Running Pace Calculator

Background.

What pace breaks 50 minutes for a 10K? Five minutes per kilometre, which is 8:02.8 per mile, and every kilometre marker has to go by within five minutes of the last. Questions like that, along with how long a half marathon takes at 5:30 per kilometre or how far 40 minutes at 6:00 per mile carries you, all come from one relationship: time equals distance multiplied by pace. Give any two of the three and the third follows, together with the same answer in the other unit system and as a speed.

Runners think in pace rather than speed because races are fixed distances and the course is marked in kilometres or miles. A pace is a split you can check against your watch at each marker; a speed is a number on a treadmill console. The two are reciprocals, and multiplying a speed in km/h by a pace in min/km always gives exactly 60, so 12 km/h on the treadmill is 5:00 per kilometre on the road. Switching between kilometres and miles uses the international mile, exactly 1.609344 km.

Two things about the answers are worth knowing before you plan a race around them. Paces are shown as decimal minutes, so 8.0467 min/mi means 8 minutes and about 2.8 seconds, not 8:05. And every result assumes an even pace held from start to finish, on flat ground, with no fatigue. That is fine for setting splits and converting treadmill speeds, but it says nothing about whether you can hold a pace for longer than you have raced before. A 50-minute 10K runner who keeps that same pace for a marathon finishes in 3:30:58.5; the Riegel endurance formula, which builds in the slowing that longer races bring, predicts closer to 3:50.

What is running pace calculator?

Running pace is the time taken to cover one unit of distance, written in minutes per kilometre or minutes per mile. It is speed turned upside down: speed is distance divided by time, pace is time divided by distance, so a faster runner has a smaller pace. Most of the world, and World Athletics, races in kilometres, while road racing in the United States and Britain still often paces by the mile. The standard road distances are fixed: 5 km, 10 km, the half marathon at 21.0975 km and the marathon at 42.195 km, a length taken from the 1908 London Olympic course and adopted as the standard in 1921. In miles those are 3.1069, 6.2137, 13.1094 and 26.2188. Because pace is per unit of distance, it maps directly onto the markers along a course and onto the paces training plans prescribe for easy runs, tempo runs and intervals. Splits describe how a pace was spread over a race: even splits run both halves in the same time, and a negative split runs the second half faster than the first.

How to use this calculator.

1. 01Under What do you want to calculate?, choose pace if you know the distance and time, time if you know the distance and pace, or distance if you know the time and pace.
2. 02Enter the distance and choose kilometres or miles. A 10K is 10 km, a half marathon 21.0975 km and a marathon 42.195 km; the box accepts 0.01 to 1,000 units.
3. 03Enter the total time in seconds. Convert a clock time by multiplying hours by 3,600 and minutes by 60, then adding the seconds: 1:52:30 is 3,600 + 3,120 + 30 = 6,750 s. Anything up to 360,000 s, which is 100 hours, is accepted.
4. 04Enter a known pace in seconds per kilometre or per mile and set the pace unit to match: 4:45 per km is 285 s, 8:00 per mile is 480 s. The box takes 60 to 1,800 s, from 1:00 to 30:00 per unit.
5. 05Read the results. Paces are decimal minutes, so multiply the part after the point by 60 to get seconds; the total time comes back in seconds, the distance in both units, and the speed in km/h and mph.

The formula.

Everything rests on time = distance × pace, rearranged for whichever value is missing. With a distance and a time, pace in min/km = (time in seconds ÷ 60) ÷ distance in km. With a distance and a pace, time in seconds = distance in km × pace in min/km × 60. With a time and a pace, distance in km = (time in seconds ÷ 60) ÷ pace in min/km. Miles are converted to kilometres first, at 1.609344 km per mile, and a pace per mile is divided by 1.609344 to give a pace per kilometre, so all three cases are worked in one unit and converted back for the display.

Speed follows from pace alone: km/h = 60 ÷ pace in min/km, and mph = km/h ÷ 1.609344. The same 60 links mph and minutes per mile, so 8 mph is a 7.5-minute mile, 7:30.

Averaging paces needs care. Run 5 km at 4:00 per km and 5 km at 6:00 per km and the 10 km take 50 minutes, a true average of 5:00. Run 25 minutes at each pace instead and you cover 6.25 + 4.1667 = 10.4167 km in the same 50 minutes, an average of 4.8 min/km, or 4:48. Averaging the two paces only works when each was held for the same distance; otherwise divide the total time by the total distance, which is exactly what solving for pace does.

The model is deliberately simple. It treats a run as one steady pace, which makes it exact for converting between units and for working out splits, but it carries no information about hills, wind, heat, the surface or fatigue. Predicting how a result at one distance translates to another needs a different kind of formula. Riegel's, published in 1981, is T₂ = T₁ × (D₂ ÷ D₁)^1.06: the exponent above 1 means each doubling of distance costs a little more than double the time. Applied to a 50:00 10K it gives a half marathon of about 1:50:19 and a marathon of about 3:50:01, against the 1:45:29.3 and 3:30:58.5 that holding 10K pace would produce.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Daniels JT. Daniels' Running Formula. 3rd ed. Champaign, IL: Human Kinetics; 2014. VDOT tables and the five training-pace prescriptions (E, M, T, I, R) used throughout coaching practice.
2. [2]Riegel PS. Athletic Records and Human Endurance. American Scientist. 1981;69(3):285–290. Original derivation of the endurance equation T2 = T1 × (D2/D1)^1.06.
3. [3]Tanda G. Prediction of marathon performance time on the basis of training indices. Journal of Human Sport and Exercise. 2011;6(3):511–520. Marathon time as a function of weekly training distance and training pace; consistently outperforms Riegel for marathon prediction.
4. [4]World Athletics. Marathon — World Records and Definitions. Marathon distance defined as 42.195 km (set 1908 London Olympics, ratified 1921 by IAAF).
5. [5]USA Track & Field. Competition Rules. Official event distances for road and track events including 5 km, 10 km, half marathon (21.0975 km), and marathon (42.195 km).
6. [6]National Institute of Standards and Technology. Special Publication 811: Guide for the Use of the International System of Units (SI). 2008 ed. International mile defined as exactly 1.609344 km.
7. [7]Jones AM, Doust JH. A 1% treadmill grade most accurately reflects the energetic cost of outdoor running. Journal of Sports Sciences. 1996;14(4):321–327. Empirical basis for the 1% treadmill incline correction.
8. [8]Boston Athletic Association. Qualifying Standards for the Boston Marathon. Age-group and gender-specific qualifying times updated annually.