Race Time Predictor

What this calculator answers

What finish time a recent race suggests at another distance, and the pace that time means per mile and per km. Give it one race and it predicts one target plus every standard distance from 1 mile to the marathon. It uses Riegel’s formula, which assumes you slow down by a fixed amount each time the distance grows. Next to the answer it shows how much the prediction moves with that assumption and where it stops being reliable.

How to use it

• Race you ran and Finish time: pick the distance, from 1 mile to the marathon, or Other distance to type one in km, mi or m. Type the time the way results print it: 24:30 is 24 minutes 30 seconds, 1:48:40 is 1 hour 48 minutes 40 seconds, and a bare 25 means 25 minutes. The line under the box says how the time was read.
• Race to predict: the distance you want a time for, standard or typed.
• Exponent: how much you slow down as the distance grows, from 1 to 1.15. Leave it at 1.06 unless you have a reason to change it (see below). The line under the box translates it: at 1.06, doubling the distance multiplies the time by 2.085, a pace 4.2% slower.
• Second race (optional): a second recent result at a different distance. The calculator then works out your own exponent from the two races and uses it instead of the number above.

Results update as you type. The Try buttons load the cases on this page, including 5K to marathon and a two-race exponent. The table of equivalent times downloads as a CSV file. To compare, press Save for comparison, change the exponent or the race, and save again: each saved scenario shows how far its time moved from the first. For mile or km splits at the predicted time, Continue in the Pace Calculator carries the race and its predicted time over.

How the race time predictor works (Riegel’s formula)

The predicted time is your time multiplied by the distance ratio raised to the exponent:

• $T_1$ is the finish time of the race you ran, and $D_1$ its distance.
• $D_2$ is the distance to predict, and $T_2$ the predicted time, in the same unit as $T_1$.
• $k$ is the exponent, often called the fatigue factor. At $k = 1$ time grows in step with distance, so the pace never changes. Above 1, each longer race is run a little slower per mile.

Peter Riegel fitted this power law to world records in 1981, and 1.06 is the exponent the formula is most often quoted with. With two of your own races, the exponent that fits both is

where $T_3$ is the time of the second race and $D_3$ its distance.

Worked example: marathon time from a 1:48:40 half marathon

A runner finished a half marathon (21.0975 km) in 1:48:40 and wants a marathon (42.195 km) time, with the usual exponent of 1.06.

1. Time in seconds: $T_1$ = 1 × 3,600 + 48 × 60 + 40 = 6,520 s.
2. Distance ratio: 42.195 ÷ 21.0975 = 2. The marathon is exactly twice the half.
3. Slowdown factor: $2^{1.06}$ = 2.08493.
4. Predicted time: 6,520 × 2.08493 = 13,593.75 s = 3:46:34.
5. Pace: 13,593.75 s ÷ 26.2188 miles = 8:38 per mile, or 5:22 per km. The half was run at 8:17 per mile, so the prediction is 21 seconds per mile slower.

The same half predicts 3:43:27 at an exponent of 1.04 and 3:49:44 at 1.08, a spread of 6 minutes 17 seconds. That spread, not the exact second, is the honest size of the answer. In a spreadsheet, =6520*(42.195/21.0975)^1.06/86400 in a cell formatted as [h]:mm:ss gives the same 3:46:34.

Race equivalency table: 5K, 10K, half marathon and marathon

Every result on the page comes with a table of equivalent times at the standard road distances. For the 1:48:40 half marathon at 1.06:

The pace slows smoothly from 7:06 per mile over 1 mile to 8:38 over the marathon. The flags are this calculator’s checks, not part of Riegel’s formula. “Far” marks distances more than 4 times, or under a quarter of, your race’s distance. “Under 3.5 min” and “Over 230 min” mark times outside the range Riegel’s records covered. “Often slower” marks distances past the half marathon (see below). A typed distance gets its own row in order.

Choosing the exponent (fatigue factor)

1.06 is the value the formula is usually quoted with, and the default here. Published values run higher:

• Riegel reported about 1.08 for elite runners and 1.05 to 1.06 for male recreational runners aged 40 to 70.
• A study of British runners’ results found that each runner’s own exponent was usually higher: a median of 1.12, with most between 1.10 and 1.15.

