Free running calculators
and training science guides

Running pace — time per distance — is the primary metric of distance running. Unlike speed (which measures distance per unit time, like km/h), pace inverts the relationship: a lower number means you’re going faster. A pace of 4:30 min/km is faster than 5:00 min/km. Runners use pace because it maps directly to race strategy: if your goal is a 45-minute 10K, you need to average 4:30 min/km.

Understanding pace also means understanding pace conversions. The world runs on two systems: min/km (used in most countries) and min/mile (used in the United States and United Kingdom). The conversion is straightforward — 1 mile = 1.60934 km — but runners constantly need to switch between them when comparing performances, reading race plans, or interpreting research. Treadmills add a third unit: km/h or mph, the speed units used by the machines but not by most runners.

Beyond pace conversion, this site covers the mathematics of race performance prediction, heart rate training, and physiological estimation. The Riegel formula predicts how fast you should run a marathon based on your half-marathon time. The Daniels VDOT equation derives equivalent performances across distances and training pace zones from a single race result. The Karvonen formula personalises heart rate training zones by accounting for your resting heart rate.

These formulas are powerful, but they’re models — approximations of complex physiology. Every guide on this site explains not just how the formula works but where it breaks down and what the limitations are. The goal is runners who understand their numbers, not just a calculator that produces them.

Each calculator on this site implements its formula directly from the primary source — not from another website that claims to use the formula. The Daniels VDOT calculator implements the Daniels-Gilbert equation from the 1979 Oxygen Power paper. The heart rate zones calculator implements the Karvonen 1957 formula and ACSM guidelines separately. The calorie burn calculator uses MET values from the 2011 ACSM Compendium of Physical Activities.

The formula implementations are unit-tested — every formula function has tests that verify known values. Population-average formulas like these have significant individual variation. A heart rate estimate based on 220 minus age has a standard deviation of ±10–12 bpm. This site states that plainly rather than presenting the estimate as precise.

This site is built by a runner-developer based in Bengaluru, India — someone who got frustrated with running calculators that gave answers without explaining the math. The approach: implement formulas from primary sources, cite those sources, explain the derivations, and be honest about the limitations. That’s the whole premise. Read more about the site →