Pace Calculator

What is running pace?

Pace is how long it takes you to cover one unit of distance: five minutes per kilometre, eight minutes per mile. Speed is the same information the other way up — distance covered per unit of time. They are exact reciprocals, so 5:00 per kilometre is 12 km/h with nothing rounded away, and this pace calculator shows both because runners think in pace and treadmills are labelled in speed.

That reciprocal relationship is also why pace behaves strangely when you start averaging it. A pace is a fraction with distance underneath, and adding fractions is not the same as adding the numbers on top. Most people never notice, because the case they meet most often is the one case where the shortcut happens to work.

The calculator handles the ordinary questions first — fill in any two of distance, time and pace and it fills in the third, with the six standard race distances built in. Underneath it, a second panel takes a set of splits and tells you what your real average was, alongside what averaging the paces would have told you.

How to use it

1. Pick a distance and enter either a time or a pace. Whichever one you type, the other is worked out immediately. Changing the distance holds your pace and updates the time, so you can ask what a marathon would take at the pace you just ran a 10K. Choose Custom for anything not in the list.
2. Read the pace in both units, and the speed. Per kilometre and per mile, plus km/h and mph for setting a treadmill. Every row has a copy button.
3. Enter your splits in the second panel. One row per piece, with the distance in metres and the time it took. The tool works out your true average pace, shows what averaging the paces would have given, and tells you which of the two answers to trust and why.

Why averaging your splits is usually wrong

Your true average pace is total time divided by total distance. That is the only definition, and it is what the top panel uses. The shortcut everyone reaches for instead is to average the paces of the individual splits — add them up, divide by how many there are. Whether that gives the right answer depends entirely on the shape of your splits, and there are two cases worth knowing.

If every split covers the same distance, the shortcut is exactly right. Not approximately: the two calculations reduce to the same fraction, so they agree to the last decimal place. Five kilometre splits of 5:00, 5:10, 5:05, 5:20 and 4:55 average to 5:06 either way. This is why the shortcut has such a good reputation — race splits are equal distances, and that is where most people meet the problem.

If every split lasts the same time, the shortcut is always wrong, and always in the same direction. Run thirty minutes covering 6 km, then thirty minutes of run-walk covering 3.6 km, and your real average is 6:15 per kilometre — but averaging 5:00 and 8:20 gives 6:40. The gap is exactly twenty-five seconds per kilometre. The reason is that you spent the same time in each piece but covered more ground in the fast one, so the fast pace deserves more weight than the shortcut gives it. Mathematically the true answer is the harmonic mean of the paces, which is never larger than the ordinary mean, so the shortcut can only ever report you as slower than you actually were.

The size of the error grows with the square of the gap between the two paces. For two equal-time pieces it is exactly the difference squared, divided by twice the sum. Double how uneven your effort was and you quadruple the mistake — which is why a pair of race splits a few seconds apart shows nothing and a run-walk session shows half a minute per kilometre.

Interval sessions, run-walk plans, treadmill blocks and anything else you time with a watch rather than measure with a marker all fall into the equal-time case. That is the everyday situation where the shortcut fails, and it is why this page asks for both the distance and the time of each split rather than just the paces.

Honest limitations

The direction of the error is only fixed for equal-time splits. If your splits are uneven in both distance and duration, the shortcut can be wrong either way — a fast kilometre followed by a slow five kilometres gives a true average of 5:50 against a shortcut answer of 5:30, so here the shortcut flatters you rather than the reverse. That is why the tool always shows both numbers and the difference between them instead of offering a rule of thumb about which way it leans.

The distances are exact rather than rounded. The mile is 1609.344 metres by the 1959 international yard and pound agreement, and the marathon is 42,195 metres by definition, so the conversions between per-kilometre and per-mile pace carry no error worth mentioning. What is approximate is your own data: a GPS watch does not measure distance to the metre, and a course measured to the standard is still only the shortest legal line through it.

Times are shown floored rather than rounded, so a pace displayed as 5:06 is somewhere between 5:06 and 5:07. That direction is deliberate — a display should never claim a time you did not achieve. It does mean that copying a pace and feeding it back in can shift the result by a fraction of a second.

This is not a race predictor. It will happily tell you what a marathon takes at your current 5K pace, and that number will be optimistic, because nobody holds 5K pace for 42 kilometres. Predicting a race time across distances needs a fatigue model and an honest one needs your training history; this page does arithmetic, and says so.

Why is it free?

All of the arithmetic runs in your browser. There is no server doing the work, so there is nothing to bill for and no account to create.

Nothing is uploaded and nothing is stored. Reload the page and it has forgotten your splits.