How to Calculate Running Pace and Predict Race Times

You ran a 5km in 26 minutes. What would you run a half marathon in? Should you enter the marathon you've been eyeing, and if so, what's a realistic goal time? These questions have precise, evidence-based answers — thanks to a formula developed in 1977 by Peter Riegel that still holds up remarkably well decades later.

Understanding your running pace isn't just about races. Training at the right intensity is arguably more important than racing correctly. Run too hard on easy days, and you accumulate fatigue without the aerobic adaptation you're after. Run too easy on interval days, and you miss the stimulus entirely.

Pace vs Speed: What You're Actually Measuring

Running pace is simply the time it takes to cover one unit of distance — expressed as minutes per kilometre (min/km) or minutes per mile (min/mi). It's the inverse of speed: a 5:00/km pace corresponds to 12 km/h. Most runners find pace more intuitive because it directly translates to race targets and GPS watch displays.

Your pace on any given run depends on: fitness level (VO₂max), running economy (how efficiently you convert oxygen to forward motion), lactate threshold (the pace you can sustain before lactate accumulates rapidly), and fatigue status. Pace is not a fixed property — it reflects your current physiological state on that day.

Riegel's Race Time Prediction Formula

In 1981, Peter Riegel published a mathematical analysis of athletic records that produced a remarkably simple and durable formula for predicting race performance across distances:

T₂ = T₁ × (D₂ / D₁)^1.06

Where T₁ is your known time for distance D₁, and T₂ is the predicted time for distance D₂. The exponent 1.06 is the "fatigue factor" — it encodes the fact that humans slow down predictably as distance increases, not linearly but in a power-law relationship.

This formula predicts race times with impressive accuracy for distances between 1.5km and marathon. For ultra-marathon distances, the fatigue factor increases and the formula becomes less reliable — ultra performance depends more on fuelling, terrain, and pacing strategy.

Why Pace Slows With Distance

The speed-endurance trade-off is driven by two main mechanisms. First, as exercise duration increases, the fraction of energy from fat oxidation increases and from carbohydrates decreases. Fat metabolism is slower and limits peak power output. Second, lactate accumulation begins to limit sustainable pace at intensities above the lactate threshold. Longer races must be run below this threshold to avoid premature fatigue.

Elite runners have remarkably high lactate thresholds — often 85–90% of VO₂max — allowing them to sustain near-maximal aerobic output for long durations. Recreational runners typically reach their threshold at 75–80% VO₂max.

Training Paces: The Jack Daniels VDOT System

Legendary running coach Jack Daniels developed the VDOT system — a performance-based VO₂max proxy derived from race times — and used it to calculate optimal training paces for each intensity zone. Unlike heart rate zones (which can be affected by heat, fatigue, and caffeine), pace-based training zones are consistent and easy to monitor.

The five training paces derived from a reference race performance:

Zone	% of 5km Pace	Purpose	Weekly Volume
Easy	118–130%	Aerobic base, recovery	60–70%
Marathon	105–110%	Specific race prep	10–15%
Tempo	107–112%	Lactate threshold	5–10%
Interval	92–97%	VO₂max development	5–8%
Repetition	85–90%	Speed, economy	2–5%

The most common training error among recreational runners is running easy days too hard — often at 110–115% of race pace instead of the prescribed 118–130%. This compresses the intensity distribution, raising chronic fatigue without delivering the high-quality aerobic stimulus of true easy running.

Using Your Pace to Estimate VO₂max

Race pace is closely correlated with VO₂max — your aerobic ceiling. A 5km time of 25:00 corresponds approximately to a VO₂max of 40 ml/kg/min; 20:00 corresponds to ~52; 17:00 to ~60+. This relationship makes race pace the most practical, no-equipment VO₂max proxy available.

Sources

1. Riegel, P.S. (1981). Athletic records and human endurance. American Scientist, 69(3), 285–290.
2. Daniels, J. (2005). Daniels' Running Formula (2nd ed.). Human Kinetics.
3. Joyner, M.J. & Coyle, E.F. (2008). Endurance exercise performance: the physiology of champions. Journal of Physiology, 586(1), 35–44. DOI: 10.1113/jphysiol.2007.143834
4. Jones, A.M. & Carter, H. (2000). The effect of endurance training on parameters of aerobic fitness. Sports Medicine, 29(6), 373–386. DOI: 10.2165/00007256-200029060-00001