Race-time prediction

Updated April 28, 2026 · 7 min read · by Samuel Yoo

You ran a 5K in 22:30 last weekend. What’s a realistic marathon goal?

The standard answer is the Riegel formula, published by Peter Riegel in 1981 as part of a paper analysing world record progressions across distances:

T2 = T1 × (D2 / D1)^1.06

For our 22:30 5K, predicting a marathon (D2 = 42.195 km, D1 = 5 km):

T2 = 22:30 × (42.195 / 5)^1.06
   = 1350 sec × 8.439^1.06
   ≈ 1350 × 9.71
   ≈ 13,108 sec
   ≈ 3:38:28

Riegel says you’d run a 3:38 marathon. The pace calculator on the home page does this for you with one click.

Why 1.06?

The naive prediction would use exponent 1.0 — assume your pace is constant across distances. That gives you a marathon in 3:09, which is wildly optimistic. Real marathons are run slower per mile than 5Ks because the glycogen runs out, the muscles fatigue, and the legs slow down.

Riegel fitted the exponent to world records and competitive results across distances from 1500m to marathon. 1.06 is empirical — it’s what the data showed. Higher exponents (1.07, 1.08) have been proposed for less trained athletes and longer distances.

Where Riegel works well

• 5K → 10K, 10K → half marathon, half → marathon: predictions are usually within 1–3%.
• Within 3× distance ratio: 5K to 15K, 10K to 30K, half to full all fall in the sweet spot.
• For trained runners with consistent volume: Riegel assumes you have the aerobic base for the longer race. Otherwise, see “where it breaks.”

Where Riegel breaks

1. Predicting a marathon from a 5K when you don’t run long

Riegel implicitly assumes you’ve put in the long-run mileage to support a marathon. A 22:30 5K runner who’s done 50 km/week with a 30 km long run will probably hit 3:38. The same runner doing 25 km/week with a 12 km long run will probably blow up around 28 km and finish in 4:15+.

Rule of thumb: don’t trust marathon predictions if you haven’t done several runs of 25+ km in the prior 8 weeks.

2. Sprint distances → endurance distances

A 1500m time predicting a 10K is optimistic. The 1500m is anaerobic; the 10K is aerobic. Different energy systems, different training. Riegel’s exponent of 1.06 starts to fail meaningfully outside the 5K– marathon range.

For 1500m → 10K specifically, exponent 1.10 fits better (van Aken’s revision).

3. Hot weather and hills

Riegel assumes flat, cool conditions — the conditions records were set in. Race in 30°C heat or on a 600m elevation course and the prediction is meaningless.

A pragmatic adjustment: add 30–60 seconds per km for a notable headwind day, similar for hills. For heat above 25°C, expect 5–8% slower (Daniels’ rule).

Compared to other predictors

There are several competing formulas. None is dramatically better than Riegel for the common case.

The differences between them are usually under 2 minutes for a marathon prediction. If you want one number, Riegel is fine. If you want to double-check, run Riegel and Daniels and split the difference.

The “improving runner” caveat

Riegel predicts based on what your body can do now. If your training is trending up and you’re 8 weeks out from a marathon, your race-day performance will probably exceed the prediction. Conversely, if you’ve been injured or lost fitness, the prediction is optimistic.

Use Riegel as a starting point, not a goal. Add or subtract 2–3% for where you think you’ll be on race day.

Practical workflow

1. Pick your most recent honest race time (not a workout, not a fun run).
2. Use the pace calculator → “Predict race” tab → enter that time and distance, then your target distance.
3. Look at the predicted time. Subtract 2–3% if you’re improving fast. Add 2–5% if you’re undertrained for the distance.
4. Set training paces from the adjusted prediction, not the raw one.
5. Re-run after every tune-up race to update.

The math is exact. The interpretation is the art.