Tools

Calculators that show their working

Running calculators are strange software. There are hundreds of them, they rank well, and a startling number will not tell you what formula they use. Some of the most-linked ones put the answer behind an email form. Others print a single number to the second, from a model whose published error bar is several minutes wide, and let you believe it.

The tools here work differently in four specific ways.

The formula is printed on the page. Not "based on proven sports science" — the actual equation, with the paper it came from, the year, and a link. If you want to check the arithmetic in a spreadsheet, you can.

Disagreement is shown, not hidden. The race predictor runs Riegel, VDOT and Cameron and prints all three, because the spread between them is the most useful thing on the page. When three published models put your marathon fourteen minutes apart, a single confident number is not an answer, it is a guess with better typography.

Nothing is gated and nothing needs an account. No email address, no sign-up, no "unlock your results". The result is in the page's HTML, so it is readable with JavaScript switched off, quotable, and it survives being pasted into a message to your running group.

The limits are stated. Every tool has a section saying where it breaks down. Heart-rate formulas carry a population standard deviation of ten beats or more, and a formula-derived zone can easily be wrong for you by that much. Race predictors extrapolate speed and know nothing about whether you have done the long runs. Treadmill conversions assume a calibrated belt, which is a real assumption. Saying this does not make the tools less useful. It makes them usable.

Each tool page also carries a worked example with real numbers, so the page answers something even before you touch a field, and a changelog, so you can see when the maths last changed and why.

If you want the explanation rather than the number, every tool links to the article behind it and to the glossary terms it uses. And if you want these numbers computed continuously from your own runs rather than typed in one at a time, that is what the app is for.