How Fast Could You Run a Marathon? The Honest Math of Race Prediction

Every runner has done the napkin math. Take your half marathon time, double it, add a few minutes, and there's your marathon. Or worse: take your 5K pace and just... assume you could hold it for 26.2 miles, give or take.

The napkin math is wrong in a specific, predictable way — and the formulas that get it right are worth understanding, because they'll also tell you when not to trust them. Race prediction is genuinely accurate between adjacent distances and genuinely flattering at the marathon. Knowing which situation you're in is the difference between a well-paced race and a death march from mile 20.

The Riegel Formula: One Number Rules Them All

In 1981, engineer Pete Riegel published a deceptively simple observation: across running, swimming, and race-walking world records, the relationship between distance and time follows a consistent power curve (Riegel, 1981). His formula:

T2 = T1 × (D2 / D1)^1.06

Take a time you've actually run (T1) at a distance (D1), and it predicts your time (T2) at another distance (D2). The whole model lives in that exponent — 1.06 — which Riegel called the "fatigue factor." If pace were perfectly sustainable, the exponent would be 1.0 and your marathon pace would equal your 5K pace. The extra 0.06 encodes how much you slow down as distance grows.

It doesn't look like much, but it compounds. A 22:00 5K runner gets:

Almost a full minute per mile slower at the marathon than the 5K — and that's the optimistic version, for reasons coming below. Run your own numbers through the race time predictor; it applies Riegel across every standard distance from a single input.

The Magic Mile: Prediction Without a Race

The Riegel formula needs a recent race time, and plenty of runners don't have one. Jeff Galloway's answer is the Magic Mile: warm up, run one mile as fast as you can sustain, and feed that into a set of multipliers he refined over decades of coaching — roughly, your 5K pace is your mile pace plus 33 seconds per mile, your half marathon pace is mile pace times 1.2, your marathon pace is mile pace times 1.3 (Galloway, 2016).

The appeal is logistics. A mile time trial needs a track or a flat stretch of road and about 20 minutes including warm-up. You can repeat it monthly as a fitness check without the recovery cost of racing. The Magic Mile calculator does the conversion for you.

The trade-off is precision. A mile leans harder on speed and running economy than a marathon does, so the extrapolation is stretched thin — Galloway himself frames the marathon multiplier as what you could run with the right training, not what you could run this weekend. Treat Magic Mile output as a goal-setting tool, and treat an actual recent race as the better prediction input whenever you have one.

Why the Marathon Lies to You

Here's what every prediction formula struggles with: the marathon isn't just a longer race. It's a different event.

Up to about the half marathon, performance is governed mostly by your aerobic engine — the same physiology that powered your 5K, scaled by the fatigue exponent. Riegel's 1.06 handles this well, which is why 5K-to-10K and 10K-to-half predictions are reliably close for trained runners.

The marathon adds a constraint the shorter races never touch: fuel. Your muscles and liver store roughly 2,000 calories of glycogen — enough for about 18-20 miles at race effort. Past that point you're running on fat oxidation and whatever carbohydrate you absorbed mid-race, and if your training hasn't specifically developed those systems, your pace doesn't drift — it collapses.

The data backs this up. A study of over 2,300 recreational runners found that Riegel's formula predicted well between shorter distances but was systematically optimistic at the marathon — finishers averaged roughly 10 minutes slower than their half marathon predicted, and the shortfall was largest for runners with low training volume (Vickers & Vertosick, 2016). Their improved model added a single variable that fixed most of the error: weekly mileage. A 70-mile-per-week runner can trust something close to 1.06. A 25-mile-per-week runner racing a marathon should mentally re-run the math with an exponent closer to 1.10 — which, for the 22:00 5K runner above, moves the marathon prediction from 3:31 to nearly 3:50.

The rule of thumb: predictions are trustworthy one step up in distance, aspirational two steps up. Your 10K predicts your half. Your half predicts your marathon only if you've done the long-run and mileage work the formula silently assumes.

Turning a Prediction Into a Race Plan

A prediction you believe is a pacing plan. A prediction you half-believe is how negative splits die.

Set your pace from the prediction, not your ego. If the formula says 3:30:46, that's 8:03 per mile — and the pace converter will give you the full split table at 5K, 10K, and halfway so you know exactly what the clock should read as you pass each mark. Bank-the-time strategies (going out faster to "buy a cushion") consistently backfire; even pacing or a slight negative split is how almost every distance record has been run.

Adjust for the course and the day. Riegel assumes flat, cool, and calm. Add time for heat above 60°F, meaningful elevation gain, or a crowded start. A prediction from a downhill or short course is contaminated input — garbage in, garbage out.

Use the freshest adjacent race. A 10K from three weeks ago beats a half marathon PR from last year. Fitness moves; the formula doesn't know that unless you feed it current data.

Re-predict as you train. Race a 5K or run a Magic Mile every 4-6 weeks of a marathon build. If the predictions are trending down, your training is working. If they're flat while your mileage climbs, something — recovery, fueling, intensity distribution — needs attention. For structuring the training itself, the VDOT system takes the same race input and converts it into exact workout paces, and the heart rate zones guide covers the effort-based version for days when pace doesn't translate.

The marathon will always punish unearned confidence — that's half its appeal. But the gap between the runners who blow up at mile 20 and the ones who finish strong usually isn't fitness. It's that one group raced the prediction their training had actually earned, and the other raced the one they wanted. Run the numbers, look honestly at your weekly mileage, and pick the right one.

References

1. Riegel, P. S. (1981). "Athletic records and human endurance." American Scientist, 69(3), 285–290.
2. Vickers, A. J., & Vertosick, E. A. (2016). "An empirical study of race times in recreational endurance runners." BMC Sports Science, Medicine and Rehabilitation, 8, 26.
3. Galloway, J. (2016). Galloway's Book on Running (3rd ed.). Aachen: Meyer & Meyer Sport.
4. Bassett, D. R., & Howley, E. T. (2000). "Limiting factors for maximum oxygen uptake and determinants of endurance performance." Medicine & Science in Sports & Exercise, 32(1), 70–84.
5. Coyle, E. F. (2007). "Physiological regulation of marathon performance." Sports Medicine, 37(4–5), 306–311.
6. Abbiss, C. R., & Laursen, P. B. (2008). "Describing and understanding pacing strategies during athletic competition." Sports Medicine, 38(3), 239–252.