Speed, distance and time calculator

Leave one blank and this finds it, converting the units properly and showing the rearrangement. Mixing up minutes and hours is where most marks go on this topic, so that conversion is shown explicitly rather than done quietly.

Distance

Time

Speed

Leave exactly one of the three blank. The units can be different from each other; the conversion is handled and shown in the working.

The formula, and why the triangle works

Speed is distance divided by time. That single relationship gives all three formulas, because rearranging it is just algebra: s = d ÷ t, d = s × t, and t = d ÷ s.

The formula triangle with d on top and s and t underneath is a memory aid for exactly that rearranging. Cover the quantity you want, and what is left shows you the calculation. It works, but it is worth knowing it is only a shortcut for the algebra, not a separate rule. Once you can rearrange the equation yourself, you do not need the triangle.

Where the marks actually go: units. If distance is in kilometres and time is in minutes, dividing gives you km per minute, not km per hour. Multiply by 60 to fix it. Most wrong answers on this topic are correct arithmetic with mismatched units, which is why the working below always shows the conversion.

Average speed is not the average of speeds

This catches people out regularly. If you drive somewhere at 40 km/h and back at 60 km/h, your average speed for the round trip is not 50 km/h. It is 48 km/h.

The reason is that you spend longer travelling at the slower speed, so the slow leg carries more weight. Average speed is always total distance divided by total time, never the mean of the individual speeds. Work out each leg's time separately, add them, then divide the total distance by that.

Common questions

What is the difference between speed and velocity?: Speed is just how fast something moves. Velocity is speed together with a direction, which makes it a vector. A car going round a roundabout at a steady 30 km/h has constant speed but changing velocity, because its direction keeps changing.
How do I convert m/s to km/h?: Multiply by 3.6. One metre per second is 3.6 km/h, because there are 3600 seconds in an hour and 1000 metres in a kilometre. Going the other way, divide by 3.6.
What if the time is given as 1 hour 30 minutes?: Convert it to a single unit first. That is 1.5 hours, or 90 minutes. Entering 1.30 would be wrong, since time is not decimal in the way money is.
Does this work for acceleration questions?: No. These formulas assume a constant speed, or that you are working with an average. If the speed is changing steadily you need the SUVAT equations instead.