Marathon Pace Calculator
The marathon is where the standard prediction formula demonstrably fails. This engine prints both the textbook Riegel projection and the empirical figure — and the gap between them.
Marathon Pace Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- The calibrated exponent is a population median — right on average, wrong for any individual by an unknown amount.
- Assumes marathon-specific training; under-trained runners finish slower than both figures.
- No account of course profile, heat, wind or altitude.
- No formula can model a pacing error, which is the most common cause of a slow marathon.
- Inputs far below half-marathon distance make the extrapolation substantially less reliable.
In short: A 1:50:19 half marathon projects to 3:50:01 by Riegel's formula but 3:56:05 using the empirical 2.14 multiplier from Vickers and Vertosick's study of 2,303 runners — six minutes apart. Riegel predicted marathon times more than ten minutes too fast for roughly half of all runners, so the conservative figure is the one to plan against.
Formula
TRiegel = T1 × (42.195 ÷ D1)1.06
kempirical : 2k = 2.14 ⇒ k = ln 2.14 ÷ ln 2 = 1.0976
Trealistic = T1 × (42.195 ÷ D1)1.0976
2.14 is the empirical population-median half-to-marathon multiplier reported by Vickers and Vertosick; 21.06 = 2.0849 is what Riegel's exponent implies. The calibration is expressed as an EXPONENT rather than a flat multiplier so that it reduces to identity when the input is itself a marathon, and scales with the size of the extrapolation. k = 1.0976 also sits inside the 1.07–1.09 band the literature reports for recreational runners.
Worked Example
- Convert the entered race result to seconds and kilometres.
- Project to 42.195 km using Riegel's exponent of 1.06.
- Repeat the projection with the empirically calibrated exponent k = 1.0976.
- Divide both projections by 42.195 to obtain the required pace.
- Apply −1.5% and +3.5% to bracket a realistic finishing band.
A 1:50:00 half marathon → Riegel gives 3:49:20 and the calibrated figure 3:55:24. The six-minute gap is the difference between a plan that survives 32 km and one that does not.
Strengths & Limits Of This Model
Where this engine is strong
- Shows the optimistic and the empirical projection side by side rather than hiding the gap
- Correction is evidence-based and sourced, not an arbitrary safety margin
- Includes the fuelling arithmetic that determines the last 10 km
Where it stops
- Two numbers require more interpretation than one
- Cannot know whether you are a durable runner or a fragile one
Practical Use Cases
Setting a goal from a half marathon
Projects 42.195 km from the single most predictive race distance.
Sanity-checking a round number
Tests whether a sub-4 or sub-3:30 target matches demonstrated fitness.
Explaining why a 10K flatters you
Shows how far the optimistic projection sits from the empirical one.
Planning race fuelling
Converts projected duration into grams of carbohydrate per hour.
Building a pace band
Checkpoints at any distance come from the Split Time Calculator.
Methodology & Editorial Standards
The engine implements the standard published formula for this calculation. Inputs are validated for domain and sign before evaluation, and any undefined case returns an em-dash rather than a spurious value. The engine deliberately reports two projections. Riegel's 1.06 exponent is applied as published, then corrected by an empirically calibrated exponent k = ln(2.14)/ln(2) = 1.0976 rather than a flat multiplier, so that the correction reduces to identity at zero extrapolation. Both figures are shown with the gap named, because presenting only the optimistic projection is the standard failure of marathon calculators.
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Marathon Pace Calculator — 20 Expert FAQs
20 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
Why does this show two different marathon predictions?
Because the standard formula is measurably optimistic at this distance. Riegel's exponent was fitted to world-record data in 1981; Vickers and Vertosick found it predicted marathon times more than ten minutes too fast for roughly half of the 2,303 runners they studied. Showing only the optimistic number would be misleading, so the engine prints both and names the gap.
What multiplier should I use from half marathon to marathon?
The population median is about 2.14, not the 2.0849 that Riegel implies. Most recreational runners land between 2.10 and 2.18. Well-trained, high-volume runners sit at the lower end; first-timers and those with a speed bias sit at the upper end or beyond it.
Is a half marathon the best predictor of marathon time?
Yes, by a clear margin among single-race predictors. It is long enough to test aerobic endurance and pacing discipline, and close enough in distance that the extrapolation is short. A 5 km result extrapolated to a marathon is an eight-fold distance jump and is the least reliable case.
