Running Pace Calculator: Race Pace, Riegel's Formula, and How to Predict Your Race Time

You ran a 5K in 25 minutes. What does that imply about your half-marathon time? Your marathon? Your easy run pace? Your tempo? These questions all have precise, evidence-based answers — most of them anchored to Peter Riegel's 1981 race-time prediction formula and Jack Daniels' VDOT training-pace framework.

This guide walks through running pace from first principles: the basic formula, Riegel's race-time predictor, how to convert pace between metric and imperial, the five Daniels training paces, grade-adjusted pace for hilly terrain, pacing strategies, and the most common pacing mistakes that cost runners time on race day.

What Is Running Pace? (Pace vs Speed, Race Pace vs Training Pace)

Running pace is the time required to cover one unit of distance, expressed as minutes per kilometre (min/km) in metric or minutes per mile (min/mi) in imperial. It's the inverse of speed: a 5:00 min/km pace corresponds to 12 km/h or 7:27 per mile. Most runners prefer pace to speed because GPS watches display it natively, race targets are stated in pace, and small differences are easier to perceive (5:00 vs 5:10 min/km is a meaningful gap; 12.0 vs 11.6 km/h is harder to feel).

Race pace vs training pace

These are very different numbers — and confusing them is the most common pacing error.

• Race pace is the all-out average pace you can sustain for a specific race distance on a specific day. It varies dramatically with distance: a 5K race pace might be 5:00 min/km; the same runner's marathon race pace might be 5:45 min/km.
• Training pace is the pace prescribed for a specific session in your weekly schedule. Easy runs should be 25–30% slower than 5K race pace. Tempo runs are typically 10–15% slower. Only intervals approach race pace, and only briefly.

The most common training mistake among recreational runners is running easy days at threshold pace — too fast to recover, too slow to drive top-end stimulus. We covered the same problem from a heart-rate angle in our heart rate zones guide; the pace-based version is identical.

The Pace Formula (How to Calculate Pace)

The basic calculation is straightforward arithmetic.

Pace (min per km) = Total Time (minutes) ÷ Distance (km)

Worked example

You ran 10 km in 50 minutes. Pace = 50 ÷ 10 = 5:00 min/km.

Or 8 km in 42:24 (42.4 minutes). Pace = 42.4 ÷ 8 = 5.30 min/km = 5:18 min/km (since 0.30 of a minute is 18 seconds).

To convert minutes per kilometre to speed (km/h), divide 60 by pace: 60 ÷ 5.0 = 12 km/h.

Pace ↔ Speed conversion

Pace (min/km)	Speed (km/h)	Pace (min/mile)	Speed (mph)
4:00	15.0	6:26	9.3
4:30	13.3	7:14	8.3
5:00	12.0	8:03	7.5
5:30	10.9	8:51	6.8
6:00	10.0	9:40	6.2
6:30	9.2	10:28	5.7
7:00	8.6	11:16	5.3

To convert min/km to min/mi, multiply by 1.609. A 5:00 min/km pace × 1.609 = 8:02 min/mi (the table rounds to 8:03 for 5:00 due to seconds rounding).

Riegel's Race Time Prediction Formula

In 1981, mechanical engineer and amateur runner Peter Riegel published "Athletic records and human endurance" in American Scientist. The paper analysed world records across distances from 100 m to ultra-marathons and produced a remarkably durable formula for predicting race performance:

T₂ = T₁ × (D₂ ÷ D₁)^1.06

Where T₁ is your known time for distance D₁, and T₂ is the predicted time for new distance D₂. The exponent 1.06 — Riegel's "fatigue factor" — encodes how pace slows with distance. A linear extrapolation (exponent 1.00) would imply you can hold the same pace forever; reality is that pace slows by a small but consistent amount each time distance doubles.

How accurate is Riegel?

For distances from 1.5 km to 21.1 km (half marathon), Riegel typically predicts within 1–2% of measured race times — exceptionally accurate for a single-formula model with no individual calibration. Daniels (2013) and Vickers & Vertosick (2016) have both validated its core form across thousands of race results.

For the marathon, Riegel is known to systematically overestimate performance by 5–10% in runners without specific marathon training. Vickers and Vertosick analysed 2,303 marathoners' data and found that Riegel works best when calibrated with two known race times rather than just one, and that the exponent for the marathon is closer to 1.10–1.15 in undertrained runners. The reason: marathon performance depends heavily on glycogen reserves, fuelling strategy, and specific 30+ km long-run adaptation that shorter races don't expose.

Worked example

You ran a 5 km in 25:00 (1,500 seconds). What's your predicted half marathon (21.1 km)?

