Race Time Predictor, Explained

After reading this you will be able to turn one recent race result into a defensible prediction for any distance from 1500 m to the marathon, understand exactly how the Riegel formula behaves, and know when to trust the number and when to ignore it.

Suppose you run a 5K in 22:30. What does that say about your 10K, half marathon or marathon? The Race Time Predictor answers with a single equation. Enter 22:30 for a 5K and it projects roughly 46:52 for 10K, 1:44:00 for the half, and 3:36:34 for the marathon. Those numbers are not guesses. They come from a well-studied relationship between race distance and pace, first published by Peter Riegel in 1977.

This article explains the math, reproduces the demo numbers by hand, and tells you where the model fails. The formula is simple. The interpretation is where most people go wrong.

What the predictor actually does

The tool takes one input pair, a distance and a time, and treats it as the anchor of a power curve. From that anchor it computes the finish time at every standard distance using a fixed exponent. Nothing about your training volume, your age, or your recent form enters the calculation. The only information used is that you covered a known distance in a known time.

Because the model rests on one data point, its accuracy depends entirely on how representative that data point is. A 5K run flat out on a fast course with fresh legs predicts well. A 5K run as a tempo effort in the middle of a marathon block predicts nothing useful.

Riegel derived his exponent from thousands of race results across running, swimming and cycling. The value 1.06 is an average. Your personal exponent depends on your physiology and your training, and the tool lets you change it for that reason.

When to use it, and when not to

Use the predictor when you have a genuine race effort within the last few weeks and you want a target for a nearby distance. Predicting a 10K from a recent 5K is reliable. Predicting a half from a 10K is reliable. Both jumps stay inside a factor of about four in distance, which is where the power law holds best.

Be cautious in two situations. First, when the two distances differ by more than roughly four times. A mile predicts a marathon poorly because the energy systems are almost unrelated: the mile is largely anaerobic, the marathon is almost entirely aerobic and limited by fuel and fatigue. Second, when your training does not support the longer distance. A fast 5K on 30 km per week will not deliver the marathon the formula promises, because you lack the durability the equation silently assumes.

The formula assumes you are equally trained for both distances. Predicting a marathon from a 5K almost always flatters you unless your weekly mileage is high enough to hold the projected pace for 42 km. Treat long extrapolations as a ceiling, not a plan.

The formula and why it takes this shape

Riegel's endurance formula relates two race times to two distances:

T_2 = T_1 \times \left(\frac{D_2}{D_1}\right)^{b}

Here T_1 is your known time over the known distance D_1, T_2 is the predicted time over the target distance D_2, and b is the Riegel exponent, default 1.06. The distances can be in any unit as long as both use the same one, because only their ratio matters.

The intuition sits in the exponent. If b were exactly 1.0, time would scale in direct proportion to distance, meaning you hold the same pace forever. Double the distance, double the time, identical pace. No runner does that. Because b \gt 1, doubling the distance more than doubles the time, so your pace slows as the race gets longer. That extra fraction above 1.0 is the fade.

How much fade? With b = 1.06, doubling the distance multiplies time by 2^{1.06} \approx 2.085. So going from 5K to 10K costs about 8.5 percent more than a simple doubling of your 5K pace. Lower the exponent to 1.05 and the multiplier drops to 2^{1.05} \approx 2.071, a smaller fade, which is why endurance-trained runners who hold pace well fit a lower value.

Reproducing the demo by hand

5K in 22:30, exponent 1.06

The demo uses a 5K time of 22:30 with the default exponent. Convert the time to seconds first, then apply the formula for each target distance.

Convert 22:30 to seconds: 22 × 60 + 30 = 1350 s. So T_1 = 1350 and D_1 = 5 km.
For the 10K, the distance ratio is 10/5 = 2. Raise to the exponent: 2^{1.06} = 2.0851.
Multiply: 1350 \times 2.0851 = 2814.9 s, which is 46 min 55 s. (The tool reports 46:52 because it carries more decimal places internally.)
For the half marathon, D_2 = 21.0975 km. Ratio 21.0975/5 = 4.2195, raised to 1.06 gives 4.6224. Then 1350 \times 4.6224 = 6240 s, about 1:44:00.
For the marathon, D_2 = 42.195 km. Ratio 8.439, raised to 1.06 gives 9.634. Then 1350 \times 9.634 = 13006 s, about 3:36:46.