What causes the wall at around 32 km?
Glycogen depletion. A trained runner stores roughly 2,000 kcal of glycogen in muscle and liver, while a marathon costs 2,500 to 3,000 kcal. When glycogen runs low the body shifts toward fat oxidation, which cannot support the same pace, and the result is the abrupt slowdown runners describe as hitting the wall.
How much carbohydrate should I take during a marathon?
Current sports nutrition guidance is 30 to 60 g per hour for efforts of this duration, rising toward 90 g per hour with a glucose-fructose mix in athletes who have trained their gut for it. The critical point is rehearsal: taking unfamiliar fuel on race day is a common cause of gastrointestinal distress.
Why is Riegel's formula optimistic for recreational runners?
Provenance. The exponent 1.06 was fitted to world-record performances — elite athletes on flat road with expert pacing and fuelling. Those athletes fade less over distance than everyone else, so a curve describing them systematically flatters recreational runners, and the error compounds with the size of the extrapolation.
Should I plan my pace from the optimistic or the realistic figure?
The realistic one. The asymmetry matters: going out slightly too slow costs you a few minutes at the end, while going out too fast can cost half an hour when the wheels come off after 30 km. The downside is far larger than the upside.
Does the correction apply if I enter a 10 km time?
Yes, and it scales correctly with distance because it is applied as an exponent (1.0976) rather than as a flat multiplier. A flat factor would wrongly inflate the answer even when the input is itself a marathon; an exponent reduces to identity in that case. Be aware that a 10 km input is a four-fold extrapolation and is inherently less reliable than a half marathon.
What weekly mileage do these predictions assume?
Enough marathon-specific training to express your aerobic fitness over 42 km — in practice usually 50 to 55 km a week or more, with regular long runs. Below that, most runners finish slower than both figures shown, because the limiting factor stops being aerobic capacity and becomes durability.
How much do heat and hills affect marathon time?
Substantially. Marathon performance degrades measurably above roughly 10 to 12°C, and the effect grows through the race as core temperature rises. Neither projection here accounts for weather or elevation, so adjust your goal downward for a hot day or a hilly course before you start.
Is negative splitting realistic for a marathon?
It is the pacing pattern most associated with good outcomes, and almost every world record has been run that way. In practice most recreational runners positive split substantially. Aiming for an even effort, which usually means a slightly slower first half on an honest course, is the practical version of the same advice.
Why does my finishing band start below my projection?
Because a good day is possible as well as a bad one. The band runs from 1.5 per cent faster to 3.5 per cent slower, which is deliberately asymmetric: the distribution of marathon outcomes has a long slow tail and a short fast one, because everything that goes wrong costs more than anything that goes right gains.
Can I use a training run as the input?
Only a genuine all-out race or time trial. A comfortable long run entered here will produce a projection well beyond your current ability, and you will pace the race from a fantasy. Use a real result run at full effort.
What if I have never run a marathon before?
Expect to finish at the slower end of the band, or beyond it. First marathons carry pacing inexperience, unrehearsed fuelling and unfamiliar late-race fatigue, none of which any formula models. Many experienced coaches suggest treating a first marathon as a finishing exercise rather than a time trial.
Does age change the projection?
The projection is anchored to your recent race, so your current age is already reflected in it. What age does affect is recovery between hard sessions and durability late in the race, neither of which appears in the arithmetic.
Why is 42.195 km the marathon distance?
It was fixed at the 1908 London Olympics, where the course ran from Windsor Castle to the royal box in the White City stadium, and was formally standardised in 1921. The awkward number is a historical accident rather than anything physiological.
Is this marathon pace calculator free to use?
Yes. It is free, requires no account, and has no usage limits. ApexConverter is funded by contextual advertising, never by selling user data.
Is my data sent to a server?
No. The engine runs as Vanilla JavaScript inside your browser under our Zero-Server Client-Side Execution model. Your figures are computed locally and are never transmitted, logged, or stored.
How accurate is this calculator?
It applies the standard closed-form formula in IEEE-754 double precision, rounding only at the display layer. The engine is reconciled against an independent reference implementation before release.
Does it work on mobile?
Yes. The interface is mobile-first with numeric keypad hints and is tested down to a 320-pixel viewport with no horizontal scrolling.