How accurate is a race time predictor?

For a step up of one distance — 5K to 10K, or half to marathon — the Riegel formula is usually within 1–2%. Across a bigger jump, like 5K to marathon, it commonly reads 3–8 minutes optimistic for runners without high weekly mileage. The formula knows your speed but not your endurance base, which is why the fatigue factor slider exists.

What marathon time does a 20-minute 5K predict?

Using Riegel's standard exponent of 1.06, a 20:00 5K predicts 3:11:49 for the marathon. That assumes you are actually trained for 42 km. A runner on 40 km a week off the same 5K speed is far more likely to run 3:20–3:30, and the difference is almost entirely long-run volume rather than talent.

What is the Riegel formula?

T2 = T1 × (D2 ÷ D1)^1.06, published by Peter Riegel in American Scientist in 1981. He fitted a power law to world records from 100 m to 100 miles and found an exponent near 1.06, meaning that doubling the distance takes about 2.085 times as long rather than exactly twice as long. That roughly 8.5% penalty per doubling is what people mean by 'fatigue factor'.

Why is my actual marathon slower than the prediction?

Three usual reasons: not enough weekly volume or long runs, so glycogen and muscular endurance run out around 30 km; fuelling and heat, which cost minutes the formula cannot see; and starting too fast, which is the most expensive mistake in the sport. Predictions describe an equivalent performance for someone properly trained at that distance, not the outcome of any given day.

Should I use Riegel or VDOT for race predictions?

They agree more closely than most people assume. A 20:00 5K is VDOT 49.8, which corresponds to a 3:11:17 marathon against Riegel's 3:11:49 — about half a minute apart. Across the usual range VDOT behaves like a Riegel exponent near 1.059, so pick either and spend your attention on the fatigue factor instead, since that is where the real uncertainty lives.

How recent does my race need to be?

Within about six weeks, and ideally at a full effort rather than a hard training run. Fitness changes faster than most people expect: a six-month-old result predicts your fitness six months ago. Time trials work fine as inputs, but solo efforts usually run 1–2% slower than a real race for the same fitness.

Free Race Time Predictor — 5K, 10K, Half & Marathon from Any Result

Turn one recent race into predicted times at every distance with the Riegel formula — then tune the fatigue exponent to match how endurance-trained you actually are.

Distance	Predicted time	min/km	min/mi
5Kyour race	25:00	5:00	8:03
10K	52:07	5:13	8:23
Half marathon	1:55:00	5:27	8:46
Marathon	3:59:47	5:41	9:09

Where the 1.06 comes from

In 1981 Peter Riegel, an engineer and course measurer, published Athletic Records and Human Endurance in American Scientist. He took world-record times across running, swimming and cycling — distances from 100 m to 100 miles — and fitted a power law to them. The result was startlingly clean: time scales with distance raised to about 1.06.

T₂ = T₁ × (D₂ / D₁) ^ 1.06 Double the distance: 2 ^ 1.06 = 2.0849 → pace 4.2% slower 5K 20:00 → 10K: 20:00 × 2.0849 = 41:42 5K 20:00 → half: 20:00 × 4.6002 = 1:32:00 5K 20:00 → marathon: 20:00 × 9.5911 = 3:11:49

The exponent is doing something physiologically real. If humans could hold one pace forever the exponent would be exactly 1.00. It is above 1.00 because sustainable intensity falls as duration rises — glycogen empties, core temperature climbs, muscle fibres accumulate damage, and the fraction of VO₂max you can hold drops from around 100% for a few minutes to roughly 75–85% for a marathon.

The exponent is a population average, not your number

Fatigue factor	Who it describes	5K 20:00 → marathon
1.03–1.05	High mileage, years of long runs, ultra background	3:00–3:08
1.06	Riegel default — a well-rounded, distance-trained runner	3:11:49
1.07–1.08	Solid 5K/10K speed, moderate weekly volume	3:16–3:20
1.09–1.10	Fast over short distances, low volume, first marathon	3:24–3:29

Riegel himself warned that the formula holds best for durations between about 3.5 minutes and 4 hours, and for athletes actually trained at both distances. Outside that window it drifts — which is also why it fails badly on trail and mountain races, where terrain and vertical gain dominate.

When predictions break

Short race → marathon, without the volume

This is the single most common failure, and it is not the formula’s fault. A 5K is limited by VO₂max and speed. A marathon is limited by how much glycogen you stored, how efficiently you burn fat, and whether your legs can absorb 30,000 more foot strikes than they are used to. Two runners with identical 5K times and 40 km versus 100 km weekly volume can finish half an hour apart.

Heat, hills and fuelling

Every degree above roughly 15 °C costs marathon time — a warm day can take 2–5% off performance for the same fitness. Net elevation gain, crowded starts, and a missed fuelling plan all sit outside the model. If conditions are bad, apply your own penalty to the number the formula gives you rather than trusting it and blowing up at 32 km.

Very short distances

Predicting a marathon from a 400 m sprint is meaningless — the energy systems barely overlap. The prediction only carries information when both the source race and the target lean on aerobic metabolism.

How to use this for pacing

A predicted finish time is only useful once it becomes a pace you can rehearse. Three rules that survive contact with race day:

Pace off the prediction you believe, not the best one. Set the fatigue factor honestly. If your longest run this cycle was 25 km, you are not a 1.04 runner.
Run the first 10 km 5–10 seconds per kilometre slower than goal pace. Negative splits are how nearly every marathon personal best is actually run.
Convert to splits before you start. Our pace calculator turns any target time into per-kilometre and per-mile splits, so you know what the watch should read at every marker.

The VDOT relationship

Jack Daniels and Jimmy Gilbert built a different model in Oxygen Power: rather than a single exponent, they used two fitted curves — the oxygen cost of running at a given speed, and the fraction of VO₂max a human can hold for a given duration. Dividing one by the other gives VDOT, a VO₂max-equivalent score.

cost = −4.60 + 0.182258·v + 0.000104·v² (v in m/min) %max = 0.8 + 0.1894393·e^(−0.012778·t) + 0.2989558·e^(−0.1932605·t) (t in minutes) VDOT = cost / %max

The two models agree far more closely than their different shapes suggest. A 20:00 5K is VDOT 49.8; the same VDOT at 42.195 km works out to 3:11:17, against Riegel’s 3:11:49 — half a minute apart over three hours. Across the usual range, VDOT behaves like a Riegel exponent of about 1.059, so anyone claiming one is dramatically more realistic than the other at the marathon is describing a preference, not a difference. Both share the same blind spot: they assume you are equally trained at both distances. If you want the VDOT view, run your race through our VO₂max calculator — it reports the VDOT value directly.

The part no formula can give you

Marathon-specific fitness is a separate quality from speed, and it is built by weeks of accumulated volume, long runs at moderate effort, and practised fuelling — not by anything visible in a 5K result. A prediction tells you what your engine is worth if the chassis holds. Whether it holds is decided in the twelve weeks before the race.

So use the table as a target-setting tool and a sanity check, not as a forecast. If the predicted marathon pace feels absurd on a 30 km long run, the run is right and the formula is wrong. And if you are absorbing that training well, your recovery data will say so — which is where HRV and sleep debt stop being abstract.

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