T₂ = 1,500 × (21.1 ÷ 5)^1.06 = 1,500 × 4.22^1.06 = 1,500 × 4.585 = 6,878 seconds = 1:54:38.

For the marathon (42.195 km):

T₂ = 1,500 × (42.195 ÷ 5)^1.06 = 1,500 × 8.439^1.06 = 1,500 × 9.55 = 14,322 seconds = 3:58:42.

Add 5–10% if you don't have specific marathon training: a more realistic prediction is 4:10–4:20 for the same runner without dedicated long-run preparation.

Race Time Prediction Table

Riegel-derived predictions for different fitness levels. Times rounded.

5K	10K	Half Marathon	Marathon (Riegel)	Marathon (realistic)
17:00	35:18	1:18:11	2:42:54	2:48 – 2:55
20:00	41:32	1:31:58	3:11:39	3:18 – 3:25
22:30	46:43	1:43:28	3:35:36	3:43 – 3:50
25:00	51:54	1:54:58	3:59:33	4:08 – 4:15
27:30	57:05	2:06:28	4:23:30	4:33 – 4:40
30:00	1:02:18	2:18:01	4:47:30	4:58 – 5:05
35:00	1:12:41	2:41:00	5:35:24	5:48 – 5:55

The "realistic marathon" column adds a 5–10% pad to Riegel's prediction to account for typical undertraining at the marathon distance. If you've completed three 30+ km long runs in your build-up, lean toward the lower end. If your longest run is 25 km, expect the upper end or worse.

The 5 Training Paces (Daniels VDOT System)

Legendary running coach Jack Daniels developed the VDOT system: a performance-based VO₂max proxy derived from race times, with five corresponding training paces calibrated to each VDOT level. Unlike heart rate, pace-based zones are direct, immediate, and unaffected by caffeine, heat, or sleep. They're the gold standard for prescribing training intensity in running.

Pace	% of 5K Race Pace	Purpose	Suggested Volume
Easy / Long	118–130% (slower)	Aerobic base, recovery, capillary density	60–70% of weekly km
Marathon	105–110% (slower)	Specific marathon prep, fuel-system training	10–15%
Threshold / Tempo	107–112% (slower than 5K but faster than marathon)	Lactate threshold, "comfortably hard"	5–10%
Interval	92–97% (faster than 5K)	VO₂max development	5–8%
Repetition	85–90% (faster)	Speed, neuromuscular economy, form	2–5%

The percentages are relative to pace, not speed — a higher percentage means a slower pace. So if your 5K race pace is 5:00 min/km, your easy pace at 125% would be 5:00 × 1.25 = 6:15 min/km.

Worked example: A 25-minute 5K runner

5K race pace = 5:00 min/km. The Daniels training paces for this runner work out to roughly:

Pace Type	Pace (min/km)	Pace (min/mile)	What it feels like
Easy	5:55 – 6:30	9:31 – 10:28	Conversational; nasal breathing possible
Marathon	5:15 – 5:30	8:27 – 8:51	Comfortably hard but sustained
Threshold/Tempo	5:20 – 5:35	8:35 – 8:59	"Just barely sustainable" feel
Interval	4:30 – 4:55	7:14 – 7:55	Hard breathing, repeats with rest
Repetition	4:15 – 4:30	6:50 – 7:14	Sprint-like, short reps with full recovery

The most common training error for this runner is doing easy runs at 5:30–5:45 min/km — too fast for true aerobic recovery, too slow for any productive stimulus. Real easy pace should feel embarrassingly slow.

Grade-Adjusted Pace (GAP) for Hills

Pace on a hill is metabolically very different from pace on flat ground. Running 6:00 min/km up a 5% grade requires roughly the same effort as 5:15 min/km on flat. Without correction, a hilly route looks slow and a downhill route looks fast — neither tells you anything useful about your fitness or training intensity.

Grade-Adjusted Pace (GAP) mathematically converts your actual pace to the equivalent flat-ground pace, given the elevation profile. Strava, Garmin Connect, and TrainingPeaks all calculate GAP automatically using calibration tables developed by Alberto Minetti and others studying the metabolic cost of running on inclines.

Rough rules of thumb:

• Each 1% uphill grade adds roughly 12–15 seconds per kilometre to equivalent effort.
• Downhill grades up to 4% reduce effort, but steeper than 4% becomes mechanically taxing (eccentric muscle contraction) and the metabolic benefit reverses.
• A 100 m elevation gain over 5 km is roughly equivalent to running 250–300 m extra on flat ground.