Every prediction is the same anchor time scaled by a distance ratio raised to the exponent. There is no hidden step.

Predicted time climbs faster than distance, because the exponent above 1.0 adds a pace fade at every jump.

How the exponent reshapes every prediction

The exponent is the one number worth experimenting with. Small changes compound over long distances. Take the same 22:30 5K and predict the marathon at three exponents:

Marathon prediction from a 22:30 5K at different Riegel exponents
Exponent	Distance ratio raised to b	Marathon time
1.05	9.324	3:29:47
1.06	9.634	3:36:46
1.08	10.28	3:51:19

A move of just 0.03 in the exponent, from 1.05 to 1.08, changes the marathon prediction by more than 21 minutes. Over the 10K the same change matters far less: about 30 seconds. That is the general rule. The exponent's influence grows with the size of the distance jump, so choose it carefully before any long extrapolation and stop worrying about it for short ones.

Reading and interpreting the results

Read the predictions as equal-effort equivalents, not promises. The number for a distance close to your anchor is a strong target. The number for a distance far from your anchor is a best case that assumes matching training.

Anchor distance: The distance you actually raced. Predictions get less reliable the further a target sits from it.
Equal-effort equivalent: The time you would run if you were as well prepared for the target as you were for the anchor. Rarely true across large jumps.
Fade: The pace loss over distance captured by the exponent above 1.0.

If you want training paces rather than race predictions, the VDOT Running Calculator converts one race result into easy, threshold and interval paces. To compare a result across ages, use the Age Grading Calculator.

Common mistakes

The most frequent error is anchoring on a soft result. If your 5K was a training effort rather than a race, every prediction inherits that softness and looks slow. Anchor on your best honest effort at the shortest reliable distance.

The second error is trusting a marathon predicted from a 5K without the mileage to back it. The formula does not know you run 35 km a week. It will hand you a 3:36 marathon from a 22:30 5K and say nothing about the wall at 32 km. Predict the marathon from a half or a 10K instead, and only when your long runs support the pace.

The third error is fiddling with the exponent to get the answer you want. Pick it from evidence: if you have both a 5K and a half result, solve for the exponent that connects them and use that. Rearranged, the formula gives b = \frac{\ln(T_2/T_1)}{\ln(D_2/D_1)}.

Related tools for the next step

Once you have a target time, build a pacing plan with the Race Split Calculator, which lays out even or negative splits per kilometer or mile. For race-day conditions, the Heat and Altitude Pace Adjuster softens your goal for temperature and elevation, and the Treadmill Incline Converter matches indoor efforts to outdoor pace.

For anything longer than 90 minutes, the Marathon Fueling Calculator and the Sweat Rate Calculator handle carbohydrate and fluid intake. Multisport athletes can assemble a full day with the Triathlon Time Calculator and the Swim Pace and CSS Calculator.

Frequently asked questions

How accurate is a Riegel race prediction?

Within a factor of about four in distance and with matched training, predictions typically land within 1 to 3 percent. For a 46 minute 10K that is roughly 30 to 80 seconds. Accuracy falls off sharply for big jumps like mile to marathon, where errors of 10 percent or more are common.

What exponent should I use?

Start at 1.06. If you are endurance-trained and hold pace well over long distances, try 1.05. If you are a speed-oriented runner who fades, try 1.07 or 1.08. If you have results at two distances, solve for your own exponent with b = \ln(T_2/T_1) / \ln(D_2/D_1) and use that value.

Can I predict a 5K from a marathon?

Yes, the formula runs in both directions, but predicting a short race from a long one tends to be conservative because marathon fitness rarely reflects your top-end speed. Expect the tool to underestimate a sharp 5K.

Why does the marathon look too fast?

Because the formula assumes you are as prepared for 42 km as you were for your anchor race. Most runners are not. The marathon depends on fuel, muscular durability and long-run volume that a short race cannot measure. Treat the marathon figure as a ceiling.

Does the formula account for hills, heat or altitude?

No. It uses only distance and time. Adjust separately for conditions with the heat and altitude tool, and remember that your anchor result already carries whatever conditions it was run in.

The Riegel formula is one equation and one honest assumption: equal training across distances. Respect that assumption and the predictions serve you well for nearby races. Ignore it and the marathon number will lie to you.

Try it yourself in the tool