Running Pace, Speed and Race Prediction

After reading this you can convert between pace, speed and finish time by hand, and predict a race time from a recent result while knowing how far off that prediction is likely to be.

What the calculator does

Three numbers describe every steady run: how far you go, how long it takes, and how fast you move. Fix any two and the third follows. This tool moves between them and adds one extra trick: it estimates your time at a new distance from a time you already ran.

Here is the hook. Suppose you run at 5:30 per kilometre. That is a speed of 10.91 km/h, and it turns a 10 km race into a 55:00 finish. Change the pace by 10 seconds per kilometre and the 10 km time shifts by 1:40. Small pace changes add up fast over distance, which is exactly why runners obsess over seconds per kilometre.

When to use it, and when not

Use pace and speed conversion whenever your watch, treadmill and race plan disagree on units. Treadmills usually show km/h or mph. Race pace charts show min/km or min/mile. Converting by hand is error-prone, and a 0.5 km/h treadmill mistake over an hour is 500 metres.

Use the race predictor to set a realistic target for a distance you have not raced recently, or to sanity-check a goal. Do not use it to plan medical or high-risk decisions, and do not treat a marathon prediction from a 5 km time as a promise. The predictor assumes you are equally trained for both distances. Most runners are not: your 5 km fitness is usually ahead of your marathon endurance, so the predicted marathon comes out optimistic.

The pace, speed and time formulas

Start with the plain relationships. Pace is time divided by distance. Speed is distance divided by time. They are reciprocals once you match the units.

Here time is the total running time in minutes and distance is in kilometres. A 50 minute 10 km gives 50 / 10 = 5.0 min/km, which reads as 5:00 per kilometre.

The 60 converts minutes to hours. A pace of 5:00 per kilometre is 5.0 min/km, so speed is 60 / 5.0 = 12 km/h. Halve the pace number and you double the speed, because they are inverses.

To switch between kilometres and miles, use 1\ \text{mile} = 1.60934\ \text{km}. Pace per mile is pace per kilometre times 1.60934. A pace of 5:00 per kilometre is 5.0 \times 1.60934 = 8.047 min/mile, which rounds to 8:03 per mile.

The Riegel prediction formula

To predict a time at a new distance, the tool uses Peter Riegel's 1977 formula.

Read it like this: T_1 is your known time over the known distance D_1, and T_2 is the predicted time over the target distance D_2. The exponent 1.06 is the key. If the exponent were exactly 1, the formula would say you hold the same pace at any distance, which no one does. Because 1.06 is slightly above 1, longer distances get a slower predicted pace.

How much slower? Doubling the distance multiplies time by 2^{1.06} = 2.085, not by 2. So your pace per kilometre gets about 4.3% slower each time the distance doubles. Over a 5 km to marathon jump (a factor of about 8.44 in distance), the pace slowdown compounds to roughly 13%.

Predicted times across distances

The chart below shows predicted finish time as a function of race distance, anchored on the demo's 50 minute 10 km. The curve bends upward: each extra kilometre costs more time than the last, because pace slows as distance grows.

Reading and interpreting the results

Pace and speed are exact conversions. If the input is correct, the output is correct to the rounding shown. There is no uncertainty in 5:00 per kilometre equalling 12.0 km/h.

The predicted times are different. They carry real error. In practice, a Riegel prediction within the same "family" of distances (say 5 km to 10 km) is usually accurate to within 1 to 2 percent for a trained runner. Extrapolating far, such as 5 km to marathon, commonly overshoots by 3 to 8 percent, meaning your real marathon is that much slower than predicted. On a 3:50 prediction, 5 percent is about 11 minutes.

Common mistakes

A few errors show up again and again.

Mixing pace units

Reading a min/mile pace as if it were min/km. At 5:00 per kilometre you would be at 8:03 per mile, a 60 percent difference in the number. Always check the unit before you plan.

Confusing pace and speed

They move in opposite directions. A smaller pace number is faster; a smaller speed number is slower. If your pace drops from 5:00 to 4:30, that is faster, and speed rises from 12.0 to 13.33 km/h.

Trusting a marathon prediction from a short race

The formula assumes equal training. Predict long distances only from long training, and add a margin.

Forgetting course and conditions

Heat, hills and wind all slow you down. The formula knows nothing about them. A hilly marathon can be 5 to 10 minutes slower than a flat one at the same fitness.

Related tools

Pace tells you how fast you are moving, not how hard the effort is. To pair a target pace with an effort level, work out your training zones with the Heart Rate Zone Calculator. Running your predicted marathon pace should sit in an aerobic zone you can hold for hours, not near your maximum.

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