Race time predictor

How the Riegel formula predicts a race time

Peter Riegel published this formula in 1981 after fitting it to a large set of world and personal best times, with the formula scoped to efforts lasting roughly 3.5 to 230 minutes. It turns one known race performance into a predicted time at a different distance.

The formula spelled out

Take the time from a recent race, T1, and its distance, D1. To predict your time T2 at a new distance D2, multiply T1 by the ratio of the two distances raised to the power 1.06. The exponent, just above 1.0, reflects the fact that pace naturally slows a little as distance increases, rather than staying perfectly flat.

Worked example

Run a 10K in 50:00 and want a marathon prediction. D2 divided by D1 is 42.195 divided by 10, which is 4.2195. Raised to the power 1.06 that comes to about 4.60. Multiply by 50:00 and the predicted marathon time is roughly 3:50:01. The same steps work in the other direction too: a marathon time predicts a shorter distance by dividing instead of multiplying, since D2 is now smaller than D1 and the exponent still applies to the ratio between them.

How Riegel derived the exponent

Riegel arrived at 1.06 by plotting the logarithm of finish time against the logarithm of distance across a large set of record and personal-best performances, then fitting a straight line through them. The slope of that line, once converted back out of log space, is the 1.06 exponent used here. A perfectly flat pace across every distance would produce an exponent of exactly 1.0. The fact that it comes out a little above that is the mathematical signature of pace slowing gradually as distance increases, rather than evidence of any single physiological mechanism.

Why Riegel, and how it compares to other methods

Riegel's 1981 formula is the most widely used race time predictor because it needs only one input race and one exponent, fitted from world-record times with the formula scoped to efforts lasting roughly 3.5 to 230 minutes.

VDOT and the Daniels tables

Jack Daniels' VDOT system estimates a runner's aerobic fitness from one race performance, then reads off equivalent times at other distances from tables built on oxygen cost curves rather than a single exponent. It tracks slightly differently at very short distances but lands close to Riegel across 5K to marathon.

Cameron's formula

Cameron's formula adds extra terms to account for aerobic and anaerobic contribution separately, aiming for more accuracy at the extremes, very short sprints and ultra-distances, where a single exponent fits less well. Across the 5K to marathon range this calculator covers, the extra complexity buys little over Riegel.

Why this calculator uses Riegel

Riegel needs no lookup table, works from any input race distance, and its accuracy for 5K through half marathon predictions is well supported in practice. Its main weakness, covered next, is specific and well documented: marathon predictions made from a much shorter race.

Critical power and other physiological models

Beyond VDOT and Cameron, exercise scientists also model endurance performance through critical power, the highest sustainable output before fatigue accelerates sharply, estimated from a handful of maximal efforts at different durations. Critical power models can be more accurate for an individual athlete who has actually done the testing, but they need several hard efforts to calibrate rather than the single race Riegel asks for. For a recreational runner without access to that kind of testing, a single-race formula like Riegel remains the practical starting point, even though a critical power model would likely narrow the error further for someone willing to do the extra testing.

How sensitive is the prediction to the exponent

The 1.06 exponent is doing all the work in the Riegel formula, so it is worth understanding what moving it actually changes. A slightly higher exponent predicts a bigger slowdown over a longer distance, and a slightly lower one predicts less of one.

What a higher exponent means

Vickers and Vertosick found that recreational marathon runners slow down more between a shorter race and the marathon than the standard 1.06 exponent assumes. In practice that means the true exponent for a marathon prediction behaves as if it were somewhat higher, which is exactly why the formula runs optimistic over that distance.

Why this calculator still uses 1.06

A single fixed exponent keeps the formula usable without asking for a training history the input race alone cannot provide. The honest fix is not a different constant, it is reading a marathon prediction with the caveat this page keeps repeating: treat it as a ceiling, not a target, unless your long runs back it up.

A worked comparison of exponents

The difference a shifted exponent makes is easiest to see side by side. At 1.06, a 50:00 10K predicts a marathon of roughly 3:50:01. Nudge the exponent to 1.10 and the same 10K predicts closer to 4:03:39, a swing of well over ten minutes from a change most runners would never think to apply themselves. That gap is exactly why the marathon caveat on this page exists: not because the formula is wrong, but because one fixed exponent cannot represent every runner's actual fatigue profile.

Predicted times at a glance

Predicted times across the standard distances, from three common input races each run at an even effort. The 10K input row is highlighted, since predicting from a 10K to a half marathon is a moderate extrapolation Riegel handles well.

Why the marathon prediction often runs optimistic

Riegel's exponent of 1.06 is a good average fit across a huge dataset, but an average hides its range. Vickers and Vertosick's 2016 study of recreational endurance runners found Riegel well calibrated for the half marathon and 10K, but poorly calibrated for the marathon, giving predictions at least 10 minutes too fast for about half of recreational runners.

