A known race result contains more information than a finish time — it implies what
your body can do at other distances. Pete Riegel's endurance formula turns that result
into a predicted time at any target distance. Enter what you know; the calculator
projects what you might run, with the formula shown in full and the caveats stated plainly.
5K, 10K, half & full marathon·Predicted time in H:MM:SS·Predicted pace per km and per mile
What this is — and is not
This is a mathematical prediction, not a guarantee. The Riegel formula works well for
extrapolations of one or two distance steps (e.g., 5K to 10K, or 10K to half marathon)
when your known result was a genuine race effort. Accuracy drops over large gaps. The output
depends entirely on training, terrain, conditions, and pacing — none of which the formula
can see. Use this for planning and goal-setting, not as a fixed target. It is not medical
advice; consult a coach for training guidance.
Select a known distance and enter your finish time. Then pick your target distance. The predicted time and pace update as you type.
Your known result
Pick a standard distance or enter your own below.
km
Enter the distance in kilometers.
Enter as MM:SS (e.g., 25:00) or H:MM:SS (e.g., 1:45:30).
Target race
km
Predicted finish time:
Predicted time
Predicted pace / km
Predicted pace / mile
The formulas, in full
The arithmetic is deterministic and open. Every number the calculator produces follows
directly from these steps — nothing is hidden, and the only judgment call is the inputs
you supply.
An exponent of exactly 1.0 would mean "twice the distance = twice the time."
The exponent 1.06 encodes the well-documented fact that runners slow
as distance increases due to fatigue.
Example: doubling from 5 km to 10 km → 2 ^ 1.06 ≈ 2.085
A 25:00 5K predicts a 10K of 25:00 × 2.085 ≈ 52:07 (not 50:00).
3 — Predicted pace per km
pace_per_km (seconds) = T2 ÷ D2
Formatted as M:SS per km.
4 — Predicted pace per mile
KM_PER_MILE = 1.60934
pace_per_mile (seconds) = T2 ÷ (D2 ÷ KM_PER_MILE)
Formatted as M:SS per mile.
Standard race distances and example predictions
The four distances below are the standard road-race events. The kilometer values for the
half marathon and marathon are official — derived from the imperial 26 miles 385 yards
set at the 1908 London Olympics and ratified by World Athletics. The example predictions
are calculated from a 25:00 5K using the Riegel formula.
Race
Distance (km)
Predicted from 25:00 5K
Predicted pace / km
Notes
5K
5.000
25:00
5:00 / km
Known result — the input itself; no prediction needed.
10K
10.000
52:07
5:13 / km
2 ^ 1.06 ≈ 2.085; 1500 × 2.085 ≈ 3127 s. One of the most reliable extrapolation steps.
Half marathon
21.0975
1:56:21
5:31 / km
Official distance: exactly 21.0975 km. A two-step extrapolation from 5K; useful as a planning ceiling.
Marathon
42.195
4:04:18
5:47 / km
Official distance: exactly 42.195 km (26 mi 385 yd). Large gap from 5K — treat as rough estimate; marathon-specific training matters greatly.
All predicted times are estimates assuming similar race effort, comparable conditions, and
adequate distance-specific training. The half-marathon and marathon predictions from a
5K time carry more uncertainty than a single-step extrapolation. Use shorter-distance known
results as your predictor whenever possible.
What the formula assumes — and where it breaks down
The Riegel formula is powerful precisely because it requires only two inputs. But
that simplicity comes with assumptions. Understanding what the model cannot see is
as important as the prediction itself.
Your known result must be a genuine race effort
The formula takes your time at face value. If you ran your 5K as a tempo workout, a paced jog, or a PR attempt on a hilly course in heat, the prediction reflects those conditions — not your fitness ceiling. For the most useful prediction, use a result from a flat, well-paced race where you ran close to maximum sustainable effort. A time trial on a track or certified road course works equally well.
Extrapolation accuracy shrinks with distance gaps
Predicting a 10K from a 5K is a small step — you're asking the formula to project across a factor of 2. Predicting a marathon from a 5K asks it to span a factor of 8.4. Over that larger gap, fueling, long-run fitness, pacing strategy, and mental endurance become the dominant variables, and a single exponent cannot capture them. The formula is most reliable predicting one or two steps up; beyond that, treat the output as a rough ceiling under ideal conditions, not a training target.
