How this is worked out
Pace is time divided by distance:
pace per km = total seconds ÷ distance in km
A 45-minute 10K is 2,700 ÷ 10 = 270 seconds per kilometre, or 4:30/km. Multiply by 1.609344 for the mile equivalent — 7:15/mile.
Race predictions use Riegel's formula:
T₂ = T₁ × (D₂ ÷ D₁)^1.06
The exponent is the interesting part. If you could hold the same pace at every distance the exponent would be 1.0. It is 1.06 because you cannot — pace degrades as distance rises, and 1.06 is the value that best fits observed race performances across a wide range of runners.
That fit is good between adjacent distances and increasingly optimistic across a large gap, because the formula knows nothing about endurance that your shorter race never tested. This calculator rates each prediction accordingly rather than printing them all with equal confidence.
A worked example
- Distance
- 10K
- Time
- 45:00
- Pace per km
- 4:30
- Pace per mile
- 7:15
- Speed
- 13.33 km/h
- Predicted 5K (Riegel)
- 21:35
- Predicted half marathon
- 1:39:17
- Predicted marathon
- 3:27:01 — optimistic
Which predictions to believe
Riegel's formula is a good predictor when the two distances are close. A 10K time predicts a half marathon well; a half predicts a marathon reasonably. A 5K predicting a marathon is extrapolating across an eight-fold gap, and it will flatter you.
The reason is that the formula only knows about speed. It cannot know whether you have done the long runs, whether your fuelling works over three hours, or whether your legs hold together past 30km. A fast 5K demonstrates none of those things, and all of them decide a marathon.
The calculator marks each prediction as reliable, rough or optimistic based on how far it is extrapolating. Treat an optimistic prediction as an upper bound on a perfect day rather than a target — going out at that pace is the classic way to walk the last 10K.
Even splits, negative splits, and what actually happens
The split table shows even pacing, which is the arithmetic ideal and close to what almost every distance record has been run on. Holding a constant pace is the most efficient way to cover ground, because surging and slowing both cost more energy than steady effort.
A negative split — running the second half slightly faster — is the practical version of the same advice, because it builds in a margin for going out too fast. Aiming to run the first half five to ten seconds per kilometre slower than target and making it up later usually produces a faster finish than aiming at even pace and drifting.
What actually happens to most runners is a positive split: too fast early, paying for it late. The gap between the first and second half of a marathon is the single clearest indicator of whether the pacing plan was realistic.
Course, weather and terrain move the number
Riegel assumes comparable conditions. A hilly course, heat, humidity or a headwind all cost time in ways the formula cannot see. Heat in particular is severe: performance degrades noticeably above about 15°C and substantially above 20°C, and the effect is larger the longer the race.
Altitude costs time above roughly 1,000m for events longer than a few minutes, unless you are acclimatised. Trail and off-road running is not comparable to road pace at all — the same effort can be a minute or more per kilometre slower.
Use the predictions to set a realistic goal on a flat road course in decent conditions, and adjust downwards for anything harder. A prediction is a ceiling, not a floor.
Pace per kilometre or per mile
Both are shown, because runners in the same race routinely think in different units. The conversion is 1.609344 kilometres to the mile, so a 5:00/km pace is 8:03/mile and a 7:00/mile pace is 4:21/km.
A useful anchor for converting in your head: a mile pace is roughly 1.6 times the kilometre pace, so add about 60% . A 4:00/km is a little over 6:26/mile; a 6:00/km is about 9:39/mile.
Race distances are metric almost everywhere — 5K, 10K, the half at 21.0975km and the marathon at 42.195km — so kilometre pacing tends to be easier arithmetic during a race even for runners who train in miles.
Assumptions and sources
- Pace
- Total time divided by distance. Mile equivalents use 1.609344 km per mile.
- Race prediction
- Riegel's formula, T₂ = T₁ × (D₂/D₁)^1.06. The exponent is the empirical best fit to observed race performances.
- Confidence rating
- Based on the ratio between the known and predicted distances — reliable to about 2.2×, rough to 4.5×, optimistic beyond.
- Race distances
- Half marathon 21.0975 km, marathon 42.195 km — the official IAAF/World Athletics distances.