Race time predictor
Predict finish times from one recent race using Riegel’s formula, with pace per kilometre and mile.
A clear answer. Here’s how.
Riegel’s formula predicts a time T2 for distance D2 from a known time T1 at D1: T2 = T1 × (D2 ÷ D1)^1.06. The exponent above 1 captures the slowdown as races get longer. It was fitted to results from races lasting about 3.5 minutes to 3.5 hours, so predictions from very short tests or far beyond a marathon are less reliable. It assumes similar endurance training for every distance. Paces divide the predicted time by the distance in kilometres or miles.
How this is checked
2 reference checks passed These 2 cases were run when this page was built, on 20 October 2026, and all reproduce within the stated tolerance. The same cases are part of the automated tests that run on every change to Toolmoz. Engine version 1.
See the checks and where each expected answer comes from
Case 1
- Inputs
- Distance of your known race 5Your time (h:mm:ss or mm:ss) 20:00
- Expected, and what Toolmoz gave
- Predicted 10 km time (seconds) expected 2501.9178, Toolmoz 2501.9178260186914Predicted half marathon time (seconds) expected 5520.2392, Toolmoz 5520.239199907903Predicted marathon time (seconds) expected 11509.3207, Toolmoz 11509.32071511395
- Where the expected answer comes from
- 1200 s × (D2 ÷ 5)^1.06, evaluated separately with 50-digit decimal arithmetic
- Allowed difference
- ±0.001 absolute
Case 2
- Inputs
- Distance of your known race 10Your time (h:mm:ss or mm:ss) 45:00Fatigue exponent 1
- Expected, and what Toolmoz gave
- Predicted 5 km time (seconds) expected 1350, Toolmoz 1350Predicted marathon time (seconds) expected 11392.65, Toolmoz 11392.65
- Where the expected answer comes from
- With exponent 1 the formula is proportional to distance: 2700 × 5 ÷ 10 = 1350 and 2700 × 42.195 ÷ 10 = 11,392.65
- Allowed difference
- ±1e-9 absolute
What this shows: the engine reproduces independently worked values for these cases. It does not prove every possible input is right. To test an answer you were given, see how to check a number; to see what is and is not checked across Toolmoz, see the accuracy ledger.
See a worked example
Worked example
A fixed demonstration, separate from the values you enter above.
- Distance of your known race
- 5 km
- Your time (h:mm:ss or mm:ss)
- 20:00
- Fatigue exponent
- 1.06
Example result
| Distance | Predicted time | Pace per km | Pace per mile |
|---|---|---|---|
| 1 mile | 6:01 | 3:44 /km | 6:01 /mile |
| 5 km | 20:00 | 4:00 /km | 6:26 /mile |
| 10 km | 41:42 | 4:10 /km | 6:43 /mile |
| 10 miles | 1:09:03 | 4:17 /km | 6:54 /mile |
| Half marathon | 1:32:00 | 4:22 /km | 7:01 /mile |
Riegel’s formula T2 = T1 × (D2 ÷ D1)^1.06. It was fitted to races lasting about 3.5 minutes to 3.5 hours. It assumes similar training for each distance; most runners slow more than predicted at the marathon without long-run training.