Training numbers are mostly extrapolations from submaximal efforts, because the maximal version is either dangerous or exhausting. The Tanaka formula puts maximum heart rate at 208 − 0.7 × age, so a 35-year-old is about 183 bpm. The Epley formula estimates a one-rep max as weight × (1 + reps ÷ 30), so five reps at 100 kg predicts about 117 kg. Pace is the exception — it is a straight division of time by distance.
Each estimate has a range where it works and a range where it drifts, and knowing which you are in matters more than which formula you picked.
How reliable is a maximum heart rate formula?
Reliable as a population average and poor as an individual prediction. The old 220 − age rule overestimates for younger adults and underestimates for older ones; Tanaka fits the data better across the age range, and both carry a standard deviation of around 10 bpm.
Ten beats is enough to shift a zone boundary, which is why zones built on a percentage of estimated maximum are approximate. The Karvonen method improves on it by using heart rate reserve — maximum minus resting — which anchors the bottom of the range to a number you actually measured.
| Zone | Heart rate reserve | What it is |
|---|---|---|
| 1 | 50–60% | Recovery |
| 2 | 60–70% | Conversational aerobic base |
| 3 | 70–80% | Tempo |
| 4 | 80–90% | Threshold |
| 5 | 90–100% | Maximal intervals |
Zone 2 is the one most recreational athletes are short of. The common failure is spending most sessions in Zone 3 — hard enough to be tiring, not hard enough to drive the adaptations Zone 4 and 5 produce, and too hard to accumulate the volume Zone 2 needs.
How far can a one-rep max be extrapolated?
From sets of five or fewer, reliably. Beyond that the estimate drifts, and the formulas disagree with each other.
Epley, Brzycki and Lombardi are different fits to different data. At three reps they agree within a per cent or two; at ten they can differ by five per cent or more. Which to prefer is largely arbitrary — the useful discipline is to pick one and use it consistently, so the number tracks your progress rather than the formula’s.
The estimate is also specific to the lift and the person. Someone with high strength endurance gets more reps at a given percentage than someone built for single efforts, and the formula cannot see the difference.
What does pace actually convert to?
Ten kilometres in 50 minutes is a pace of 5:00 per kilometre, 8:03 per mile, at 12 km/h. Any two of pace, time and distance give the third, which is the whole of the arithmetic.
The conversion between minutes per kilometre and minutes per mile is where people trip, because it is not a division anyone does reliably in their head. A mile pace is always the kilometre pace multiplied by 1.609344 — so 5:00/km is 8:03/mi, not 8:00.
Pace is also the only one of the three that is a measurement rather than an estimate. What it does not do is transfer between distances: a 5K pace does not hold for a marathon, and race-prediction tables that map one to the other are models with their own error bars.
Where does a formula stop working?
At the edges of the data it was fitted to. The heart rate formulas were built on adult populations and are least reliable at both extremes of age; the rep-max formulas were fitted to trained lifters and are least reliable for beginners, whose limiting factor is technique rather than force production.
A beginner will often find a genuine one-rep max well below what a five-rep set predicts, because the skill of a maximal single has not been learnt yet. That gap closes with practice, and it means an improving estimate can reflect technique rather than strength — which is still progress, and is not the progress the number claims to measure.
What links the three?
All three are attempts to locate an intensity without going to the point of failure, and all three are more useful as a way of setting today’s session than as a number to be proud of.
The practical use of an estimated one-rep max is to calculate working weights: 75 per cent of an estimate is a perfectly good training load whether or not the estimate is exactly right. The practical use of an estimated maximum heart rate is to set a zone ceiling. Neither needs to be accurate to be useful, and both become less useful when treated as the point of the exercise.
Questions people ask
Should I test my actual maximum heart rate? It requires a genuinely maximal effort and is not appropriate for everyone. A well-executed field test gives a better number than any formula; a formula is the reasonable default for anyone not doing that.
Which one-rep max formula is best? None consistently. Consistency matters more than choice, because the value of the number is in comparing it with your own previous one.
Why is my watch’s zone different from the calculator’s? Because it may be using a different maximum, a different method, or lactate-threshold zones rather than heart-rate-reserve ones. Zones are only comparable within one method.
Does the Epley estimate work for every lift? Better for compound lifts with a long strength curve than for isolation work, where fatigue accumulates differently and the rep–weight relationship is less predictable.
Three estimates, three ranges of validity, and none of them worth testing to destruction. The heart rate calculator applies Tanaka and Karvonen, the one rep max calculator compares the formulas across rep ranges, and the pace calculator does the one part of this that is arithmetic rather than estimation.