Riegel-formula prediction of finish time at any distance from a known race result.
Riegel's formula t₂ = t₁ · (d₂ / d₁)^k assumes equivalent training and effort. Lower k (1.04) suits trained runners; higher k (1.10) reflects steeper fade for less-trained runners stepping up.
Runners stepping up in distance — from 5K to 10K, 10K to half marathon, half to marathon, marathon to ultra — need a defensible target time before they show up at the start line. The training plan, the pacing strategy on race day, and the post-race recovery all depend on knowing approximately what finish time is realistic. The most widely used predictor in running circles is the Riegel formula, published by Pete Riegel in Runner's World in 1977: it captures the empirical relationship between race times across distances using a single power-law exponent. The formula is simple, falsifiable, and accurate to within ~3 % for well-trained runners stepping up two-fold or less in distance. It does break down at extremes — sprinters trying to predict a marathon, or marathoners trying to predict a 5K from the marathon — but for the working middle of the running population (5K to marathon) it is the gold standard.
This calculator takes a known race result, projects to the target distance, and also lays out a curve of predicted times across the full 1 km – 50 km range so runners can sanity-check the prediction against their own performance at intermediate distances. Race-pace dots highlight the canonical reference distances (5K, 10K, half marathon, marathon).
Riegel's law of equivalence:
t₂ = t₁ · (d₂ / d₁)^k
with t₁, d₁ the known time and distance, t₂, d₂ the target time and distance, and k the fatigue exponent. Riegel's original value, fit empirically to thousands of races, is k = 1.06 — meaning that doubling the distance multiplies the time by 2¹·⁰⁶ = 2.085, i.e. the per-distance pace slows by about 4.3 % per doubling.
The exponent depends on training and runner profile:
Lower k means a smaller pace fade with distance — the hallmark of high aerobic capacity and good muscular endurance. Triathletes and ultra runners tend to k ≈ 1.04; pure sprinters reaching for a 10K may be k > 1.12.
The calculator clips the input to [1.00, 1.15]. k = 1.00 would mean no fatigue at all (perfect pace at any distance); k = 1.15 is severely fatigued. Outside that range the formula loses physical meaning.
Enter the known race distance in km. The standard reference distances are pre-loaded in the example dropdown: 5K, 10K, half marathon (21.0975 km), full marathon (42.195 km). Enter the time of that race in minutes and seconds (combined into total seconds for the math). Enter the target distance you want to predict for. Set the Riegel exponent. The result panel shows the predicted target time as a hh:mm:ss KPI, the per-km target pace, and predicted times at the four canonical distances (5K, 10K, half, marathon) so you can see them in context.
The chart plots the full Riegel curve from 1 km to 1.05 × the larger of (target_distance, 42.195). The horizontal axis is distance, vertical is time. Reference dots mark the canonical distances along the curve. The curve's concavity is the visual fingerprint of the fatigue exponent — a flatter curve means lower k.
10K race in 50:00, predicting marathon at k = 1.06:
Same 10K, but k = 1.04 (fitter runner): t₂ = 3 000 × 4.2195^1.04 = 3 000 × 4.534 = 13 601 s = 3:46:41. Five-minute difference.
5K in 22:00, predicting half marathon at k = 1.06:
Half marathon in 1:45 (105 min = 6 300 s), predicting marathon:
Course profile and weather. Riegel assumes an equivalent course. A flat fast 10K predicting a hilly hot marathon will overestimate. Subtract 5–8 % from the prediction for hilly courses, 5–10 % for hot conditions.
Same training cycle assumption. The formula assumes you're maintaining the training that produced the known time. If your 10K PR was three years ago and you've been off training, the prediction is wildly optimistic.
Race vs time-trial. Race-day tactics (start adrenaline, mid-race pack pacing) typically produce 1–3 % faster times than solo time trials at the same fitness. Use the calc with race-context inputs for race-context predictions.
Distance ratio extremes. The formula is empirical and well-fit for ratios under 4× (e.g. 10K → marathon). Predicting an ultra (100 km) from a 5K is not Riegel's regime — use ultra-specific predictors.
Sprinter quirk. Below 800 m, the energy system is different (anaerobic-dominant). Predicting marathon from a 200 m sprint is meaningless even with very high k.
Aging. Riegel's k slowly increases with age past ~35 (slightly more pace fade with distance for older runners). Effect is small (< 0.01 per decade) but cumulative.
Walking. Walking marathons have completely different energetics. Riegel was fit for runners.
Mental component. The marathon's last 8 km are notoriously where untrained runners "hit the wall" — glycogen depletion and mental fatigue. The formula doesn't model this; it assumes your training has built the endurance to extend the pace.
k-tuning by personal history. Best practice: solve for your personal k from two known race times across distances, then use that k for predictions. The calculator's default k = 1.06 is a population average.
Not for predicting downwards. Predicting a 5K from a marathon time tends to under-estimate the 5K, because the runner's anaerobic capacity isn't tested at marathon pace. Use lower k (1.04) when predicting shorter from longer.