Formula, in endurance

Running Pace Formula: Riegel & VDOT Race Pace Conversion

Pace is time per unit distance, usually minutes per kilometre or per mile. Dividing a 45:00 10K by 10 gives 4:30 per km. Holding one pace across distances overstates long-race speed, so race-equivalent paces use Riegel's exponent (1.06) or Daniels' VDOT tables. Riegel was well calibrated up to the half marathon in 2,303 recreational runners and optimistic at the marathon (Vickers & Vertosick 2016).

4 variables. Published Mar 12, 2026. Updated Oct 19, 2026. By AI Fit Hub.

Education, not medical advice. The result comes only from the published formula and your inputs. How we check our formulas.

Formula

pace_per_km = total_time_seconds / total_distance_km   (seconds per km; divide by 60 for minutes)
pace_per_mile = pace_per_km × 1.609344
# Riegel race-equivalence:
T_new = T_known × (D_new / D_known)^1.06

Variables

pace

Pace

Time per unit distance. Minutes per kilometre is the metric standard; minutes per mile is the US standard.

total_time

Total time

Seconds or minutes. Convert decimal minutes to minutes:seconds at the end.

total_distance

Total distance

Kilometres or miles. Keep one unit within a calculation; 1 mile = 1.609344 km.

1.06

Riegel exponent

Models the slowdown over longer races. Well calibrated up to the half marathon; optimistic at the marathon for most recreational runners (Vickers & Vertosick 2016).

Step by step

1

Express the known race time in seconds.

10K in 45:00 = 2,700 seconds.
2

Divide by the distance for pace per km, and multiply by 1.609344 for pace per mile.

2,700 / 10 = 270 s/km = 4:30/km; 270 × 1.609344 = 434.5 s = 7:15/mile.
3

For a race-equivalent time at a new distance, apply Riegel: T_new = T_known × (D_new / D_known)^1.06.

Half marathon from the 10K: 2,700 × (21.0975 / 10)^1.06 = 2,700 × 2.2064 = 5,957 s ≈ 1:39:17.
4

Divide the predicted time by the new distance for the race-equivalent pace.

5,957 / 21.0975 = 282 s/km = 4:42/km, 12 s/km slower than the 10K pace.

Worked example

A 45:00 10K, converted to pace and to a half-marathon target

Known distance

10 km

Known time

45:00

Target distance

21.0975 km (half)

Pace at 10K = 2,700 / 10 = 270 s/km = 4:30/km (7:15/mile) Even-pace half = 4.5 × 21.0975 = 94.9 min = 1:34:56 Riegel half = 2,700 × (21.0975 / 10)^1.06 = 5,957 s = 1:39:17 (4:42/km)

4:30 per km (7:15 per mile), or 13.3 km/h. Held for a whole half marathon, that pace would take 1:34:56, the calculator's even-pace projection. A realistic half-marathon target is slower: steps 3 and 4 apply Riegel's slowdown to the same 10K.

Common variations

Daniels' VDOT tables map a race result to equivalent times at other distances and to training paces for easy, marathon, threshold, interval and repetition work.

Even-pace projections, like the calculator's race list, hold the same pace at every distance. They suit pacing a run of known length; for a race target over a longer distance, use Riegel or VDOT.

Marathon caution: in 2,303 recreational runners, Riegel gave marathon times at least 10 minutes too fast for half of them (Vickers & Vertosick 2016).

Run the numbers next

Cardio Race Time Predictor
Race Time predictor: predict finish times across 5K, 10K, half marathon, and marathon from any known race result using Riegel's formula.
Cardio Treadmill Pace Converter
Convert treadmill speed to running pace with incline-adjusted flat equivalent, projected race times, and calorie estimates.

Questions people ask next

How do you calculate running pace per kilometer?

Divide total time in seconds by distance in kilometres, then convert to minutes:seconds. A 10K in 45:00 is 2,700 seconds; 2,700 / 10 = 270 s/km = 4:30/km. Multiply by 1.609344 for pace per mile: 7:15.

What is the Riegel formula for predicting a race time at a new distance?

T_new = T_known × (D_new / D_known)^1.06. The exponent above 1 reflects that longer races are run slower per kilometre. It was well calibrated up to the half marathon in a 2,303-runner survey but optimistic at the marathon.

How do I predict my half marathon time from a 10K?

Apply Riegel to your 10K. For a 45:00 10K: 2,700 × (21.0975 / 10)^1.06 = 2,700 × 2.2064 = 5,957 s, about 1:39:17, or 4:42/km. That is about 12 s/km slower than the 10K pace.

How does the Riegel formula compare to VDOT?

Both turn one race into equivalent times at other distances. Riegel is a single power law; Daniels' VDOT tables also give training paces for easy, threshold, interval and repetition work. For the marathon, a published test of 2,303 runners found Riegel optimistic for most of them.

Sources

Riegel PS (1981). Athletic records and human endurance. , American Scientist 69(3):285–290
Vickers & Vertosick (2016). An empirical study of race times in recreational endurance runners. , BMC Sports Science, Medicine and Rehabilitation — Riegel tested on 2,303 runners
Daniels J. Daniels' Running Formula, 4th edition , Human Kinetics — VDOT tables