# Pace and Speed Conversion

min/km, km/h, min/mi and mph — the formulas, a worked example and a reference table.

## Overview
Pace and speed describe the same run from two angles. Pace is time per distance — 5:00 per kilometer. Speed is distance per time — 12 km/h. Race splits, GPS watches and training plans speak in pace; treadmills, bike computers and weather reports speak in speed. Moving between them is a single division, but which number goes on top is what trips people up.

This guide covers all three conversions a runner needs: pace to speed (min/km and km/h), the imperial pair (min/mi and mph), and pace to pace across the metric boundary (min/km and min/mi). Every number in the table below is computed from the formulas explained here, using the same Calcpace library that powers the converter.

## The formulas

- `km/h = 60 / min per km`
- `min per km = 60 / km/h`
- `mph = 60 / min per mile`
- `min per mile = min per km * 1.609344`

## min/km to km/h, and back
An hour holds 60 minutes. If a single kilometer costs you p minutes, then in one hour you cover 60 divided by p kilometers. That is the entire derivation: km/h = 60 / (min per km). Because the relationship is a reciprocal, the same expression runs in reverse — min per km = 60 / (km/h) — so there is only one formula to remember.

The catch is the pace format. A pace of 4:45/km is not the number 4.45: the seconds are sixtieths, not hundredths. Turn them into a decimal first (45 / 60 = 0.75, so 4:45 is 4.75 minutes), then divide: 60 / 4.75 = 12.63 km/h. Skipping that step is the most common arithmetic error in pace conversion, and it gets worse the larger the seconds part is.

## Miles: min/mi and mph
The imperial pair works identically, because nothing in the reasoning above mentioned kilometers. An hour is still 60 minutes, so mph = 60 / (min per mile). A pace of 9:39/mi is 9.65 minutes per mile, and 60 / 9.65 = 6.22 mph.

Crossing between metric and imperial needs one constant: an international mile is exactly 1.609344 km. A mile is the longer unit, so it takes longer to run — multiply a kilometer pace by 1.609344 to get the mile pace, and divide to come back. 5:00/km becomes 300 × 1.609344 = 482.8 seconds, or 8:02/mi. For speeds the operation flips: divide km/h by 1.609344 to get mph, because a bigger unit means fewer of them fit into an hour.

## Worked example: 7:00 min/km
Seven minutes per kilometer needs no decimal step — it is already 7.0 minutes — so the speed is 60 / 7 = 8.57 km/h. For miles, multiply the pace: 420 seconds × 1.609344 = 675.9 seconds, which is 11:15 per mile, or 5.33 mph. Those are exactly the four values on the 7:00 row of the table below. It is a very common easy-run pace, which is why it is the conversion runners look up most often.

## Pace conversion table

| Pace /km | Speed km/h | Pace /mi | Speed mph |
| :--- | :--- | :--- | :--- |
| 3:00 | 20.00 | 4:49 | 12.43 |
| 3:30 | 17.14 | 5:37 | 10.65 |
| 4:00 | 15.00 | 6:26 | 9.32 |
| 4:30 | 13.33 | 7:14 | 8.28 |
| 5:00 | 12.00 | 8:02 | 7.46 |
| 5:30 | 10.91 | 8:51 | 6.78 |
| 6:00 | 10.00 | 9:39 | 6.21 |
| 6:30 | 9.23 | 10:27 | 5.74 |
| 7:00 | 8.57 | 11:15 | 5.33 |
| 7:30 | 8.00 | 12:04 | 4.97 |
| 8:00 | 7.50 | 12:52 | 4.66 |

Computed from the formulas above — km/h = 60 / (min per km), with the mile values derived from the exact 1.609344 factor. Paces run from 3:00 to 8:00 per kilometer in 30-second steps.

## Common mistakes
- Reading a pace as a decimal. 4:30/km is 4.5 minutes, not 4.30. Divide the seconds by 60 before you divide 60 by the pace.
- Mixing up which direction is better. Pace is time per distance, so lower is faster: 4:00/km beats 5:00/km. Speed is distance per time, so higher is faster: 15 km/h beats 12 km/h. The two scales run in opposite directions, and confusing them is how a training plan ends up prescribing the wrong effort.
- Multiplying a speed by 1.609344 instead of dividing. The mile factor scales distances and paces up, but speeds down: 16 km/h is 9.94 mph, not 25.7.

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