Race time
predictor

Enter a race you have already run and get your predicted finish time and pace at any other distance, in min/mi or min/km. Built on Riegel's endurance formula — with the distance range where the prediction actually holds.

How the math works

The predictor uses one relationship, Peter Riegel's endurance formula. Your finish time at one distance sets a curve; the time at any other distance is a fixed power of the distance ratio. The exponent is what makes longer races slower per mile — it is above 1, so distance costs you pace.

The exponent 1.06 is the value Riegel fitted to record times from 100 m to 100 miles (Riegel 1981). Because it sits above 1, doubling the distance multiplies predicted time by 2^1.06 = 2.0849 rather than 2 — a 4.25% slower pace on the longer race. The formula behind your watch's race predictor, your training app's, and this one is the same 1981 power law; most of the difference between them is the interface.

Worked example

Take a runner with a 5 km (3.11 mi) best of 25:00 and predict up the distances with T2 = T1 × (D2 / D1)^1.06:

• 10 km (6.21 mi): 25:00 × (10 / 5)^1.06 = 25:00 × 2.0849 = 52:07
• Half marathon (13.11 mi): 25:00 × (21.0975 / 5)^1.06 = 25:00 × 4.6002 = 1:55:00
• Marathon (26.22 mi): 25:00 × (42.195 / 5)^1.06 = 25:00 × 9.5911 = 3:59:47 (about 9:09/mi, 5:41/km)

The 10 km is a 2× step from the raced distance and is the one to trust. The marathon is an 8.44× jump — that sub-4:00 is a ceiling the runner hits only with marathon-specific endurance the formula cannot see, not a time to line up expecting. The predicted times are unit-independent; only the distances carry a unit.

When this calculator is wrong

The formula applies one fatigue exponent fitted to world records, so it flatters you more the further the predicted distance is from the one you raced. Riegel fitted 1.06 to record times from 100 m to 100 miles, and because that exponent is constant, doubling the distance always multiplies predicted time by 2^1.06 = 2.0849 — whoever you are. The model has no term for an individual's endurance base relative to their speed. So a marathon predicted from a 5 km, an 8.44× jump, assumes distance-specific endurance you may not have built, and it comes out optimistic. The exception is a modest ratio, roughly ½× to 3× — a 10 km from a 5 km, a half from a 10 km — for a runner whose training is balanced across the range, where the single-exponent model is close enough to program from.

• Extrapolation flatters the under-trained. The bigger the gap between the race you ran and the one you are predicting, the more the number assumes about training you may not have done. A 5K runner who never runs long will not hit the marathon time this prints — the shortfall is missing endurance, not a broken formula.
• The prediction is only as good as the race you feed it. Enter a race you paced conservatively, ran in heat, or covered on a hilly course and every predicted time inherits that slow input. Use a hard, evenly-run race on a flat course, from the last few weeks.
• It says nothing about the day. Heat, wind, elevation, fuelling and taper move a real result by several percent in either direction. The predictor gives the fitness-implied time in ideal conditions, which the day rarely supplies.

What to do with the result

Use the prediction closest to your raced distance to set a goal pace, and treat the far ones as direction, not a target. Then use the gap as a signal: run the longer race, and if you come in slower than the prediction from a shorter one, that shortfall is your endurance relative to your speed — the fix is more distance-specific volume, not a faster 5K. If you beat it, your base is ahead of your top-end speed, and sharper intervals are the lever. Re-run the prediction after any race or hard time trial; a result more than a few weeks old, or from before a training gap, misprices every distance it touches.

Common questions

How accurate is a race time predictor?

Within a modest distance ratio — say predicting a 10K from a 5K, or a half from a 10K — Riegel's formula is close enough to set a goal pace for a runner whose training is balanced across the range. Accuracy falls as the gap grows: a marathon predicted from a 5K is an 8.44× distance jump, and it tends to print a time faster than an under-trained runner will actually race.

Can I predict my marathon time from a 5K?

The formula will do it, but treat the answer as an optimistic ceiling. It assumes you can hold the same fatigue curve across a distance eight times longer, which only holds if you have built marathon-specific endurance. Predict the marathon from a half marathon or a recent long race if you can — the closer the raced distance, the more the number holds.

What is the Riegel formula?

It is a power law from Peter Riegel's 1981 paper "Athletic Records and Human Endurance": predicted time equals your known time times the distance ratio raised to the power 1.06. The 1.06 exponent, fitted to records from 100 m to 100 miles, is why pace slows as distance grows. Most race predictors, running watches and training apps use it.

Why does the predictor say I can run faster than I actually do?

Because the exponent is a single number fitted to world records, with no term for your own endurance relative to your speed. If your training skews toward shorter, faster running, the model over-credits your endurance at long distances and prints a time you are not yet trained to hold. The gap is useful — it tells you distance-specific volume is the thing to add.

What race should I enter?

A hard, evenly-run race on a flat course from the last few weeks, at a distance not too far from the one you are predicting. A recent parkrun or 10K predicts your half well; a recent half predicts your marathon far better than a 5K does.

Is this the same as VDOT?

Related but not identical. VDOT (Daniels) converts a race into a fitness score and a set of training paces; Riegel converts a race directly into a predicted time at another distance. They agree closely over the middle distances and diverge at the extremes. Use the VDOT calculator for training paces and this one for a target time.