Each step changes the prediction more the further you predict. For the 1:48:40 half marathon:

Your own exponent from two races is the most direct evidence for your value. If the same runner also ran a 10K in 48:10, the two results give k = ln(6,520 ÷ 2,890) ÷ ln(21.0975 ÷ 10) = 0.81362 ÷ 0.74657 = 1.0898. At that exponent the half predicts a 3:51:18 marathon, 4 minutes 44 seconds slower than 1.06 suggests. Two races far apart in distance give a steadier exponent than two close together: with races only 1.5 times apart, a 1% slower time in either one moves the exponent by about 0.025, and the page tells you so. When two races give an exponent below 1 or above 1.15, the calculator uses the nearest limit and says why.

How accurate are race time predictions?

There is no single accuracy figure. The error depends on how you train, and an uncertain exponent matters more the further you predict. From the 1:48:40 half marathon, the 10K passes every check below, while the mile, under a quarter of the distance, is flagged. The page checks three things for every prediction:

• How far the jump is. Targets more than 4 times, or less than a quarter of, your race’s distance are flagged, and a warning appears above the result.
• How long the times are. Riegel’s records ran from about 3.5 to 230 minutes. A time outside that range is flagged as a rougher estimate.
• Whether the target is past the half marathon. In a survey of 2,303 recreational runners, the formula was well calibrated for races up to the half marathon, but not for the marathon (next section).

Why marathon predictions often come out too fast

In that same survey, the formula’s marathon predictions were at least 10 minutes too fast for half of the runners. The authors’ own models, which added weekly training mileage and, in one, the exponent between two earlier races, predicted marathon times much better. That is consistent with the other study’s finding that most runners’ own exponents sit above 1.06.

In practice, treat a marathon prediction at 1.06 as a best case. Without a second race, the rows for 1.08 to 1.12 in the exponent table show what the higher exponents reported in these studies would mean for you.

Reading the result

• The headline is the predicted time for the race you chose, with the race and exponent it came from.
• Pace is the average needed to run that time, per mile and per km.
• At exponents 1.04 to 1.08 shows the prediction 0.02 either side of your exponent. With a second race, this tile shows your own exponent instead, next to what 1.06 would give.
• Your race pace compares the pace you ran with the pace predicted.
• How far to trust this prediction fills in the checks above with your numbers.
• The table and chart give every standard distance. In the chart, the lines for your exponent and 0.02 either side meet at your race and fan out with distance from it, which is the uncertainty in picture form.
• The exponent table shows the target at 1.04 to 1.15 with the change from your prediction.

Assumptions and limitations

• One exponent covers every distance. Real runners are relatively better at some distances than others, which is why a personal exponent from races near your target helps.
• The race you enter was an all-out effort, and you are as well trained for the target distance. The formula can’t see whether you have trained for the longer race.
• Courses and conditions are alike. No allowance is made for heat, hills, altitude, wind, age, sex or pacing.
• Standard distances follow World Athletics road-race rules: the marathon is 42.195 km, the half marathon 21.0975 km and the mile 1.609344 km exactly.
• Times and paces are shown to the second; the calculation keeps full precision.
• The result is an estimate for planning, not a guarantee, coaching advice or medical advice.

Common mistakes

• Typing 1:45 for a 1 hour 45 minute half marathon. Two numbers with one colon are read as minutes and seconds, so 1:45 is 1 minute 45 seconds, far too fast for the distance. The calculator stops and explains how to type hours: 1:45:00 is what you meant.
• Holding your shorter-race pace over a longer race. At an exponent of 1 the 1:48:40 half predicts a 3:37:20 marathon, 9 minutes 14 seconds faster than 1.06 gives. Nearly every runner slows as the distance grows.
• Trusting a far jump to the second. A mile or 5K predicting a marathon extrapolates more than eight times the distance. The time is a rough guide, and the higher-exponent rows are the safer plan.
• Entering a race that wasn’t flat out. A race run as a workout, in heat or on a hilly course makes every prediction slower than your real ability; a short or downhill course makes them faster.
• Picking the exponent that gives the time you hope for. Lower exponents give faster predictions. Choose it from evidence, such as your own two races, not from the answer.