How Running Pace Is Calculated

摘要

Running pace is the time it takes to cover a unit of distance — typically expressed as minutes per kilometre (min/km) or minutes per mile (min/mi). This calculator operates in three modes: calculating pace from a known distance and time, calculating finish time from a known pace, and predicting race times at new distances using Riegel’s formula.

工作原理

Pace from time

Given a distance and finish time, pace is simply the time divided by the distance. A 25-minute 5K means you ran each kilometre in an average of 5 minutes.

Time from pace

The reverse: given a target pace and distance, multiply to get the finish time. Running a half marathon at 5:00/km gives a finish time of approximately 1:45:29.

Race prediction (Riegel’s formula)

If you know your time for one distance, you can predict your time for another distance. The key insight is that you can’t maintain the same pace over longer distances — fatigue slows you down. Riegel (1981) quantified this by analysing world records and found that the relationship follows a power law with an exponent of 1.06.

The formulas

Pace calculation

Speed from pace

Mile pace conversion

Riegel’s race prediction formula

The exponent 1.06 means that doubling the distance increases the time by slightly more than double (by a factor of 2^1.06 ≈ 2.085). This captures the reality that runners slow down over longer distances due to glycogen depletion, muscle fatigue, and thermoregulation demands.

Official race distances

All distances are standardised by World Athletics (formerly IAAF):

The marathon distance was standardised in 1921 at 42.195 km. The half marathon is exactly half this distance.

Worked examples

Example 1: Pace from a 5K time

Example 2: Predicting marathon time from a 5K result

假设与局限

• Riegel’s formula is most accurate between 1500m and marathon. For ultramarathon distances or very short races, the fatigue factor changes and predictions become less reliable.
• The 1.06 exponent is a population average. Individual fatigue factors vary — endurance-trained runners may have a lower exponent (closer to 1.04), while speed-focused runners may have a higher one (up to 1.08).
• Predictions assume equal training and conditions. A 5K time from a flat course in cool weather won’t accurately predict a hilly marathon in heat.
• Pace is an average. Even splits (constant pace throughout) are shown, but real runners typically vary their pace, often running negative splits (faster second half) or positive splits (slower second half).
• Speed and pace are inversely related. A “faster” pace is a lower number (fewer seconds per km), while a “faster” speed is a higher number (more km per hour). This can be counterintuitive.

验证

All values verified against manual calculation and cross-checked with reference calculators (Omnicalculator, Calculator.net, rat.run).