endurance Formula

Running Pace Formula

Pace is time per unit distance. Most coaches think in minutes per kilometer or per mile. Race-equivalent paces across distances follow Daniels' VDOT or Riegel's exponent (~1.06).

4 VARIABLESPublished Mar 12, 2026Updated May 10, 2026Live Content

By Orbyd Editorial · AI Fit Hub Team

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Running Pace Calculator

Calculate pace per km and mile and project race finish times from one run.

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Formula 4 variables Worked example Variations

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Formula

Copy the exact expression or work through it step by step below.

 pace_per_km = total_time_seconds / total_distance_km / 60
# Riegel race-equivalence (Pete Riegel, 1977):
T_new = T_known × (D_new / D_known)^1.06

Variables

pace

Pace

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

total_time

Elapsed time

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

total_distance

Distance covered

Kilometers or miles. Be consistent within one calculation.

1.06

Riegel exponent

Empirical constant from Riegel 1977. Models the fact that longer races are slower per km. Works well for 5K–marathon; drift increases beyond marathon distance.

Step By Step

1

Express the known race time in seconds.

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

Compute pace per km.

2,700 / 10 = 270 sec/km = 4:30/km.
3

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

Predicting half marathon from 10K: T_HM = 2,700 × (21.0975 / 10)^1.06 = 2,700 × 2.226 = 6,010 sec ≈ 1:40:10.
4

Compute the predicted pace at the new distance.

6,010 / 21.0975 = 285 sec/km = 4:45/km. Half marathon pace is 15 sec/km slower than 10K pace at this fitness.

Worked Example

10K time 45:00, predict half marathon

Known distance

10 km

Known time

45:00

Target distance

21.0975 km (half)

Pace at 10K = 4:30/km. T_HM = 2,700 × (21.0975/10)^1.06 = 6,010 sec → 1:40:10

Predicted half marathon ~1:40:10 at 4:45/km. Real-world performance depends on long-run training and pacing discipline.

Common Variations

Daniels' VDOT tables: more refined race-equivalence with separate training-pace zones for easy, marathon, threshold, interval, and repetition work.

Cameron formula: T₂ = T₁ × (D₂ / D₁)^1.13. Slightly less optimistic than Riegel at long distances.

Race-equivalent calculators (RunningAhead, McMillan) blend multiple models for race-distance predictions.

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Sources & References

Riegel PS. Athletic records and human endurance — American Scientist (1981)
Daniels J. Daniels' Running Formula, 4th edition — Human Kinetics