Pace is time per distance, usually minutes per kilometre or minutes per mile. Speed is the opposite: distance per time, such as kilometres per hour. Runners use pace because it maps directly onto race targets. If you know you need 5:00 per kilometre, you can check every kilometre marker against your watch. Treadmills, though, are usually set by speed, which is why converting between the two is one of the most common tasks for runners.
Why pace isn't linear
Because pace and speed are inverses, equal changes in one don't produce equal changes in the other. Going from 6:00 to 5:30 per kilometre raises speed from 10.0 to about 10.9 km/h. Going from 4:00 to 3:30 per kilometre, the same 30-second improvement, raises speed from 15.0 to about 17.1 km/h. Small pace improvements at the faster end require much bigger jumps in speed, which is one reason they're so much harder to achieve.
Averaging pace correctly
The same maths catches people out when averaging. If you run one kilometre at 5:00 and another at 6:00, your average pace isn't simply halfway between paces measured in speed terms. Add the times and divide by the distance: 11 minutes for 2 kilometres is 5:30 per kilometre. But if you run for equal times at two speeds, rather than equal distances, the average pace is slightly faster than the midpoint. Running watches handle this automatically; spreadsheets often don't.
Worked conversions
A 25-minute parkrun is 5:00 per kilometre, or about 8:03 per mile. A treadmill set to 10 km/h is running at 6:00 per kilometre, about 9:39 per mile. For a sub-four-hour marathon, you need an average of about 5:41 per kilometre, or 9:09 per mile, over the full 42.195 km, and in practice a little quicker to allow for drinks stations and congestion. Splitting the race evenly or slightly faster in the second half, a negative split, usually produces better times than starting fast and fading.
Pace on hills and trails
Pace targets are designed for flat roads. On hilly courses and trails, even pace is the wrong goal: running uphill at your flat-road pace takes far more effort, and you can't fully make it back on the descents. Many runners switch to effort-based pacing or heart rate on hills, accepting slower splits on climbs. For off-road races, the time difference can be large; a hilly trail 10k might take 15 to 30% longer than a flat road 10k at the same effort.
GPS and measured courses
Running watches measure distance by GPS, which can drift, especially among tall buildings or under tree cover. That makes displayed pace less reliable than the official distance of a measured course. On race day it's common for a watch to show slightly more than the official distance, because runners don't follow the shortest racing line around every corner. If you're pacing to a time, allow for that by aiming a few seconds per kilometre faster than the exact target.
Checking your answer
Six minutes per kilometre is 10 km/h, and five minutes per kilometre is 12 km/h. A mile at 8 minutes is about 5 minutes per kilometre. If a pace converts to a speed above about 20 km/h for a long run, or below 6 km/h for a run rather than a walk, double-check the units.
One more worked example
A runner targeting a half marathon in 1 hour 50 minutes needs to average about 5:13 per kilometre, or 8:24 per mile, over 21.1 kilometres. Setting a treadmill to match means about 11.5 km/h. For long runs in training, many coaches suggest running 45 seconds to 1 minute per kilometre slower than race pace, so around 6:00 to 6:15 per kilometre for this runner, which keeps easy runs genuinely easy.