About Pace Numbers

Pace Numbers is a set of free calculators for runners: pace, time and distance; marathon and half-marathon pacing and splits; race-time prediction; Daniels VDOT training paces; heart-rate zones; and treadmill speed, incline and calories. Each one is built on a formula a coach or exercise physiologist would recognise, and each page shows the arithmetic rather than asking you to trust a number.

Where the numbers come from

Pace, time and distance are definitions, with race distances as certified by World Athletics (a marathon is 42.195 km, a half 21.0975 km). Race prediction uses Pete Riegel's 1981 formula, T2 = T1 × (D2/D1)^1.06, and the VDOT model from Jack Daniels and Jimmy Gilbert's 1979 regression of oxygen cost against running speed, as published in Daniels' Running Formula. Heart-rate zones use the Karvonen heart-rate-reserve method with maximum heart rate from Tanaka, Monahan and Seals (2001), 208 − 0.7 × age, shown beside the older 220 − age estimate. Calories use the American College of Sports Medicine metabolic equations for walking and running, including their incline term, at roughly 5 kcal per litre of oxygen. Treadmill incline equivalence comes from the same ACSM grade term; the "set it to 1%" convention is from Jones and Doust (1996). Where a number is a rule of thumb rather than a measurement, the page says so.

What this site doesn't do

It doesn't store what you enter, require an account, or replace a coach or a doctor. A predicted marathon time assumes you have trained for a marathon; a heart-rate zone built on an age formula can be 10-15 beats off for an individual until you measure your real maximum; a calorie figure is a population equation applied to one person. Use the numbers as starting points and adjust to what your body and your watch tell you.

Corrections

If you are a coach or exercise physiologist and a formula, coefficient or threshold here is out of date, email hello@pacenumbers.com. Sources are named on each page so a correction can be checked against them.