Mile Pace Calculator

Why four 400 m laps do not make a mile

A mile is 1609.344 m. Four laps of a standard 400 m track are 1600 m, which leaves 9.344 m of the mile unrun. That leftover is small enough to disappear inside the rounding of a watch, but it is a real distance: at an eight-minute mile it is worth about 2.79 seconds, at a six-minute mile about 2.09 seconds, and at a ten-minute mile about 3.48 seconds. A time recorded after four laps is therefore a 1600 m time, not a mile time, and converting between the two is a division by 1609.344 rather than by 1600. This page keeps the exact distance as the divisor and gives the leftover its own row, so the printed clocks still land on the time you asked for.

The imperial quarter behaves differently. One mile is 1760 yd, so a quarter of it is 440 yd, which is 402.336 m. Four of those quarters are 1609.344 m with nothing left over, and the half mile is 880 yd or 804.672 m. The 800 m mark is therefore not halfway: it is 4.672 m short. In kilometres the same awkwardness appears once more, because one whole kilometre is 1000 m and leaves 609.344 m of the mile beyond it. Three different whole-number landmarks, three different leftovers, and only the 440 yd quarter divides the mile exactly. The table below prints each landmark in its own unit rather than quietly assuming they line up.

There is a second, quieter kind of leftover: rounding. Race clocks and watches display whole seconds, but dividing a target by 1.609344 almost never produces a whole number of seconds per kilometre. A watch that shows 298 s/km will not land on the target if you hold it for the full mile, while the mile column shows the target itself because the distance is exactly one mile. Worse, those two rounded paces are no longer a clean conversion of one another: 298 multiplied by 1.609344 is 479.584512 s/mile, not the 480 s/mile the watch shows. This page prints the exact pace, the whole-second pace, the speed and each of those gaps, then sets the finish row to the exact target so that no rounding residue is quietly discarded. Nothing on the page asks you to accept a number that cannot be traced back to a printed formula.

Every formula used on this page

Target time in seconds

T = 3600 x hours + 60 x minutes + seconds. The whole page uses this one number; the three time fields feed nothing else.

The distance

D_m = 1609.344 m exactly = 1.609344 km = 1760 yd = 5280 ft. One mile is 1.609344 km by definition, and there is no distance input on this page.

The distance in miles

D_mi = D_m / 1609.344 = 1.000000000 miles. Because the page fixes the distance at one mile, the per-mile pace is the target time itself.

The two leftovers

stub_lap = 1609.344 - 4 x 400 = 9.344 m. stub_km = 1609.344 - 1000 = 609.344 m. Four 440 yd quarters are 4 x 402.336 = 1609.344 m, so that breakdown leaves zero.

The half and quarter marks

half_m = 1609.344 / 2 = 804.672 m = 880 yd = 0.5 mi. quarter_m = 1609.344 / 4 = 402.336 m = 440 yd = 0.25 mi. The halfway clock is T / 2 exactly.

Exact pace and speed

p_km = T / 1.609344 seconds per kilometre; p_mi = T / 1 seconds per mile. speed_kmh = 3600 / p_km; speed_mph = 3600 / p_mi. Pace times speed is 3600 in each unit, so the two pairs check each other in closed form.

The pace a watch shows

w_km = round(p_km) and w_mi = round(p_mi), in whole seconds, printed as minutes and seconds. Both sit next to the exact values so the difference is visible rather than hidden.

Whole-second drift over the full distance

drift_km = w_km x 1.609344 - T; drift_mi = w_mi x 1 - T. The mile-side drift is zero because the target itself is a mile time; the kilometre-side drift is not.

The gap between the two rounded paces

cross_gap = w_km x 1.609344 - w_mi seconds per mile; cross_drift = cross_gap x 1 seconds. This is why converting one watch pace into the other unit does not reproduce the watch pace that was displayed there.

A mark clock and its split

clock(d) = round(T x d / D), where d and D are in the same unit for that row. split(d_i) = clock(d_i) - clock(d_(i-1)), with the first split taken against zero. For the finish row the page uses clock(D) = T exactly, with no rounding, so the splits in a group sum to T.

The sections around the 1 km mark

first_km = round(T x 1000 / 1609.344); last_section = T - first_km. The first covers 1000 m, the second covers 609.344 m, and their sum is T exactly.

Lap and leftover timings

lap = T x 400 / 1609.344 seconds; four_laps = T x 1600 / 1609.344 seconds; stub_time = T x 9.344 / 1609.344 seconds. The last two add back to T.

Three worked examples

Every row below is recomputed on load by the same function that drives the results above, from the target time printed beside it. Nothing is typed in by hand.

What this page deliberately does not do

• No prediction. You supply the target; this page does not read a recent race or tell you what you can run.
• No other distance and no distance field. One mile, 1609.344 m, is the one distance on this page.
• No grid of many finish times and no mile-by-mile split table. One target, one set of results.
• No negative splits and no even-versus-negative toggle. Every clock is even timing.
• No printable pace band, no course presets, no aid-station markers and no watch or GPS sync.
• No age or sex grading, no sex selector, and no invented factor table.
• No elevation, hill, weather, heat, humidity or wind correction.
• No training plan, session prescription, weekly volume, coaching or medical advice.
• No good-or-bad label, no cut-point and no grade for any finish time.
• No account, no upload, no saved history and no server-side arithmetic.