Endurometry
What does this calculator do?
The race time predictor estimates how a recent result would scale to another distance. Enter a race you have already run and a target distance; the page returns three finish times: Daniels–Gilbert (the large figure, recommended), Riegel with exponent 1.06, and a 1.10 power-law variant that drops off faster as the target gets longer.
Typical uses: turning a 10K into a half-marathon or marathon goal, checking whether a cutoff is realistic before you sign up, or seeing how much “room” a shorter race leaves you at a longer one. It is a scaling model, not a training plan.
How does it work?
Two published ideas sit behind the three numbers. Riegel’s power law says that as distance grows, time grows a little faster than linearly: T₂ = T₁ × (D₂ / D₁)^1.06. The 1.10 column uses the same formula with a steeper exponent, so longer targets come out slower (and shorter targets faster).
Daniels–Gilbert starts from physiology rather than a single exponent. Your known race implies a VDOT (an endurance index from the oxygen cost of that pace and the fraction of VO2max you can hold for that duration). The predictor then searches for a target time whose oxygen cost matches what that VDOT can sustain at the new duration. That is why Daniels often sits between the two power laws, and why it is the headline result.
Formula
Riegel
T2 = T1 × (D2 / D1)^k k = 1.06 or 1.10
Daniels–Gilbert (Oxygen Power, 1979)
v = distance (m) / time (min) // m/min
VO2 = −4.60 + 0.182258 v + 0.000104 v² // ml/kg/min
%VO2max = 0.8 + 0.1894393 e^(−0.012778 t)
+ 0.2989558 e^(−0.1932605 t) // t in minutes
VDOT = VO2 / %VO2max
solve T2 so that VO2(v2) = VDOT × %VO2max(T2)Distances are official road-race lengths (5K = 5.000 km, half = 21.0975 km, marathon = 42.195 km). The Daniels solver is a damped numerical search starting from a Riegel 1.06 guess; times are rounded to the second only when displayed.
Worked example
A runner has just run 10K in 48:30 and wants a half-marathon prediction. (These are the calculator’s default inputs.)
- Known: D₁ = 10,000 m, T₁ = 2,910 s. Target: D₂ = 21,097.5 m
- Riegel 1.06: 2,910 × (21,097.5 / 10,000)^1.06 ≈ 6,421 s → 1:47:01 (5:04/km)
- Riegel 1.10: same formula with k = 1.10 → 1:50:15 (5:14/km)
- Daniels–Gilbert: VDOT ≈ 41.5; solve for the half-marathon time that VDOT can sustain → 1:47:32 (5:06/km)
- The large figure on the page is the Daniels time; the table lists all three
Clicking Predict with the defaults above returns exactly these three times.
How to interpret the result
Treat the Daniels time as the central estimate, Riegel 1.06 as a close cross-check, and 1.10 as a cautious longer-race bound. They will never replace the question “have I trained for this distance?” A 10K specialist who has not run beyond 12 km should not read 1:47 as a guaranteed half.
To turn the prediction into even splits, use the pace calculator or a printable pace band. Training paces that match the same VDOT are on the training pace calculator. Course cutoffs are a separate check: the cutoff calculator.
Assumptions and limitations
Assumptions
- The known result is a genuine race effort, not an easy run or a downhill-aided time.
- You are trained for the target distance, not only for the known one.
- Course profile, weather, altitude and pacing are similar enough that physiology — not conditions — dominates the difference.
Limitations
- These are models of typical endurance scaling, not a promise. Errors of several minutes at the marathon are common when training does not match the target.
- The further the two distances, the weaker the estimate. 5K → 10K is more trustworthy than 5K → marathon.
- Riegel’s single exponent cannot represent how %VO2max falls with duration; that is why a second exponent (1.10) is shown as a conservative long-race check.
- Daniels–Gilbert’s VDOT is an endurance index, not a laboratory VO2max. Two runners with the same race time share a VDOT even if their lab tests differ.
- Downhill courses, wind, heat, altitude and drafting are not modelled.
- Inputs faster than 1:00/km or slower than 2:00:00/km are rejected as almost certainly a unit or typing error.
Methodology and sources
Method type: Published model
This calculator implements two published models: Riegel’s 1981 power law (exponents 1.06 and 1.10) and the Daniels–Gilbert 1979 oxygen-cost / %VO2max equations. The Daniels target time is found numerically; the equations themselves are unchanged. Results are estimates of scaling, not official predictions.
Sources: Riegel 1981 · Daniels–Gilbert 1979 · World Athletics Book of Rules
Last reviewed: October 5, 2026