Mile Splits Calculator

What this page does

A mile splits calculator normally answers one question: if I want to finish in x, what should the clock read at every mile mark? The usual answer is a single pace, repeated, with a running clock beside it. That is the right answer for a flat course and a wrong one for every other course, because the effort of holding one pace up a hill is not the effort of holding it down the other side.

This page keeps the clock and changes the pace. Give it the finish time you want and the elevation change inside each mile, and it prints a split for every whole mile in which the climbs are slower and the descents are faster, so what stays level is the effort rather than the pace. Your finish time is held exactly: the shares add to one, so the splits add to your target and the last row prints it unchanged.

The unit is the point of the page. The distance can be kilometres or miles, the rows are always miles, and the profile is always feet per mile — the shape a race profile is published in on an imperial course. The site's other two hill pages price a profile in metres per kilometre; this is the imperial one, and it goes down to any distance rather than one fixed race.

Everything runs in your browser. There is no server, no account and no upload, and the profile you paste in never leaves the page. If you want even splits with no hills at all, drawn as a band you can wear, that is the running split calculator. If you want the same hill model in metres per kilometre, that is the marathon split calculator for 42.195 km and the race time calculator for a course you are aiming at.

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, the cost of running a metre on the level. Every ratio below is taken against this number.

The only thing this page does differently from the site's kilometre hill pages is the unit of the profile, and it makes the arithmetic shorter rather than longer. A mile is 5280 feet exactly, so a mile that rises h feet has gradient:

i = h ÷ 5280

No unit conversion is needed at all: 100 feet per mile is 100 / 5280 = 0.018939, a 1.8939% climb, and 1% is exactly 52.8 feet per mile. From there the page does four things, and you can redo all of them on a calculator:

Grade each mile. A mile with a net change of h feet has gradient i = h / 5280.
Price each mile. Multiply the cost at that gradient by the length of a mile in metres: E_k = C(i_k) × 1609.344. Add them up to get E, the whole course's cost.
Hand out the time. Each mile gets its share of your target 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 and only the distribution moves.
Quote the flat-equivalent. The same effort on a level course would have produced T_flat = T × (3.6 × D) / E, with D the race distance in metres. That is the number that says what the hills actually cost you.

A worked mile

Take one mile with 100 feet of climb in it, so i = 100 / 5280 = 0.018939. The equation gives C(0.018939) = 3.9856. Divide by the flat cost: 3.9856 / 3.6 = 1.1071, so that mile costs about 10.7% more than the same mile on the level. A mile you would run in 7:30 on the flat is priced by the model at 7:30 × 1.1071 = 8:18.

The same arithmetic the other way is worth seeing, because it is where the whole page's honesty lives. At −100 feet per mile, C(−0.018939) = 3.2476, so the ratio is 0.9021 and the mile is worth about 9.8% faster — visibly less than the 10.7% the climb cost. A climb costs more than the matching descent saves. That asymmetry is why a course that starts and finishes at the same height is still slower than a flat one of the same length, and the demo profile below is exactly that case.

A worked course: ten miles in 1:15:00

The example the page opens on. The demo profile in the box is not a real race — it is a made-up shape with 10 numbers, one per mile: +120, +240, −90, +60, −180, +300, −240, +90, −150, −150 feet. It climbs 810 feet and drops 810 feet, so it starts and finishes at the same height, and its biggest single mile is 300 feet, a 5.68% climb. Priced against a 1:15:00 target the page returns:

Flat-equivalent — 1:13:56. The same effort on the level would have produced 4435.837 s, so the profile is costing about 64 seconds.
Splits — the climbs are the slow rows and the descents are the fast ones: mile 2 (+240 ft) at 9:24, mile 6 (+300 ft) at 9:58, mile 7 (−240 ft) at 5:47. Every row is in the table above; change any number in the profile box and they all rebuild.
The clock still lands on the target — the ten splits sum to 4500.000 s exactly, and the finish row prints 1:15:00 rather than a rounded version of it. The largest rounding gap on the whole table is 0.4593 s.

One detail is worth naming, because it is the difference between a cost ratio and a split. The ratio C(i)/3.6 tells you how much dearer a mile is than a level mile; the table's numbers are that cost turned into a share of your target, normalised against the whole course's cost rather than against the flat cost. On this profile the course costs 1.014465 times the flat cost, so the 240-foot mile prints 9:24 where the flat-cost illustration alone would say 9:32. Both are the same model; only the first one adds up to your finish time.

A cross-check against a page you can read

Set the profile box to Flat course and the page must reduce to even splits, with nothing left of the hill model. It does: ten miles in 1:15:00 becomes 7:30 per mile, ten rows from 7:30 to 1:15:00, every one of them exact, and a largest rounding gap of 0.0 s. Those are the identical figures the running split calculator publishes for its own ten-mile example. Two pages, two different jobs, one arithmetic on the flat — which is the cheapest available check that this page's model has not drifted.

Getting the numbers for your course

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

Your watch. Run any part of the course and read the per-mile elevation column rather than the cumulative chart. A mile with 180 feet of gain and 30 feet of loss is a net +150 feet for that mile.
The race website. Courses with a reputation for hills usually publish a profile. Read it off at mile 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-mile elevation readout, then subtract each mile's cumulative figure from the one before it.