The 1.06 exponent is a population average, not your personal constant
Some runners fatigue more slowly than average (a lower personal exponent), and some more quickly. Elite marathon specialists often show a lower exponent because their training makes them disproportionately efficient over longer distances. Recreational runners who have done little long-run training may show a higher exponent. Over time, if you have results at multiple distances, you can fit your own exponent — but for most people, 1.06 is a reasonable starting point.
How to use the prediction effectively
The number the formula produces is most valuable as a planning tool, not a finish-line
commitment. Here is how to get the most from it.
Choose the right known result
Use the most recent race result closest to your target distance. A 10K result predicts a half marathon more reliably than a 5K does. The result should be from within the past few months and at a comparable level of fitness to where you are now.
Treat the output as a training-plan ceiling, not a goal
Set your goal pace slightly slower than the prediction — especially at a new distance or in uncertain conditions. The Riegel prediction represents approximately what a well-trained runner who executes perfectly might run. A 5–10% cushion makes for a smarter first attempt at a new distance.
Account for terrain and conditions
The formula knows nothing about course elevation, surface, temperature, or humidity. A hilly trail half marathon will take longer than a flat road race at the same effort. If your known result was on a flat course and your target race has significant elevation gain, add time beyond the prediction rather than targeting it directly.
Verify with distance-specific training
A 10K result can predict a half marathon, but you still need the long-run fitness to race one. The formula says nothing about whether your body is prepared to sustain that predicted pace for 21 km. Use the prediction alongside an honest assessment of your long-run training, not instead of it.
Re-run the calculation as your fitness changes
Race fitness is not static. A 5K PR from 18 months ago is a less reliable predictor than one from last month. After every race, update your known result and re-check your target prediction. If the new prediction has drifted significantly, your fitness has likely changed.
Where to buy
Got your numbers? Here's where to pick up what you need:
The terms and units that appear in race prediction, training plans, and GPS watch data —
in plain English.
Riegel formula
The power-law model T2 = T1 × (D2 ÷ D1) ^ 1.06, published by Pete Riegel in Runner's World in 1977. It predicts finish time at any distance from a known result at another distance. The exponent 1.06 encodes empirically observed human fatigue across a large population of runners.
Fatigue exponent
The 1.06 constant in the Riegel formula. An exponent above 1.0 means performance degrades as distance increases — runners slow proportionally the farther they go. An exponent of exactly 1.0 would imply pure proportionality; 1.06 reflects the real-world cost of sustained effort over longer distances.
Pace (per km / per mile)
The average time it takes to cover one unit of distance. Pace per km is used in most countries; pace per mile is common in the US and UK. They express the same effort in different units. A predicted pace is the even-effort pace required to hit the predicted finish time — it does not prescribe how to split a race.
5K
A 5-kilometer road or track race (3.107 miles). The most widely run distance globally and a reliable base for Riegel extrapolations to 10K. The shortest standard distance the formula is intended for.
10K
A 10-kilometer race (6.214 miles). Double the 5K, it is the most direct one-step extrapolation and where the Riegel formula is most consistently accurate.
Half marathon
Exactly 21.0975 km (13.109 miles) — half the official marathon distance of 42.195 km. The 21.0975 figure is the precise conversion of 26 miles 385 yards ÷ 2; using a rounded figure would produce small but real errors in the predicted time.
Marathon
Exactly 42.195 km (26 miles 385 yards), the distance standardized by the 1908 London Olympics and ratified by World Athletics. Predicting a marathon time from a 5K or 10K result is a large extrapolation — marathon-specific long-run fitness matters far more than the formula can capture.
Personal record (PR)
Also called a personal best (PB). Your fastest official finish time at a given distance. A PR is the ideal input for the Riegel formula because it represents a genuine maximum effort. Using a non-PR result as the input will tend to produce a conservative (slower) prediction.
Tempo run
A sustained effort run at roughly 80–90% of maximum heart rate — comfortably hard, not all-out. Tempo times are not the same as race times and should not be used as the known input for the Riegel formula, which assumes a true race-effort result.
Frequently asked
The Riegel formula, published by Pete Riegel in Runner's World in 1977, is T2 = T1 × (D2 ÷ D1) ^ 1.06 — where T1 is your known finish time in seconds, D1 is the distance you ran, D2 is the target distance, and 1.06 is an empirically derived fatigue exponent. For most recreational to competitive runners, it produces estimates accurate to within a few percent when the known result was run at genuine race effort on similar terrain.
