Race Pace: Predicting Your Marathon From a 10K

Type a recent result into any race time predictor and the number that comes back is almost certainly Pete Riegel's. His endurance equation, published in American Scientist in 1981, needs one input — a distance and time you actually raced — and one constant: an exponent of 1.06 that describes how performance decays as races get longer. Feed it a 50-minute 10K and it predicts a 3:50:01 marathon. Not the 3:30:58 you would get by holding your 10K pace for the full 42.195 km — nineteen minutes slower, and that gap is the entire reason the formula exists.

The method fits in a sentence: divide the target distance by the distance you raced, raise that ratio to the power 1.06, multiply by your time. Everything below is the arithmetic run in the open on real numbers, the reverse trick that turns a marathon goal into a 10K requirement, and — because the marathon is exactly where this model is least trustworthy — the documented limits to check before betting 42.195 km on the output.

T2 = T1 × (D2 ÷ D1)^1.06 — T1 is your time at raced distance D1; T2 is the predicted time at target distance D2

What the exponent is claiming

Riegel derived the equation from record performances across running distances — his 1981 paper is titled "Athletic Records and Human Endurance" — and found one exponent fitted trained endurance running across a wide span of distances. The number is worth staring at. If the exponent were exactly 1.00, time would scale in strict proportion to distance: your 10K pace would carry to the marathon untouched, and prediction would be multiplication. The extra 0.06 is the fatigue term, and it compounds per doubling: 2^0.06 = 1.042, so each doubling of race distance slows your sustainable pace by about 4.2% — near a 5:00/km base, that is 300 s × 0.042 ≈ 13 seconds per kilometre, every time the race doubles.

The prediction, digit by digit

Take that 50:00 10K — 5:00/km, or 8:03/mi. Three steps:

1. Distance ratio. The marathon is 42.195 km (fixed at the 1908 London Olympics, ratified in 1921), so D2 ÷ D1 = 42.195 ÷ 10 = 4.2195.
2. Apply the exponent. 4.2195^1.06 = 4.6002.
3. Multiply by your time. 50 min × 4.6002 = 230.01 minutes = 3:50:01.

The implied race pace follows by division: 230.01 ÷ 42.195 = 5.451 min/km, and 0.451 × 60 = 27 seconds, so 5:27/km — or 8:46/mi, via 5.451 × 1.609344 = 8.77. The model is telling you to concede a full 27 seconds per kilometre to the distance before the gun even fires. The running pace calculator will turn that 5:27/km into everything else a race plan needs — kilometre or mile splits, the treadmill speed equivalent, a total-time cross-check — through the same identity it solves everything with: time = distance × pace.

The naive alternative shows why the exponent earns its keep. Holding 5:00/km for the marathon means 42.195 × 5 = 210.975 minutes, which is 3:30:58. Riegel's prediction sits 230.01 − 210.975 = 19.035 minutes above it. Runners who pace a first marathon off their 10K pace discover those nineteen minutes one kilometre at a time, in the wrong half of the race.

One 10K, a ladder of predictions

The same input predicts every other distance at once, downward as well as upward:

Read the pace column top to bottom: 4:48, 5:00, 5:14, 5:27 — steps of 12 to 14 seconds per kilometre, the compounding 4.2%-per-doubling made visible. And note the 5K row: half your 10K time would be 25:00, but the formula predicts 23:59, a minute quicker. The exponent works in both directions — shorter races support proportionally faster paces, which is why "double your 5K and add a bit" underestimates almost everyone's 10K.

Running it in reverse

Because the formula is a single power law, it inverts cleanly: T1 = T2 ÷ (D2 ÷ D1)^1.06. That turns a marathon ambition into a concrete short-race requirement you can test this month.

Suppose the goal is 3:10:00 — the Boston Athletic Association's 2026 qualifying standard for men aged 40–44. That is 190 minutes, so the Riegel-equivalent 10K is 190 ÷ 4.6002 = 41.30 minutes, a 41:18 10K. This inversion is the cheapest honesty check in marathon planning: if your current 10K sits minutes away from the anchor your goal implies, the problem is not yet pacing strategy — it is fitness, and the racing calendar should say 10Ks before it says marathon.

The known limits

Riegel's sweet spot is well mapped: for trained runners, between the mile and the half marathon, prediction errors typically run under 2%. Outside that band, four failure modes matter.

The marathon crosses a fueling boundary. The exponent models fatigue as one smooth curve, but marathon-specific limiters — glycogen depletion, accumulated thermal load, gait economy deteriorating under fatigue — are not captured by any single exponent. The formula systematically overpredicts marathon performance for runners stepping up from shorter distances; real results come in slower. Treat the Riegel marathon number as a ceiling, not a target.

The anchor distance sets the leverage. Predicting the marathon from a half asks the exponent to cover a ratio of exactly 2 (21.0975 × 2 = 42.195). From a 10K the ratio is 4.2195; from a 5K it is 42.195 ÷ 5 = 8.439. Every extra unit of ratio is extrapolation resting on that one fitted constant, so anchor to the longest recent race you own.

It assumes you are trained for the target. The records Riegel fitted were set by athletes prepared for each distance. The equation silently carries that assumption to you: a 50:00 10K earns the 3:50:01 only alongside marathon-appropriate long runs and weekly volume.

It assumes the anchor is current. A personal best from last year predicts the runner who set it. Use a result from this training block, even a slower one.

What actually predicts the marathon better

Two alternatives the running literature backs, both usable alongside Riegel rather than instead of it. Tanda's 2011 model predicts marathon time from training indices — weekly training distance and average training pace — and consistently outperforms Riegel for marathon prediction in trained runners, precisely because it measures the preparation that a single race result cannot see. Yasso 800s, Bart Yasso's Runner's World workout from the 1990s, offer a track-session sanity check: run 10 × 800 m at the fastest repeatable pace, and the average in minutes:seconds tends to match the marathon in hours:minutes — a 3:10 marathoner runs 3:10 repeats. Its known bias runs both ways: it flatters runners with thin aerobic bases and undersells highly trained marathoners.

The training volume Tanda measures is also an energy budget, and no race predictor sees that variable at all. A desk worker moving from three or four sessions a week ("moderately active", multiplier 1.55) into a six-day marathon build ("very active", 1.725) changes maintenance needs materially: for the TDEE calculator's reference case — a 30-year-old male, 70 kg, 175 cm, with a Mifflin-St Jeor BMR of 1,648.75 kcal/day — the shift is 1,648.75 × 1.725 = 2,844 kcal/day against 1,648.75 × 1.55 = 2,556, an extra 288 kcal every day. Chronically underfueling the block erodes exactly the endurance the 1.06 assumes you will bring to the start line.

Forty-five years after publication, Riegel's one-liner endures because it makes a falsifiable claim: a finish time written down before the gun, checkable against the clock at the line — the same standard every tool on Quanta is built to meet. So grade it. Predict from your freshest race, temper the marathon number with Tanda or a Yasso session, and then let the race mark the exam. When the clock and the prediction disagree by more than a few percent, send us the pair: the 10K you anchored on and the marathon you actually ran. A formula this simple deserves auditing, and the only audit that counts happens at a finish line.

Sources

• Tanda (2011) — prediction of marathon performance time from training indices, Journal of Human Sport and Exercise
• World Athletics — marathon records and the 42.195 km distance
• Boston Athletic Association — Boston Marathon qualifying standards
• Jack Daniels — Daniels' Running Formula, 3rd ed. (VDOT tables)