Workout Math Calculators

How to predict your race time

If you have run a 5K, you already have enough data to estimate your 10K, half-marathon, or beyond. Riegel's formula converts a known performance at one distance into a predicted time at another, accounting for the fact that pace inevitably slows as distance grows.

Riegel's formula

Peter Riegel published this model in American Scientist in 1981 after analyzing world record progressions across events ranging from 100 meters to 200 miles. The formula is:

T2 = T1 × (D2 ÷ D1)1.06

Where T1 is your known finishing time, D1 is the known distance, D2 is the target distance, and T2 is the predicted finishing time. Both distances must be in the same unit (kilometers, miles, or meters — it does not matter which, as long as they match).

What the 1.06 exponent means

The exponent 1.06 is the fatigue factor. If humans could hold pace perfectly regardless of distance, the exponent would be exactly 1.0 and the formula would just be a simple ratio. The value of 1.06 reflects the empirical observation that performance degrades slightly faster than the distance ratio alone would predict — roughly 6% additional slowing per doubling of distance.

Concretely: if you double the distance, your time more than doubles. A runner who finishes 5 km in 25:00 would need more than 50:00 for 10 km — the 1.06 exponent predicts the margin of slowdown.

This is an estimate, not a guarantee. Riegel's formula assumes you race both distances at similar relative effort, under comparable conditions, with fitness appropriate for the longer event. Real race-day variables — heat, hills, fueling, training specificity, and pure motivation — all shift the actual result.

Worked example: 5K to 10K

A runner completes a 5K in 25 minutes 30 seconds (25.5 minutes). What 10K time does Riegel predict?

T2 = 25.5 × (10 ÷ 5)1.06

First, compute the distance ratio raised to the power 1.06:

(10 ÷ 5)1.06 = 21.06 ≈ 2.0845

Then multiply:

T2 = 25.5 × 2.0845 ≈ 53.2 minutes

That is approximately 53 minutes 11 seconds for the 10K. The pace slows from about 8:11/mile at 5K to roughly 8:34/mile at 10K — the model bakes in a modest but real pace degradation over the longer distance.

What the formula assumes

Riegel's prediction is most reliable when several conditions hold:

Where predictions break down

The larger the distance jump, the less reliable the estimate. This is most visible at the marathon.

Many runners discover that Riegel's half-marathon-to-marathon projection is optimistic if they lack sufficient aerobic base. The formula is calibrated on world-class performers who have trained specifically for every event in the range. For recreational runners, the marathon demands a disproportionate amount of additional endurance work that a shorter race time alone cannot capture.

A common real-world observation: a runner whose Riegel-predicted marathon time is, say, 3:45 may find they run closer to 4:00–4:10 on their first marathon attempt if they are primarily a 5K or 10K runner by training habit. Adding 10–15 minutes to the formula's output is a reasonable conservative buffer for marathon first-timers.

Adjusting for personal tendencies

Some runners consistently outperform the Riegel estimate at longer distances — they are naturally strong at endurance relative to speed. Others consistently fall short. Once you have a few data points across different distances, you can compare your actuals to the formula's predictions and build a rough personal correction factor.

Using the prediction practically

Race time predictions have two main practical uses: setting a goal pace for race day, and confirming whether a goal is realistic given current fitness. If the formula predicts 2:02 for a half-marathon and you want to break 1:55, the gap tells you exactly how much fitness you need to build before the event.

For pace planning, take your predicted finish time, divide by the distance, and use that as your target pace per mile or kilometer. Starting 5–10 seconds per mile slower than predicted pace and building to it in the second half is generally a more successful strategy than going out at predicted pace and fading.