How Pace Math Works

What pace is, how to work it out, how the split chart stays exact, and how to print a band at real size.

What pace means

Pace is the time it takes you to run one kilometer or one mile. An 8:00 mile pace means each mile takes eight minutes. Always write the unit: 8:00 /mi and 8:00 /km are very different runs.

Pace is the flip side of speed, so a smaller pace number is faster. Treadmills often show speed instead, so this calculator gives km/h and mph too.

Race distances come from World Athletics. Technical Rule 55 lists the standard road distances, including 5km, 10km, Half-Marathon and Marathon (42.195km), and the World Athletics half marathon page puts the half at 21.0975km.

Distance, time and pace math

Pace is time divided by distance. A 4:00:00 marathon is 14,400 seconds over 42.195 km, which is 341.3 seconds per km, or a 5:41 /km pace.

Time is pace times distance, and distance is time divided by pace. Run 10 km at 5:00 /km and you finish in 50 minutes. Run 30 minutes at 6:00 /km and you cover 5 km.

To switch to miles, one mile is 1,609.344 m. NIST lists that value as exact, and the World Athletics rules list the road mile as 1609.344m. Multiply a per-km pace by 1.609344 to get the per-mile pace.

What this calculator does

On the first page, pick what to solve for (pace, time or distance) and fill in the other two. You get pace per km and per mile side by side, whichever unit you typed, and every pace carries its /km or /mi label.

The math uses whole numbers, not floating point. Distance is kept in millimeters and time in seconds, and rounding happens once, when a number is shown. It rounds to the nearest value, and exact halves round up.

The split chart works out each cumulative time exactly, rounds it to the second, and takes each split as the gap between two rounded cumulative times. That is why the splits add up to your goal time to the second. The total under the chart is the actual sum of the split column.

Split charts and pacing

Pick splits every 1 km, every mile or every 5 km. The last row is the finish, and when the distance is not a whole number of intervals the last split is short. A marathon in 1 mile splits ends with a 0.22 mile piece after mile 26.

Even pace is the default. You can also set the second half 1% to 5% faster (a negative split) or slower. The chart shows first-half and second-half pace above the table.

This app does not claim any pacing plan runs faster. It has not checked evidence for that, so it gives you the menu and leaves the call to you.

Printing a pace band

The pace band page turns your split chart into a paper strip. Pick a width of 25, 30 or 35 mm, and the length follows from the number of rows. A marathon in 1 mile splits is 27 rows and 147 mm long.

Set the print scale to 100% or Actual size so the band comes out at the size shown. Fit to page can shrink it, so measure the 100 mm ruler printed with it.

A strip longer than 230 mm is split into two or three strips side by side. It is paper, so sweat and rain can soak it.

Common snags

A mile band in a km race will not line up with the course markers. Check whether your course marks km or miles and pick the same interval.

Your watch distance and the course markers can drift apart. The World Athletics rules say a course is measured along the shortest route a runner could take, so line your band up with the markers.

The min and sec boxes take up to 59. Enter 1 hr 5 min, not 65 min. And 26.2 miles is 42.16 km, a little short of 42.195 km, so use the Marathon button for the full distance.

Sources

Race day gear

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