 (worst)
Cycling:
Arena: 182.8, +0.08, 4.10%, 9.28, p=0.80
Fox 220−age: 183.1, +0.46, 4.41%, 10.07, p=0.23
Tanaka: 182.2, −0.48, 4.11%, 9.26, p=0.16
Londeree: 180.1, −2.58, 4.31%, 9.61, p<0.001
Fairbarn 201−0.63·age: 177.8, −4.90, 4.68%, 10.38, p<0.001 (worst)
The counter-intuitive result (full text): the oldest and most-criticised formula, 220−age, was among the closest in this cohort for both running (−0.18 bpm) and cycling (+0.46 bpm), while Tanaka — usually presented as its replacement — was significantly low in runners.
Authors' conclusion: prediction models "allow for limited precision" and present inaccuracies; predicted HRmax can be a supplemental method, but CPET is the preferable one.
Practical Application
In 4043 runners and 1026 cyclists (abstract; 1268 cycling CPETs in the Results, corrected 2026-10-12, full text) tested to exhaustion, 9 of 13 age-based HRmax formulas differed significantly from the measured maximum, and every formula carried an RMSE of 9.1-10.5 bpm (MAPE up to 4.7%) — so treat an age-estimated HRmax as ±10 bpm, and say so whenever zones are built on it: the athlete's real maximum is routinely a full zone away from the estimate, even when the formula is unbiased across a crowd of five thousand.
Never adjust a session because measured heart rate sat below an estimated percentage of an estimated maximum. Two estimates stacked is not a signal; it is arithmetic. If the ceiling is an estimate, a percentage of it cannot gate a decision.
Record whether HRmax was measured or estimated, and treat those as different data. A measured maximum from a race finish or a maximal test earns zone prescriptions; an estimate earns a range and a caveat.
If the athlete will train by heart rate, get a real maximum once — a maximal ramp to exhaustion, or the highest value seen in a hard race or hill effort — rather than choosing between formulas that all carry the same ±10 bpm.
Do not switch formulas hoping for accuracy. The spread between the best and worst equation here is about 5 bpm of bias; the individual error inside every one of them is twice that.
Expect the maximum to differ between sports: running was ~2 bpm higher than cycling in this population (184.6 vs 182.7). A cyclist's running zones are not their cycling zones.
Limitations
83.5-89.7% male, mean age in the mid-30s; the authors name sex, age and racial homogeneity as limits on generalisability (racial homogeneity is from the full text).
Not a masters cohort. Age-based formulas are most consequential for older athletes and the age range here does not test that end well.
HRmax is protocol-dependent: a different ramp, a different ergometer or a different motivation level shifts the measured value, so "measured" is itself not a constant.
Cross-sectional. It does not test whether zones built on an estimate produce worse training — only that the number is wrong by a known amount.
The finding that 220−age fits well is specific to this population's age distribution; it is not a claim that 220−age is physiologically correct.
The abstract's own summary of direction is inconsistent (8 over / 5 under vs "more often underestimated"); rely on the RMSE, not on the sign.
How this entry was checked and changed
Why this level
regraded 2026-09-27 from A: cross-sectional measurement study, n=5069 in the abstract, 5311 in the Results (corrected 2026-10-12, full text)
Content correction 2026-09-27
Headline "the two that agreed on average" -> the four non-significant model-mode combinations (Fox in running; Arena, Fox and Tanaka in cycling).
Added the abstract's sentence "HRmax was more often underestimated than overestimated" and flagged that it conflicts with the 8-over/5-under count in the same abstract.
Per-model table and "Caucasian only" marked as full text; n=5069 added (the abstract's total; the Results give 5311, corrected 2026-10-12, full text); Level A -> B+ (cross-sectional measurement study).
Lines labelled "full text; not checked" were read against the open-access full text (PMC10146295): 1 confirmed and relabelled.
Full text (checked 2026-10-12)
Correction: the entry gives the abstract's total sample and "1026 cyclists", but the Results and Table 1 report a cohort of 5311 EA with 1268 cycling CPETs (1137 males, 89.67%), so the paper is internally inconsistent on the cycling sample (full text, Table 1).
Cycling protocol: 5 min free-wheel warm-up, then resistance increased every 2 min (20 W for females and 30 W for males); running protocol: 5 min walk or slow jog, then +1 km·h−1 every 2 min at a constant 1% treadmill incline (full text).
Maximal effort was accepted on volitional exhaustion with Borg RPE ≥ 18 and an HR or VO2 plateau (VO2 increase < 100 mL·min−1); HR came from an ANT+ chest strap and HRmax was the unaveraged peak value (full text).
Women were 15.01% of participants (666 running, 131 cycling); female HRmax was 185.22 (9.33) bpm running and 184.38 (9.97) bpm cycling versus 184.47 (9.88) and 182.46 (10.30) bpm in males (full text, Table 1).
Measured VO2max was 53.24 (7.12) mL·min−1·kg−1 in runners and 51.67 (7.86) mL·min−1·kg−1 in cyclists (full text, Table 1).
Participants were healthy adults (≥18 years) with ≥3 months of endurance training, non-smokers on no medication, tested in one Warsaw laboratory between 2013 and 2021 (full text).
The authors state that despite statistical significance, values of ~4% and 8 beats/min at peak exercise are not necessarily clinically significant and significance may reflect the large sample (full text).