Why the marathon is different

The marathon draws heavily on fuel availability and fatigue resistance built up over months of long runs, not just the aerobic power a 5K or 10K reveals. Riegel's own error confirms this: across the runners Vickers and Vertosick studied, the formula's mean squared error for the marathon was 381, against 228 for a model that added weekly mileage to a single prior race, meaning mileage carries information a lone finish time and a fixed exponent cannot capture. Glycogen depletion, the drop-off commonly described as hitting the wall past 30 kilometres, is a training-volume problem more than a pure speed problem, and no formula based on a single shorter race can see it coming.

A practical adjustment

If your longest weekly run is well under 25 to 30 kilometres, treat this calculator's marathon prediction as an optimistic ceiling rather than a target, and lean towards a more conservative goal time on race day. The closer your input race is to marathon distance, the smaller this effect becomes.

Choosing the right race to predict from

The prediction is only as good as the race you feed it. A recent, well paced effort at close to maximum sustainable effort for its distance gives Riegel the cleanest signal to work from, which is why a genuine race result almost always beats a guessed-at training pace as the input.

Use a recent result

Fitness changes over weeks, so a race from the last 8 to 12 weeks reflects your current form far better than a personal best from a year ago.

Avoid a poorly paced race

A race run with a fast start and a big fade, or one run conservatively as a training effort, understates or overstates your true current fitness and carries that error straight into the prediction.

Pick a distance close to your target

Predicting a 10K time from a 5K is a smaller extrapolation than predicting a marathon time from a 5K, and smaller extrapolations are consistently more reliable, for the reasons covered above.

Time trial versus race

A solo time trial can work as an input, but a competitive field usually pulls a slightly better effort out of most runners than training alone does. If you only have a time trial to go on, treat the prediction as a touch conservative rather than exact.

Averaging more than one input race

If you have raced two or three distances recently, predicting from each and comparing the results is more informative than trusting a single number. Close agreement between predictions from, say, a 5K and a 10K suggests your current fitness is well represented by both efforts. A wide spread between predictions is itself useful information: it usually points to one of the input races being poorly paced, run in bad conditions, or simply stale, rather than to a flaw in the formula.

How to use a predicted race time

Treat the prediction as a planning number, not a promise. Use it to set an opening goal pace, then adjust as training and race-day conditions confirm or challenge it.

Setting a goal pace

Once you have a predicted time, the running pace calculator turns it into the exact per kilometre or per mile split to hold on the day.

Re-predicting through a training block

Re-run the prediction from a fresh time trial or tune-up race every few weeks during a training block. As fitness, and for the marathon, weekly mileage build, the gap between prediction and reality typically narrows.

Building in a buffer

For a marathon goal built from a shorter input race, it is reasonable to set two numbers: an ambitious pace close to the raw prediction, and a fallback pace a few minutes slower per hour. Deciding between them at halfway, based on how the day actually feels, beats locking in a single optimistic number before the start.

Checking a predicted time against your training plan

A predicted time is only as good as the training behind it. If a plan's long runs, weekly mileage and key sessions do not support the predicted pace, the number is aspirational rather than realistic, regardless of how well the input race was run. Cross-checking a marathon prediction specifically against your longest recent run, held at or near goal pace for at least part of it, is a better sanity check than the formula alone can offer.

Common mistakes

Predicting a marathon from a single short race. Treat it as an optimistic ceiling rather than a goal, as covered above.

Using an old result. A personal best from a year ago no longer reflects current fitness as accurately as a race from the last few months.

Ignoring the conditions of the input race. Heat, wind, hills or a crowded start on the race you are predicting from distort the number in either direction.

Chasing the prediction on a bad day. Illness, heat or poor sleep on race day can make even an accurate prediction unreachable, and that is a pacing decision, not a formula problem.

Comparing predictions across very different distances without caution. A 5K to 10K prediction is far more reliable than a 5K to marathon one.

Locking in one goal pace and refusing to adjust it. Conditions and how the day actually feels beat a number calculated days earlier, especially over marathon distance.

Assuming a longer race averages out a shorter one. A strong 5K and a weak 10K a month apart do not combine into a reliable input; use the more recent, better paced effort rather than picking whichever prediction looks the most flattering.

How coaches use a race time predictor

For a coach setting goal times ahead of a race, a formula-based prediction is a fast, defensible starting point before layering in what training has actually shown, especially with a squad of clients targeting different distances on the same calendar.

A workable routine: predict from the most recent solid time trial or tune-up race, cross-check a marathon prediction against actual long-run mileage and pace, and set the final goal in a check-in conversation rather than handing over a number cold.

Scraler keeps race results, training paces and check-ins together, so a predicted time sits alongside the mileage and sessions that will decide whether it holds up. See client check-ins, or read how hybrid personal training programmes endurance clients alongside strength work.

A predicted time is also a useful early warning when it stops moving. If a client's predicted time from repeated tune-up races plateaus or slips over several weeks despite consistent training, that is worth a conversation before the goal race, not after it, since it usually points to accumulated fatigue, an illness building, or a training load that has quietly outpaced recovery rather than a fitness ceiling.