# Running pace calculator

> Running pace per km or mile from distance and time, or finish time or distance from pace, with even splits and Riegel race predictions.

Interactive version: https://www.calcopenly.com/health/running-pace-calculator
Subject: Health and fitness calculators

Pace is finish time divided by distance, shown per kilometre and per mile; enter two of distance, time and pace (or speed) to get the third. Race predictions use Peter Riegel's 1981 formula, T₂ = T₁ × (D₂ ÷ D₁)^1.06, which scales one result to the 5K, 10K, half marathon and marathon. Even splits are listed per kilometre or mile.

Runners use it to plan race pacing and training targets. The default 10 km in 50:00 is 5:00 per km, 8:03 per mile or 12 km/h, and Riegel's formula turns it into a 23:58 5K, a 1:50:19 half marathon and a 3:50:00 marathon.

Riegel predictions assume equal preparation for each distance. In a study of 2,303 recreational runners, Vickers and Vertosick (2016) found the formula well calibrated up to the half marathon but at least 10 minutes too fast at the marathon for half of them.

## Inputs

- **Solve for** (options: Pace, Finish time, Distance)
- **Distance**
- **Finish time**: mm:ss or h:mm:ss
- **Pace and splits per** (options: Kilometre, Mile)
- **I know my** (options: Pace, Speed)
- **Pace**: mm:ss per kilometre or mile, as chosen above
- **Speed**

## Results

- Pace per km (per km) — main result
- Pace per mile (per mile)
- Finish time
- Distance (km)
- Distance in miles (mi)
- Speed (km/h)
- Speed in miles per hour (mph)
- Predicted 5K
- Predicted 10K
- Predicted half marathon
- Predicted marathon

## Formula

$$
\text{pace} = \frac{t}{d},\qquad T_2 = T_1\left(\frac{D_2}{D_1}\right)^{1.06}
$$

## Worked examples

### Marathon in 3:30:00

- Solve for: Pace
- Distance: 42.195 km
- Finish time: 3:30:00
- Pace and splits per: Kilometre
- **Pace per km: 4 min 58 s**
- **Pace per mile: 8 min**
- **Speed: 12.06 km/h**
- Checked against: Python 3.8 decimal: 12600 s ÷ 42.195 km; 12600 ÷ (42195/1609.344) mi; 42.195 ÷ 3.5 h

### 5K at 8:00 per mile

- Solve for: Finish time
- Distance: 5 km
- Pace and splits per: Mile
- I know my: Pace
- Pace: 8:00
- **Finish time: 24 min 51 s**
- **Pace per km: 4 min 58 s**
- Checked against: Python 3.8 decimal: 480 s × 5000/1609.344 = 1491.2909 s

### Distance from 1:45:00 at 5:00 per km

- Solve for: Distance
- Finish time: 1:45:00
- Pace and splits per: Kilometre
- I know my: Pace
- Pace: 5:00
- **Distance: 21 km**
- **Distance in miles: 13.049 mi**
- Checked against: Python 3.8 decimal: 6300 s ÷ 300 s/km = 21 km = 13.04880 mi

### Riegel predictions from 10 km in 50:00

- Solve for: Pace
- Distance: 10 km
- Finish time: 50:00
- Pace and splits per: Kilometre
- **Predicted 5K: 23 min 58 s**
- **Predicted 10K: 50 min**
- **Predicted half marathon: 1 h 50 min 19 s**
- **Predicted marathon: 3 h 50 min**
- Checked against: Python 3.8 decimal: 3000 × (D₂/10000)^1.06 for 5000, 21097.5 and 42195 m

### Speed instead of pace: 12 km/h over 10 km

- Solve for: Finish time
- Distance: 10 km
- Pace and splits per: Kilometre
- I know my: Speed
- Speed: 12 km/h
- **Finish time: 50 min**
- **Pace per km: 5 min**
- Checked against: 10 km ÷ 12 km/h = 5/6 h = 3000 s; 3600/12 = 300 s/km

### Edge: one mile at 7:00 per mile

- Solve for: Finish time
- Distance: 1 mi
- Pace and splits per: Mile
- I know my: Pace
- Pace: 7:00
- **Finish time: 7 min**
- **Pace per mile: 7 min**
- **Distance: 1.609 km**
- Checked against: One split equals the whole race: time = pace; 1 mi = 1.609344 km (NIST)

## Questions

### How do you calculate running pace?

Divide finish time by distance. A 10 km run in 50 minutes is 50 ÷ 10 = 5:00 per km; the same run is 6.214 miles, so the pace is 8:03 per mile. Speed is the inverse: 60 ÷ 5 = 12 km/h. One mile is exactly 1.609344 km (NIST SP 811), the factor used to switch between per-kilometre and per-mile pace.

### What pace do you need for a sub-4-hour marathon?

Faster than 5:41 per km, or 9:09 per mile, held for all 42.195 km: 14,400 s ÷ 42.195 km = 341.3 s per km. A sub-2-hour half marathon needs exactly the same pace, because 21.0975 km is half the marathon distance. Any time lost at aid stations or on a slow start has to be made up with faster running later.

### Are Riegel race time predictions reliable?

Up to the half marathon, mostly. Vickers and Vertosick's 2016 study of 2,303 recreational runners found Riegel's formula well calibrated to that distance but too optimistic for the marathon, giving times at least 10 minutes too fast for half the runners. Their own models, which used training data and prior races, cut the marathon prediction error by about 40 %. Riegel fitted his 1.06 exponent to world-record performances.

### How long is a marathon and a half marathon?

A marathon is 42.195 km (26.219 miles) and a half marathon is 21.0975 km (13.109 miles), the standard road distances in World Athletics rules. At an even 5:00 per km they take about 3 h 31 min and 1 h 45 min. Use the distance presets to fill in these exact values.

### How accurate is the running pace calculator?

Accuracy depends on your inputs and the method's assumptions. Decimal arithmetic uses 50 significant digits, but estimates, numerical methods and source data can be less precise; the displayed rounding does not remove those limits. It is checked against 6 worked examples whose answers come from independent sources; for example, “Marathon in 3:30:00” is checked against Python 3.8 decimal: 12600 s ÷ 42.195 km; 12600 ÷ (42195/1609.344) mi; 42.195 ÷ 3.5 h.

### Where does the method come from?

Riegel PS. Athletic records and human endurance. American Scientist 1981;69(3):285–290; World Athletics Competition Rules — standard road distances: half marathon 21.0975 km, marathon 42.195 km; NIST SP 811 — 1 mile = 1609.344 m exactly.

## Sources

- [Riegel PS. Athletic records and human endurance. American Scientist 1981;69(3):285–290](https://pubmed.ncbi.nlm.nih.gov/7235349/)
- World Athletics Competition Rules — standard road distances: half marathon 21.0975 km, marathon 42.195 km
- [NIST SP 811 — 1 mile = 1609.344 m exactly](https://www.nist.gov/pml/special-publication-811)