Prediction Science

Riegel Formula Predictions: 4 Accuracy Factors

Plug a 20:00 5K into the race predictor and Riegel's formula — t2 = t1 × (d2/d1)^1.06 — spits out a projected marathon. The exponent 1.06 accounts for fatigue growing faster than distance, and it works surprisingly well. But it is a model, not a promise. Four factors decide whether that number is close or a fantasy.

1. Course elevation comes first

Riegel assumes a flat course. Add 1,000+ feet of climbing and your marathon will run slower than the formula says. The safe play: treat the projection as a flat-course number, then add the well-worn rule of thumb — roughly 3–5 seconds per km of climbing per 100 meters.

2. Weather shifts speed more than you think

The single biggest off-model surprise is heat and humidity. For every 5°C above 15°C, expect to lose 1–2% off the projected pace. Cold and rain are the runner's ally; hot and muggy are the formula's blind spot.

3. A real taper changes the exponent

Formula projections assume you are equally fresh at every distance. But you taper specifically for the marathon — 2–3 weeks of reduced volume — so your actual day lifts the projection. A short-track 5K run mid-training underestimates what a fully tapered you can do at 42.2 km. Prefer a race result that is at least 3–4 weeks from the target.

4. Pacing error compounds across 26.2 miles

The formula predicts potential, not execution. Going out 3% too hot in a marathon erases more than a 3% time through the fade. Your real marathon is the projection minus whatever pacing discipline you can't hold. Prediction is only as good as your restraint.

How to use it honestly

Feed in your most recent, most representative race — not your best-ever memory. Add a small reserve for course and conditions, and run the real race conservatively for the first half. Build your pace from your own numbers in the calculator, and let the formula set the ceiling you sneak under.