For extrapolations of one or two steps — predicting a 10K from a 5K, or a half marathon from a 10K — accuracy is commonly within 2–5% for trained runners at similar effort and terrain. Accuracy degrades over large gaps (e.g., 5K to marathon) or when the known result was run in different conditions. The formula cannot see training volume, race-day weather, course elevation, or pacing — treat the output as a planning estimate, not a fixed target.
Pete Riegel derived the 1.06 fatigue exponent empirically by fitting a power law to world-record and elite-level performances across many distances. An exponent of 1.0 would mean pure proportionality — twice the distance, exactly twice the time. The exponent 1.06 reflects the observed reality that runners slow as distance increases due to cumulative fatigue. Some researchers have proposed slightly different values for specific populations, but 1.06 remains the most widely cited figure for standard road distances.
The formula will produce a number, but reliability decreases sharply over a large distance gap. The marathon is 8.44 times longer than a 5K; individual variation in aerobic base, fueling, long-run training, and pacing strategy matters far more than the single-exponent model can capture. A more reliable approach is to use a 10K or half-marathon result as the input for a marathon prediction. A 5K-to-marathon projection is still useful as a rough ceiling estimate under ideal conditions, but treat it with extra caution.
No. The Riegel formula was developed from running data and is not validated for walking, run-walk strategies, or ultra-marathon distances. Walking biomechanics follow a different fatigue curve. For ultras beyond the marathon, factors like fueling, sleep deprivation, and terrain complexity cause performance patterns that diverge fundamentally from road running. This calculator is intended for standard road and track distances: 5K through marathon.
Enter it as 52:07 in the time field. The calculator accepts both MM:SS and H:MM:SS formats. For a time under one hour, use MM:SS (e.g., 25:00 for a 25-minute 5K). For a time of one hour or more, use H:MM:SS (e.g., 1:45:30 for one hour, 45 minutes, and 30 seconds). Both formats are parsed automatically and converted to seconds before the formula runs.
Both pace outputs show the average pace you would need to run at the target distance to hit the predicted finish time. Pace per km suits metric training (most countries and GPS watches set to metric). Pace per mile is standard in the US and UK. They describe the same effort in different units and represent an even-pace equivalent — they do not prescribe how to split the race, and in practice most runners go out slightly faster and slow through the back half.
The four standard distances are: 5K (5 km), 10K (10 km), half marathon (21.0975 km), and marathon (42.195 km). The half and full marathon distances are official conversions of 26 miles 385 yards — the distance set at the 1908 London Olympics and ratified by World Athletics. This calculator uses the exact values (21.0975 and 42.195) rather than rounded approximations, because even small rounding differences compound in the Riegel formula and shift the predicted time by seconds.
Common mistakes
The Riegel formula takes your known result at face value. The most common errors
come from feeding it a result that doesn't reflect a genuine race effort, or from
treating a large-gap extrapolation as a reliable target.
Using a workout time, not a race time
The Riegel formula is calibrated on race-effort results — times produced when you run close to your maximum sustainable pace for that distance. Tempo runs, paced long runs, and time trials run at a controlled effort all produce times that are slower than your race capability. Enter a non-race time and the formula predicts slower than you can actually run. Use the most recent result from a flat, evenly paced race at full effort.
Jumping more than one distance step for a first-time race
Predicting a 10K from a 5K is a factor-of-2 extrapolation — a reasonable step. Predicting a marathon from a 5K spans a factor of 8.4, and the Riegel formula's 1.06 exponent was not designed to absorb that much distance-specific fitness variation. For first attempts at a new distance, the formula's output is best treated as an optimistic ceiling under perfect conditions, not a realistic target without distance-specific training.
Ignoring course and weather differences between races
The formula has no inputs for elevation, surface, temperature, or humidity. A hilly trail 10K and a flat road 10K are not interchangeable inputs. If your known result came from a different type of course than your target race, the prediction will be off — sometimes by several minutes. Account for course differences manually: add time for significant elevation gain or off-road surfaces.
Setting the predicted time as a race goal rather than a planning ceiling
The Riegel prediction represents what a well-trained runner executing perfectly might run under comparable conditions. Setting it as your race goal on a new distance — especially a first half-marathon or marathon — leaves no margin for the variables the formula can't see: fueling, heat, the mental demands of the distance, or an off day. Use it to set a training-plan ceiling and start your actual race slightly slower.