Marathon Split Calculator

What this page does

A marathon split calculator normally answers one question: if I want to finish in x, what does each kilometre look like? The answer it gives is a single pace, repeated forty-two times, with a running clock beside it. That is a correct answer for a flat course and a misleading one for every other course.

This page keeps the clock and changes the pace. Give it the finish time you want and the elevation change in each kilometre, and it prints a split for every kilometre of the 42.195 km in which the climbs are slower and the descents are faster, so the effort — not the pace — is what stays level. The clock still lands exactly on your target.

Everything runs in your browser. There is no server, no account and no upload; the profile you paste in never leaves the page.

How the number is calculated

The adjustment is not a rule of thumb. It uses the energy cost of running as a function of gradient, measured on a treadmill across gradients from −45% to +45% and published by Minetti and colleagues in 2002. In their fit, the metabolic cost of running one metre at gradient i is:

C(i) = 155.4·i⁵ − 30.4·i⁴ − 43.3·i³ + 46.3·i² + 19.5·i + 3.6

• C(i) — metabolic energy cost of running, in joules per kilogram of body mass per metre travelled.
• i — the gradient, written as a decimal ratio of vertical to horizontal distance. A 2% climb is i = 0.02. Flat is i = 0.
• 3.6 — the value of C at i = 0, i.e. the cost of running a metre on the level. Every ratio below is taken against this number.

From there the page does four things, and you can redo all of them on a calculator:

1. Grade each kilometre. A kilometre with a net change of h metres has gradient i = h / 1000. So +22 m in a kilometre is i = 0.022, a 2.2% climb.
2. Price each kilometre. Multiply the cost at that gradient by the segment length: E_k = C(i_k) × d_k × 1000, with d_k in kilometres. Add them up to get E, the whole race's cost.
3. Hand out the time. Each kilometre gets its share of your target time in proportion to what it costs: t_k = T × E_k / E. Because the shares add to 1, the splits add to T exactly — the finish time is preserved, only the distribution moves.
4. Quote the flat-equivalent. The same effort on a level course would take T_flat = T × (3.6 × D) / E, where D is the race distance in metres. That is the number that tells you what the hills are actually costing.

A worked kilometre

Take one kilometre at a 2% climb, so i = 0.02. The equation gives C(0.02) = 4.0082 J·kg⁻¹·m⁻¹. Divide by the flat cost: 4.0082 / 3.6 = 1.1134. That kilometre costs about 11.3% more than the same kilometre on the level. If your flat pace is 5:00 per kilometre, the model asks for 5:00 × 1.1134 = 5:34.

The same arithmetic at −2% gives 3.2289 / 3.6 = 0.8969, so a gentle descent is worth about 10.3% faster — noticeably less than the 11.3% the climb cost you, which is why hilly courses are slower overall even when they come back down to the same altitude.

On the demo course in the box above (169 m of climbing, 146 m of descending) a 3:30:00 target has a flat-equivalent of 3:29:10. The profile costs about fifty seconds.

Getting the numbers for your course

The box wants one number per kilometre: the net change in elevation over that kilometre, in metres, positive for climbing and negative for descending. Three sources usually have it:

• Your watch. Run any part of the course and look at the per-lap elevation column rather than the cumulative chart. A lap with +18 m of gain and −3 m of loss is a net +15 m for that kilometre.
• The race website. Courses with a reputation for hills usually publish an elevation profile. Read it off at kilometre intervals — you do not need the shape between them, only the change across each one.
• A route builder. Draw the course and use the per-kilometre elevation readout, then subtract each kilometre's cumulative figure from the one before it.

If you only have the totals — say 300 m of climbing spread over three climbs — do not guess the shape. Enter what you know and leave the rest flat; the page will tell you what the profile it received is worth, and you can see how much of your target is being spent on the parts you could not describe.

What this page deliberately does not do

• No course presets. Selecting "Boston" from a dropdown would mean shipping an elevation profile for a real race, and profiles change when a course is re-measured. There is no source I can point at for a per-kilometre series I did not measure myself, so the box stays yours to fill.
• No weather correction. Heat, humidity and wind move marathon times by more than most hills do, and the published models for them are not in a form I can apply without inventing coefficients.
• No walk-run transitions. The model is a running cost model. On very steep gradients a walk can be more economical than a run, and this page will still price that kilometre as a run.
• Even effort, not even pace. The whole method assumes you can and will hold a constant metabolic effort. Nobody does that perfectly, and the back half of a marathon is where the assumption is weakest.
• No fatigue model. The cost of a kilometre at 40 km is treated as identical to the cost of the same kilometre at 2 km. Real marathons do not work that way.
• One model, stated. The coefficients come from a treadmill study of ten runners and are a fit, not a law. The paper reports a level cost of about 3.40 J·kg⁻¹·m⁻¹ while the published polynomial returns 3.6 at zero gradient; this page uses the polynomial as published, so the two do not agree exactly on the flat. Gradients outside −45% to +45% are clamped to that range, because the study did not go further.

Questions

What is a marathon split calculator?

A marathon split calculator turns one number — the finish time you are aiming for — into the pace and elapsed clock for every kilometre of the 42.195 km. This one goes a step further: it also takes the elevation change in each kilometre, so the splits it prints are the splits for your course rather than for a flat one.

How do I use it on a hilly marathon?

Type the metres you climb or drop in each kilometre into the course profile box, km 1 first. The page converts each kilometre into a gradient, looks up the metabolic cost of running at that gradient, and hands out the time in proportion to effort — so the uphill kilometres get a slower split and the downhill ones get a faster split, while the clock still finishes on your target time.

Why does my pace change from kilometre to kilometre?

Because the energy cost of running is not constant on a gradient. Running a kilometre at a 2% climb costs about 11.3% more energy than the same kilometre on the flat. Holding one pace the whole way therefore means the hills are run at a much higher effort than the flats. Spreading the effort evenly is what makes the pace change.

What is a flat-equivalent time?

It is the time the same course would take if the whole 42.195 km were level, at the same effort as your target. If your target is 3:30:00 on a course with 169 m of climbing and 146 m of descending, the flat-equivalent is about 3:29:10 — the climbs are costing you roughly fifty seconds.

Where do I get the elevation for each kilometre?

Three places usually work: the race website's course page if it publishes a profile, the elevation chart your GPS watch produces from a training run on the course, or a route builder's elevation readout. Take the net change per kilometre — the number the watch shows for each lap — rather than the cumulative elevation, and paste them in order.

Does this replace a pace chart?

It replaces the flat pace chart, which is the version most runners print. A standard marathon pace chart is a lookup table: one pace, one column of clock times, identical for every course. This page keeps the clock column but lets the pace move with the profile, which is the part a flat chart cannot do.

Can I see the splits for a flat course?

Yes — press Flat course and every kilometre's change becomes zero, which collapses the table back to a single repeated pace. Switching between that and the demo profile is the quickest way to see how much of a marathon is decided by the profile rather than by fitness.