Marathon Time Predictor

Enter a recent 5K, 10K or half marathon and get an estimated marathon time. You get a range, not one number, because a short race shows your speed, but not how your legs, fuel and pacing will hold up over 42.195 km. Every result here is an estimate.

How it works

1. Choose the race distance: 5K, 10K or half marathon.
2. Enter your time. Use a race, or an all-out time trial, from the last couple of months on a flat course. A hilly or hot race makes the estimate too slow; an old race may no longer fit your fitness.
3. You get three estimates and the range between them. The fastest and slowest of the three set the range.
4. Pick a goal from the range (see "Which number should I aim for?" below), then turn it into paces and splits in the marathon pace calculator.

The longer the race you enter, the better. A half marathon tells you more about marathon endurance than a 5K does.

The three methods (all estimates)

1. Riegel's formula, exponent 1.06

Marathon time = race time × (42.195 ÷ race distance in km)^1.06

Peter Riegel (1981) showed that record times over many distances follow a simple power law. For world records the fitted exponent was about 1.08; for men's age-group records, from the over-40 to the over-70 groups, it was about 1.05 to 1.06. We use 1.06.

Example: a 10K in 50:00 → 50:00 × (42.195 ÷ 10)^1.06 = 3:50:01.

2. Daniels–Gilbert (VDOT)

Jack Daniels and Jimmy Gilbert (1979) wrote two equations. The first gives the oxygen cost of running at a given speed:

VO₂ = −4.60 + 0.182258 × v + 0.000104 × v² (v in metres per minute)

The second gives the share of your maximum you can hold for a race lasting t minutes:

% max = 0.8 + 0.1894393 × e^(−0.012778 × t) + 0.2989558 × e^(−0.1932605 × t)

Your race time gives a fitness score, VDOT = VO₂ ÷ % max. The predictor then finds the marathon time that gives the same score. Example: a 10K in 50:00 gives a VDOT of 40.0 and a marathon of 3:49:34.

VDOT is a score from races, not a lab value. If you want to know what it says about your VO₂ max and your potential, see VO₂ max and marathon time on vo2max.io.

3. Riegel's formula, cautious exponent 1.08

The same formula with 1.08 instead of 1.06. It assumes you slow down more as the distance grows, so it gives a slower time. Example: a 10K in 50:00 → 3:56:44.

Worked examples

Estimates from common race times. "Range" is the fastest to the slowest of the three.

Notice that the range is narrow from a half marathon and wide from a 5K. The shorter your race, the less it tells you about the marathon.

How accurate is it?

All three methods assume you have actually trained for the marathon, with long runs and enough weekly running. Real marathons often come out slower than that.

The largest study we know of in everyday runners is Vickers and Vertosick (2016). They surveyed 2,303 recreational runners. Riegel's formula predicted 10K and half marathon times well, but marathon times were clearly too fast: for about half of the runners, the prediction was at least 10 minutes too fast. Using the exponent 1.08 helped only slightly; marathon speed was still overestimated for about three in four runners. Their own model, which also uses typical weekly mileage, did better, which tells you how much training volume matters.

So read the result as "what this race says you could run if the training goes well", not as a promise.

Which number should I aim for?

• Plan your pace from the slower end of the range, unless your training clearly says otherwise.
• Low weekly running or short long runs? Expect the slow end, or slower. Our marathon training plans show what "trained for the marathon" means week by week.
• Run a tune-up race mid-plan and enter it again. Our suggestion: a half marathon four to six weeks out is the most useful check.
• First marathon? Choose a goal you can hold back on in the first half. Finishing strong teaches you more than chasing a time.

Once you have a goal, set your training paces and heart rates in the training pace and heart rate calculator.

Questions and answers

How do I predict my marathon time from a half marathon?

Put your half marathon time into the predictor. With Riegel's formula, a 1:50:00 half gives about 3:49:21, and the three methods together give about 3:48 to 3:53. It assumes you have trained for the full distance.

Is doubling my half marathon time and adding 10 minutes accurate?

It is a rough rule of thumb, not a formula from a study. For a 1:50:00 half it gives 3:50:00, close to Riegel's estimate. Use it as a sanity check, not as your goal.

Why does the predictor say I'm faster than I really am?

Because the formulas assume full marathon training. In a study of 2,303 recreational runners, Riegel's formula gave marathon times at least 10 minutes too fast for about half of them (Vickers and Vertosick, 2016). Low weekly mileage is a common reason.

Which race should I use: 5K, 10K or half?

The longest recent race you ran all-out on a flat course. A half marathon gives the narrowest range. A 5K mostly measures speed.

Can I predict my marathon from my VO₂ max?

Only roughly. Running economy and how long you can hold a high share of your VO₂ max matter as much. Read VO₂ max and marathon time on vo2max.io for what the number can and can't tell you.

Sources

• Riegel, P. S. (1981). Athletic records and human endurance. American Scientist, 69(3), 285–290.
• Daniels, J. & Gilbert, J. (1979). Oxygen Power: Performance Tables for Distance Runners. Equations as given in Daniels, J., Daniels' Running Formula, Human Kinetics.
• 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. https://doi.org/10.1186/s13102-016-0052-y

Health note: these are general calculators, not medical advice. If you have a heart condition, chest pain, dizziness or an injury, check with a doctor before hard training.

Related

• Tools: Marathon pace calculator · Training paces and heart rate
• Plans: All marathon plans · Half marathon to marathon · Sub-4 hour plan
• Coaching: Personal coaching with Flemming — he reviews every session his athletes log and adjusts the plan when training, sleep or stress call for it.
• On RunPerform: Race time predictor (any distance) · Marathon taper and race week
• On vo2max.io: VO₂ max and marathon time