Body FormulaFitness

Running calculators

Four of the five tools here run two or more published models side by side, because on this cluster the models disagree by more than most runners realise.

Running is the part of this site where the published formulas disagree most visibly. Two race-prediction models put a marathon four minutes apart; two zone methods put the bottom of zone 2 twenty-four beats apart; three VO2 max protocols land nine points apart on the same person. Every page here runs the alternatives beside the headline and prints the gap, because the gap is the only error bar these methods can honestly offer.

Calculators in this section

Where to start

You have a run and want to know what pace it was. The pace calculator. It is the only tool in this cluster whose headline number is exactly right rather than estimated, because pace is a definition and not a fitted model.

You have a race result and want a target for a different distance. The race time predictor, which runs Riegel and Cameron together. Use a half marathon to predict a marathon if you have one; it is by far the most reliable single input.

You want a training intensity rather than a pace. Start at the max heart rate calculator to get a maximum, then the zone calculator to turn it into bands. That order matters: an error in the maximum propagates into every zone below it at about two thirds its size.

You want a single number for aerobic fitness. The VO2 max calculator, with the warning that field estimates of VO2 max are the least comparable numbers on this site.

Three named disagreements, in one place

Every page in this cluster is built around a specific published gap, and it is worth seeing them together:

Riegel against Cameron. Predicting a marathon from a 1:45 half, Riegel says 3:38:55 and Cameron says 3:43:08 — four minutes and thirteen seconds. That is an entire pacing band. A predictor showing only one of them is not more accurate, only quieter.

Karvonen against percentage of maximum. With a maximum of 184 and a resting rate of 60, the bottom of zone 2 is 134 bpm by Karvonen and 110 bpm by percentage of maximum. Twenty-four beats: walking against running. The size of that gap is (1 − the zone fraction) × the resting heart rate, so it is largest for people with a high resting rate — and it never closes until you reach maximum.

Three VO2 max protocols. The same person tests at 42.4 by the Cooper 12-minute run, 38.3 by Daniels & Gilbert VDOT from a 25:00 5K, and 47.2 by the Uth heart-rate ratio. Nine points, more than a fifth of the figure.

None of these is a scandal. They are what estimation from limited inputs looks like, and the useful response is to pick one method, use it consistently, and compare your own numbers against your own past numbers rather than against anybody else's.

The one input worth measuring properly

Across this whole cluster, one number does more damage than any other when it is wrong: maximum heart rate. An age estimate carries a residual of about ten beats a minute. Ten beats of error moves every Karvonen zone boundary by six or seven, and it moves the Uth VO2 max estimate by more than three points.

Nothing else here is nearly as leveraged. Choosing between Riegel and Cameron is worth 2%; choosing between five max-heart-rate equations is worth six beats; getting your actual maximum wrong by twenty beats, which is entirely ordinary, is worth far more than either.

What this cluster is not

These are training tools. None of them assesses your health, interprets a heart rate, produces a cardiac risk figure or a “fitness age”, and there is no fat-burning zone anywhere on this site — the label describes a real observation about fuel mix that has been repackaged as a training instruction it does not support.

Every page states its formula by name, states its limitations in a visible section rather than a footnote, and says plainly that it is not medical advice. Where a figure rests on an assumption rather than a measurement — the standard deviation behind the height percentile, the residual behind every heart-rate equation — the page names the assumption. That is the whole differentiation claim of this site, and the running cluster is where it does the most work.

Common questions

Which running calculator should I use first?

If you have just finished a run, the pace calculator. If you are planning a race, the race time predictor. If you are setting up training intensities, start with a maximum heart rate and then build zones from it — in that order, because the maximum is the input everything else inherits.

Why does every page here show more than one formula?

Because they disagree, and the disagreement is information. Two race predictors put a marathon four minutes apart; two zone methods put zone 2 twenty-four beats apart. Showing one number and hiding the other does not make the estimate better, it just conceals how much confidence it deserves.

Do I need a heart rate monitor to use these?

No. The pace calculator and the race predictor need nothing but a distance and a time. The heart-rate pages need a monitor to be worth much — and a chest strap rather than a wrist optical sensor, which frequently misreads during intervals and sometimes locks onto cadence instead of pulse.