The Riegel Formula: Predicting Any Distance
Run a 10K in 50 minutes — what could you run a marathon in? In 1977, American engineer and runner Peter Riegel published a beautifully simple answer after analyzing world records across distances: T2 = T1 × (D2/D1)^1.06. Your time scales with distance raised to the power 1.06. The exponent captures a physiological truth: you slow down as distance grows, but slower than distance itself grows — endurance is sub-linear. Plug in 10K in 3,000 seconds and the formula predicts a marathon in about 3:50, which matches what well-trained runners actually do.
The 1.06 exponent was fit to elite world records, yet it works remarkably well for ordinary runners too — typically within a few percent for distances between 5K and the marathon, provided the input race was a genuine all-out effort. It is not magic; it is the statistical shape of human endurance, and the calculator above applies it to any pair of distances you choose.
How Accurate Is It, Really?
For adjacent distances (5K → 10K, 10K → half marathon), Riegel is usually within 2–3% for trained runners — often closer than the runner's own intuition. Accuracy degrades at the extremes: predicting a marathon from a 1-mile time, or a 100-mile ultra from a 10K, stretches the formula past its design. Ultras introduce fueling, terrain, and sleep deprivation that no exponent can capture; sprints introduce anaerobic energetics the formula ignores.
The biggest real-world error source is not the math but the input effort. A 10K "time trial" run at 90% effort predicts a marathon you cannot actually run, because the formula assumes maximal effort. Use a recent race — all-out, on a fair course, in decent conditions — and the prediction earns its keep. Treat course differences honestly too: a hilly trail 10K predicts a flat road marathon poorly.
From Prediction to Training Paces
A goal time is only useful if it tells you how to train, so the tool converts your predicted race pace into four training zones. Easy pace (about 30% slower than race pace per km) builds the aerobic base — this should be 70–80% of your weekly mileage, genuinely conversational. Steady pace adds controlled endurance. Tempo pace (roughly your 1-hour race effort) trains your lactate threshold — the famous "comfortably hard" 20–40 minute run. Intervals (slightly faster than race pace) build VO2max and leg turnover in short reps with recovery jogs.
These multipliers are starting points from exercise physiology, not prescriptions carved in stone. If tempo pace feels impossible to hold for 20 minutes, your input race may have been soft — or you may need more base. The zones should feel like their descriptions; perceived effort outranks the stopwatch.
Goal Bands: Racing With a Range
Smart racers convert a prediction into a band, not a bullseye. Take the Riegel time ± 2%: for a predicted 3:50 marathon, that is roughly 3:45–3:55. Plan A (the stretch goal) sits at the fast edge for a perfect day; Plan B (the solid goal) is the prediction itself; Plan C (the floor) is the slow edge, for heat, hills, or a bad patch. This is not pessimism — it is how experienced runners avoid the classic blowup of chasing an exact number through mile 20.
Pacing strategy follows from the band: even or slightly negative splits (second half as fast or faster) beat the optimistic-start-and-hang-on approach in almost every dataset ever collected. Your predicted even pace, shown under the big number, is the metronome — check it at every mile or kilometer marker and adjust early, not late.
What the Formula Cannot See
Riegel knows nothing about you. It does not know you have run 80 km weeks for a year (good — marathons reward mileage) or 25 km weeks (the prediction will flatter you). It does not know the course profile, the forecast, your fueling plan, or that you are coming back from injury. Two runners with identical 10K times can have marathon times 20 minutes apart based on training volume alone.
Use the prediction as the ceiling of what is possible with proper preparation, then train into it. The runners who hit their Riegel numbers share a pattern: high easy mileage, one tempo session weekly, long runs that practice race-day fueling, and a taper that leaves them restless and hungry to race. The formula gives you the target; the training gives you permission.
A Short History of Predicting Performance
Before Riegel, coaches used tables and rules of thumb — "double your half marathon time and add 10 minutes" for the marathon, which works okay but breaks down elsewhere. Riegel's 1977 paper in Runner's World (later formalized in the American Scientist) was the first principled curve, and it has survived five decades of challengers. Later refinements — Cameron's adjustments, the Purdy point tables, VDOT (Jack Daniels' system, which adds a fitness score to similar math) — all orbit the same insight: human endurance follows a power law.
The power law shows up everywhere in physiology: metabolic rate scales with body mass to the 3/4, and race time scales with distance to the ~1.06. These are not coincidences — they are signatures of how biological systems distribute effort and dissipate heat. Your marathon prediction is, in a small way, a window into the physics of being alive.
Putting It to Work This Season
Here is the workflow: race something short all-out (a 5K or 10K time trial counts), enter it above, and read your target distance's prediction. Set your training paces from the zone table — most runners should spend the next 8–12 weeks doing 80% easy miles at the easy pace, one tempo session, and one long run. Re-test with another short race mid-cycle; if the prediction moves, your fitness moved — adjust the goal band, not your self-worth. On race week, trust the taper, and on race day, run the even pace the card shows. The formula did the math; you just have to do the miles.
Taper Week and Race-Day Execution
A prediction is only as good as the legs that chase it, and the final 10 days decide how fresh those legs are. The taper is simple: cut volume by 40–60% over two to three weeks (one week for shorter races), keep some intensity so your legs remember speed, and resist the urge to "test" your fitness — you cannot gain fitness in taper week, but you can absolutely spend it. Sleep more, eat normally (the famous carb-load matters mostly for races over 90 minutes), and lay out everything the night before. Pre-race anxiety is universal; a written plan is the antidote.
On the day, execute the band strategy from the card. Start at the slow edge of your goal band for the first 10–20% of the race — adrenaline makes goal pace feel easy early, and that feeling is a liar. Check your even pace at every timing mat; if you are more than 10 seconds per kilometer off, correct gently, not frantically. Take fuel and water on schedule from the start (your stomach stops cooperating late, so front-load calories), and save your surge for the final quarter, where passing fading runners delivers the biggest psychological boost in sports. Cross the line, check the clock, and compare it to the prediction — then enter the new result above and start planning the next one. The formula loves fresh data.
When Predictions Miss
No formula accounts for weather, hills, or race-day nerves. Heat is the biggest spoiler: every five degrees above sixty Fahrenheit can cost one to two percent, which turns a predicted 3:50 marathon into 3:55 on a warm day. Hilly courses punish optimistic predictions too — a flat 10K time says little about a trail half marathon with a thousand feet of climbing.
For the sharpest prediction, feed the calculator your most recent race at the closest distance below your goal, run in similar conditions. A 10K from last month predicts a half marathon far better than a marathon PR from three years ago. Fitness changes; the formula only knows the numbers you give it, so give it fresh ones.