Pace Calculator

How to use it

1. Pick km or miles, then a race (5K, 10K, 15K, half marathon 21.0975 km, marathon 42.195 km) or type your own distance.
2. Type the second number you know: a goal time to get the pace you must hold, or a pace to get your finish time. Work out shows which box is being calculated; tap another to swap. Typing into the calculated box swaps it too.
3. Choose where you want splits (every km, every mile or every 5 km) and how you want to run it: Even, or a Negative or Positive split by a percentage.
4. Name the plan, download the pace band, print it at 100% and check the 10 cm line with a ruler. Cut a strip along the dashed lines and tape it round your wrist with clear tape, times facing out.

Pace, time and speed

Pace is time divided by distance. 10 km in 50:00 is 3000 s ÷ 10 = 300 s, so 5:00 per km. A mile is exactly 1.609344 km, so the same run is 300 × 1.609344 = 482.8 s, 8:03 per mile. Speed is the other way up: 60 ÷ 5 = 12.0 km/h, or 12 ÷ 1.609344 = 7.46 mph. Time is pace × distance (5:00 per km for a marathon is 300 × 42.195 = 3:30:59) and distance is time ÷ pace.

Some useful targets: a 2-hour half marathon and a 4-hour marathon are both 5:41 per km (9:09 per mile), because the marathon is exactly twice the half. A 3-hour marathon is 4:16 per km (6:52 per mile). Paces are shown to the whole second, and a second per km is 42 seconds over a marathon, so the finish time printed beside a rounded pace is worked out from the exact one.

How the splits are worked out

An even split holds the same pace all the way: a 1:45:00 half is 4:59 per km (298.6 s) and reaches 10 km at 49:46. A negative split runs the second half faster than the first by the percentage you give; a positive split runs it slower. Instead of jumping from one pace to another at halfway, the pace changes in a straight line from the start to the finish:

p(x) = P + b × (x − D/2),   P = T / D,   b = 4 × (T₂ − T₁) / D²

where D is the distance, T the target time, x the distance run so far, and the halves are T₁ = T / (1 + r) and T₂ = r × T / (1 + r) with r = 1 − 2% = 0.98 for a 2% negative split (1.02 for a 2% positive one). The time at any marker is the area under that line, C(x) = (P − bD/2) × x + b × x² / 2, which is exactly T at the finish, so the plan always ends on your target and every lap is a little quicker (or slower) than the last.

Worked example: a half marathon in 1:45:00 with a 2% negative split. T₁ = 6300 ÷ 1.98 = 53:02 and T₂ = 51:58, which is 98% of T₁. The pace starts at 5:05 per km and finishes at 4:53, and the plan still reads 1:45:00 at 21.1 km.

Treadmill speeds

Treadmills are set by speed, not pace. The table puts the speeds just above and below your plan beside the pace each gives and the finish time it would mean over your distance, in 0.5 km/h steps (0.5 mph in miles). 12.0 km/h is 5:00 per km; 10.0 km/h is 6:00.

Race time equivalents

Peter Riegel, an American research engineer, published a simple rule in 1977 and expanded it in American Scientist in 1981: T₂ = T₁ × (D₂ / D₁)^1.06. Doubling the distance multiplies the time by 2^1.06 = 2.085, not 2, because pace slows as races get longer. A 25:00 5K gives 52:07 for 10K, 1:55:00 for a half and 3:59:47 for a marathon. Riegel fitted it to efforts of about 3.5 to 230 minutes, and it assumes the same training for both races. Some calculators change the 1.06 because it can give marathon times from a short race that many runners do not reach, so treat the long-distance figures as the best case.

Wearing a pace band

The band lists the cumulative time at each marker, the number your watch shows if you start it on the line, so a glance at a km or mile marker tells you whether you are ahead or behind. Race courses are measured along the shortest possible line, so a GPS watch usually reads a little more than the race distance and its automatic km beeps drift ahead of the course markers; the band is written for the markers. 15 mm strips are easiest to wear; 25–30 mm strips have bigger numbers for a long marathon list. A band with more splits than fit one strip continues on a second strip.

What it cannot do

• It has no course data, so it does not allow for hills, heat or wind. A hilly course or a hot day needs a slower plan than the arithmetic gives; the splits assume a flat, still course.
• The race equivalent is an estimate from a formula, not a prediction for you.
• It is not a training plan and gives no health advice: it does not tell you what pace you are fit enough to run.
• Splits are worked out to the second and printed to the whole second; a split strategy changes by at most 20% between halves.

Privacy and what is stored

Everything is worked out on this device. The plan is saved in this browser’s local storage so a reload keeps it, and Clear deletes it and your saved plans in one tap. A shared link carries the plan after the #, the part of a link browsers do not send to any server. The page sends an anonymous page-view count and, at most, two fixed words (pace-calc, pace-band); never a distance, a time or a plan name.

Questions

What pace do I need for a sub-2 hour half marathon?

2:00:00 over 21.0975 km is 341.3 seconds per kilometre, so 5:41 per km or 9:09 per mile, about 10.5 km/h. Because the pace is rounded to the second, running exactly 5:41 per km finishes in 1:59:54, which leaves 6 seconds of margin; 5:42 per km would finish just over 2 hours.

What pace is a 4 hour marathon?

4:00:00 over 42.195 km is 5:41 per km or 9:09 per mile, the same pace as a 2-hour half marathon, because the marathon is exactly twice the half. A 3:30 marathon is 4:59 per km (8:01 per mile) and a 3-hour marathon is 4:16 per km (6:52 per mile).

How do I convert pace per km to pace per mile?

Multiply the seconds per km by 1.609344, the number of kilometres in a mile. 5:00 per km is 300 s × 1.609344 = 482.8 s, which is 8:03 per mile. To go the other way, divide by 1.609344: 8:00 per mile is 4:58 per km.

What is a negative split?

Running the second half of a race faster than the first. With a 2% negative split a 1:45:00 half marathon is 53:02 for the first half and 51:58 for the second (98% of the first). The pace changes evenly across the race, from 5:05 per km at the start to 4:53 at the finish in that example, so every split is a little quicker than the last and the total is still exactly 1:45:00.

How accurate is the race time equivalent?

It is an estimate from Riegel’s formula, not a prediction for you. It assumes you are as well trained for the longer race as for the shorter one, so a marathon worked out from a 5K is often faster than a runner without the long-run training will manage.