For race-pace prescription on hilly courses, calculate target pace based on flat ground, then adapt — slow on uphills (don't blow up) and don't try to make the time back on downhills.

Why Pace Slows With Distance

The exponential relationship encoded in Riegel's exponent 1.06 reflects underlying physiology. Two main mechanisms drive the slowdown:

1. Substrate switching. At higher intensities, your body relies on glycogen (carbohydrate) for fuel, which produces fast ATP regeneration. As distance increases and intensity necessarily decreases, the proportion of energy from fat oxidation rises. Fat metabolism is slower per unit time, capping peak sustainable power.

2. Lactate accumulation. Running above your lactate threshold causes blood lactate to accumulate exponentially. This is sustainable for ~30–60 minutes (defining the threshold) but not for marathon durations. Longer races must be run sub-threshold to avoid premature fatigue, which means slower paces.

Elite endurance runners have remarkably high lactate thresholds — often 85–90% of VO₂max — allowing them to sustain near-maximal aerobic output over long durations. Recreational runners typically hit threshold at 75–80% of VO₂max, capping marathon-pace VO₂max usage at correspondingly lower fractions.

Race pace is a strong proxy for VO₂max. A 5K race pace can be back-translated to estimated VO₂max with ~10% accuracy. See our VO₂max explained guide for the conversion and what the number actually means for fitness.

Pacing Strategies (Even, Negative, Positive Splits)

How should you distribute effort across a race? Three patterns recur in the literature:

• Even pacing. Same pace for every kilometre. Generally optimal for 5K, 10K, and shorter half-marathon efforts. Maximises efficiency by avoiding excess lactate accumulation early.
• Negative split. Second half faster than the first, by 1–3%. Optimal for the marathon, where conserving glycogen and avoiding early-blow-up dominates strategy. Most marathon world records have been set with slight negative splits.
• Positive split. First half faster than the second. Common in unintentional cases (going out too hard) and dominant in shorter, all-out efforts (mile, 1500 m) where the first lap can naturally be faster.

The single biggest pacing mistake in distance racing is going out too hard in the first 5–10%. Runners feel fresh, the crowd is electric, the legs feel light — and they bank a 30-second lead in the first 2 km that costs them 3 minutes by km 35. Even pacing or a deliberately conservative first 5K is the most common path to a personal best.

Limitations

Three honest caveats:

1. Riegel was derived from world records, not recreational runners. The 1.06 exponent fits elite performances well. Recreational runners often have a slightly higher fatigue factor (1.07–1.10), which means Riegel's predictions become optimistic at longer distances. For accurate marathon predictions in particular, calibrate with a recent half-marathon time rather than a 5K.

2. Pace alone ignores terrain, weather, and altitude. A 5:00 min/km on a flat track in cool weather is metabolically very different from 5:00 min/km on rolling trails in 30°C heat. GAP partially corrects for elevation; nothing fully corrects for heat. Heat at race time can slow expected pace by 5–15% above 25°C.

3. Single-race calibration assumes specific training. A runner with great 5K times and no long runs will overpredict their marathon time. A runner with great long runs and limited speed will underpredict 5K performance. The Daniels VDOT system explicitly addresses this by encouraging recalibration after each race.

Sources

1. Riegel, P.S. (1981). Athletic records and human endurance. American Scientist, 69(3), 285–290. Journal page
2. Daniels, J. (2013). Daniels' Running Formula (3rd ed.). Human Kinetics. Publisher link
3. Vickers, A.J., & Vertosick, E.A. (2016). An empirical study of race times in recreational endurance runners. BMC Sports Science, Medicine and Rehabilitation, 8, 26. DOI: 10.1186/s13102-016-0052-y
4. 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
5. 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
6. Minetti, A.E., Moia, C., Roi, G.S., Susta, D., & Ferretti, G. (2002). Energy cost of walking and running at extreme uphill and downhill slopes. Journal of Applied Physiology, 93(3), 1039–1046. DOI: 10.1152/japplphysiol.01177.2001
7. Foster, C., & Lucia, A. (2007). Running economy: the forgotten factor in elite performance. Sports Medicine, 37(4–5), 316–319. DOI: 10.2165/00007256-200737040-00011
8. Tjelta, L.I. (2016). The training of international level distance runners. International Journal of Sports Science & Coaching, 11(1), 122–134. DOI: 10.1177/1747954115617868
9. Esteve-Lanao, J., Foster, C., Seiler, S., & Lucia, A. (2007). Impact of training intensity distribution on performance in endurance athletes. Journal of Strength and Conditioning Research, 21(3), 943–949. DOI: 10.1519/R-19725.1