If the profile you have is in metres per kilometre, this box will not take it, and it is not a matter of taste: a metre-per-kilometre number is a different quantity from a feet-per-mile number, and converting one into the other by eye is where wrong tables come from. Multiply metres per kilometre by 5.2801 to get feet per mile if you must — 1 m/km is 5.2801 ft/mi — but a profile read off a race page at kilometre intervals will not line up with mile rows anyway, so the cleaner move is to take the profile in the unit the box asks for or use the site's kilometre pages instead.

If you only have the totals — say 900 feet 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.

Supported range and limits

Distance: 0.25 to 100 miles (about 402 metres to 161 km), entered in kilometres or miles. The unit control sets how you enter it; the arithmetic converts to metres either way.
Target time: 1 minute to 47:59:59, entered as hours, minutes and seconds, with minutes and seconds between 0 and 59.
Profile: one net elevation change per whole mile, in feet, mile 1 first. Miles you leave out count as flat, and entries past the last whole mile are ignored. Gradients are clamped to the ±45% the published study covered, which is ±2376 feet per mile; a mile beyond that is priced at the clamp and the page says so.
Rows: one per whole mile, plus a finish row. A ten-mile race is 11 rows; a 100-mile race is 101.
Partial miles: a race that is not a whole number of miles ends with a short tail — a marathon is 26 whole miles plus 352.056 metres — and the tail is priced as flat and labelled as the finish, because no profile entry describes it.
Pacing: even effort only. There is no even-pace mode and no negative-split mode; the whole point of the page is that the pace varies with the ground.
Cost: none. No account, no email, no paywall, no daily limit, no request to a server.
Privacy: every number is computed in your browser. Nothing you type is sent anywhere or stored — reload the page and it is gone.
Works offline once the page has loaded, and on a phone.

What this page deliberately does not do

No printable band. Nothing here is drawn to be cut out and worn. The running split calculator prints an even-split band for any distance and the marathon pace band does it for 42.195 km.
No two clocks. The table carries one clock, the one you keep. If your race is chip-timed and you want to know what the gun clock above each mile marker will read, the splits calculator carries both, in kilometres.
No metres per kilometre. The profile box is feet per mile, always. The marathon split calculator and the race time calculator are the two pages that take a profile in metres per kilometre, and this page does not accept that unit rather than silently guessing which one you meant.
No prediction. This page starts from a target time you already believe. It does not tell you what you are capable of: the predictor on the home page moves a recent race result along the distance curve, and the race time calculator prices a target course on top of that.
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-mile series I did not measure myself, so the box stays yours to fill.
No weather correction. Heat, humidity and wind move race 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 mile as a run.
No fatigue model. The cost of a mile at 25 miles is treated as identical to the cost of the same mile at 2 miles. Real races do not work that way, and the back half is where this page's number is weakest.
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 mile splits calculator?

A mile splits calculator turns a target finish time into the clock you should be reading at every mile mark of the course. This one goes one step further: it prices the climb and the descent inside each mile, so the uphill miles are slower and the downhill miles are faster while the finish time you asked for is preserved exactly.

Where do I get the elevation change for each mile?

The box wants one number per mile: the net change in elevation over that mile, in feet, positive for climbing and negative for descending. A watch's per-mile elevation column gives it directly, a race website's profile can be read off at mile intervals, and a route builder's per-mile readout works too. Take the net change rather than the cumulative figure. Miles you leave out count as flat.

Why is the elevation in feet and the distance in miles?

Because a mile is 5280 feet exactly, so a profile in feet per mile converts to a gradient with one division: 100 feet per mile is 100 / 5280 = 1.8939 per cent, and 1 per cent is 52.8 feet per mile. The site's other two hill pages price a profile in metres per kilometre. The two units are not interchangeable, so this box asks for the imperial one and says so rather than converting behind your back.

Why does a course with no net climb still cost time?

Because a climb costs more than the matching descent saves. At a 4.5455 per cent climb the model's cost is 1.2716 times flat; at the same gradient downhill it is 0.7814, so the pair is dearer than two flat miles. The demo profile in the box climbs 810 feet and descends 810 feet and still costs about 64 seconds over ten miles, which is the whole reason a rolling course is slower than a flat one of the same length.

Does the page change my finish time?

No. Your target is held fixed and the time is redistributed across the miles: the shares add to one, so the splits add to your target exactly and the finish row prints the target itself. What the page adds is the flat-equivalent, the time the same effort would have produced on the level. On the demo profile a 1:15:00 target has a flat-equivalent of 1:13:56, so the profile is costing about 64 seconds.

Does it work for a race measured in kilometres?

Yes. The distance control takes kilometres or miles and the rows are always miles, so a metric race shows its short final mile: a marathon is 26.2188 miles, which is 26 whole miles plus a 352.056 metre tail, and that tail is priced as flat and labelled as the finish.

How is this different from the running split calculator?

The running split calculator draws even splits and a printable band, and it refuses hills. This page has no band and no even-split mode: every row is priced for the gradient of its own mile, and the profile is in feet per mile. The one place the two must agree is a flat profile, and they do: ten miles in 1:15:00 is 7:30 per mile on both, with every row exact and no rounding gap at all.