Worked example

How Milemarq solves pace, splits, and the race math behind them

Type 3:30:00 into the time field and 42.195 km into distance, leave pace blank, and Milemarq reads back 8:00 per mile before you lift your finger. Pace, finish time, and distance are one equation with three slots, and filling any two solves the third. This page runs a single goal through all three directions, shows where the seconds hide, and says plainly which numbers you can plan a race around.

The math

Solving a 3:30:00 marathon three ways

A 3:30:00 marathon is 12,600 seconds over 42,195 metres. Divide one by the other and you have the pace; multiply pace back through the distance and you have the finish time; divide elapsed time by pace and you have how far you went. Two inputs, always the third out, in whichever direction you left blank.

Required pace
8:00
min / mile for a 3:30:00 marathon
Min / Mile8:00
Min / KM4:58
Speed MPH7.5
Speed KPH12.1

Pace

pace = time ÷ distance

12,600 s over 42,195 m is 0.29861 s/m, which prints as 8:00 per mile and 4:58 per kilometre.

Finish time

time = pace × distance

480 s × 26.21875 mi is 12,585 s, or 3:29:45. Rounding the true 8:00.6 pace down to a flat 8:00 hands 15 seconds back to the clock.

Distance

distance = time ÷ pace

45:00 of running at 9:00 per mile is 2,700 s divided by 540, giving 5.0 miles or 8.05 km. Most single-purpose calculators never expose this direction.

Precision

Pace floors down while the clock rounds

One precision rule runs through every number above, and it is a choice we made deliberately rather than a rounding accident. A pace truncates to the whole second, because a pace is a floor you have to hold: read 8:00 and you commit to 8:00, not 8:01. A clock time rounds to the nearest second, the way a watch does. So the same 3:30:00 marathon shows a required pace of 8:00 per mile while the split clock ticks over to 8:01 at the first mile marker. The two disagree by a second on purpose. Hold the floor and you finish on plan; chase the rounded number and you leave time on the course.

Splits

A split sheet built from unrounded seconds

A split sheet answers two questions at once. The split column is how long one mile should take on its own; the elapsed column is what your watch should read as you cross that marker. Milemarq accumulates every elapsed value from unrounded seconds and rounds only when it prints, so error never compounds down the column, and it pins the final row to the exact solved finish time instead of a sum of rounded segments.

Races rarely end on a whole mile. A marathon is 26.22 miles, so the sheet lists 26 full rows and then a labelled partial covering the last 0.22 of a mile. That fragment earns its own row because at 8:00 pace it is worth about 1:45, and it sits exactly where goal times quietly go missing. Past 110 rows the interval steps out to every 5 miles so a 100-mile ultra stays readable, and the trailing partial still shows.

Treadmill

Belt speed to pace at the settings a console offers

The treadmill console gives you a speed; your plan gives you a pace. Converting is 60 divided by the belt speed in mph for decimal minutes, then the fractional part times 60 for the seconds. Belts step in 0.1 mph increments, so one arrow press is worth several seconds per mile up near 8 mph.

Treadmill belt speed converted to running pace per mile and per kilometre
MPHKPHMin / MileMin / KM
5.08.012:007:27
6.09.710:006:12
7.011.38:345:19
8.012.97:304:39
10.016.16:003:43
Constants

The certified metre and the time it hides

A half marathon is not 21 km and a marathon is not 42 km. The certified distances are 21,097.5 and 42,195 metres, gaps of 97.5 and 195 metres over the round figures. That is real time on a real clock: about 33 seconds off a two-hour half, and close to a minute off a 3:30 marathon. This is a crowded search, led by incumbents like Calculator.net, so the edge we chose to build on was precision rather than arithmetic: Milemarq carries the certified value into the presets, the solved answer, and every split row, so nothing you plan rests on a rounded course.

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Questions

Pace questions, answered

How do you calculate running pace?

Pace is time divided by distance, and that one line covers everything else on this page. Milemarq converts whatever you type into metres and seconds first, divides, then shows the answer in the units you asked for. A 3:30:00 marathon is 12,600 seconds over 42,195 metres, which comes out at 8:00 per mile and 4:58 per kilometre. You get both at once, plus the mph and kph equivalent, because the pace you talk about with training partners and the number on a treadmill console are rarely the same unit.

How long is a half marathon exactly?

21,097.5 metres, or 13.10938 miles. Calling it 21 km quietly drops 97.5 metres, and at a two hour half that gap is worth about 33 seconds. The marathon has the same problem in a bigger form: 42,195 metres, not 42 km. Milemarq holds the certified values and builds every split row from them.

What pace is 7.5 mph on a treadmill?

8:00 per mile, or 4:58 per kilometre, or 12.1 kph if the console speaks metric. The arithmetic is 60 divided by the belt speed in mph, which gives you decimal minutes, then multiply whatever sits after the decimal point by 60 for the seconds. Belt speeds usually step in increments of 0.1 mph, and one step is worth several seconds per mile at the fast end of the dial and a lot more at walking speed. The table above covers the settings most consoles offer, and the calculator handles everything in between.

Why does the last split row cover a shorter distance?

Because races don't end on a round mile. A marathon is 26.22 miles, so an imperial split sheet gets 26 full rows and then a trailing partial covering the last 0.22, labelled as partial rather than folded quietly into mile 26. That fragment is where a goal time is usually won or lost, and dropping it would make the sheet look tidier than the race actually is. The partial row carries the exact solved finish time, so the bottom of the elapsed column and your target always agree.

Why do the split and elapsed columns disagree by a second?

They round in opposite directions, deliberately. A split is a pace, a floor you have to hold, so it truncates to the whole second: 8:00 means eight minutes flat or quicker. An elapsed time is a clock reading, so it rounds to the nearest second the way a watch does. Mile 1 of a 3:30:00 marathon takes 480.62 seconds, which prints as an 8:00 split next to an 8:01 elapsed. Both are correct. Milemarq accumulates elapsed time from unrounded values and pins the final row to the solved duration, so the foot of the column reconciles to your finish time with no drift, however long the run is.

Does Milemarq send my times anywhere?

No. Every calculation runs in your browser, and nothing goes out over the network to do the maths. No account, no upload, no server that ever sees a pace. The one thing kept between visits is which unit system you used last, stored locally so imperial or metric leads when you come back. Times, distances and split tables aren't saved anywhere.

Can I get splits for a distance that is not a standard race?

Yes. Type any distance up to 100 miles, or 160.9 km, in either unit, and the splits table follows it. Presets for the 5K, 10K, half and marathon are there to save you the typing, but the solver treats a preset and a typed distance identically, so nothing about the maths changes when you use one. Long distances get a single adjustment: past 110 rows the interval steps out to every five miles or kilometres instead of every one, with the trailing partial still shown, so a 100 mile plan stays readable instead of becoming a wall of rows.