Speed, distance and time calculator with working

A formula triangle with $d$ on top and $v$ and $t$ underneath is a quick way to remember the three forms. In exams, write the equation first, then substitute: the first mark is often for the equation.

• Speed: a runner covers 100 m in 20 s. $v = 100 \div 20 = 5$ m/s.
• Distance: a car travels at 30 m/s for 5 s. $d = 30 \times 5 = 150$ m.
• Time: a cyclist travels 3 km at 6 m/s. Convert first: 3 km = 3,000 m, so $t = 3000 \div 6 = 500$ s, which is 8 minutes 20 seconds.

The SI unit of speed is metres per second (m/s). To convert:

• km/h to m/s: divide by 3.6 (because 1 km/h $= 1000 \div 3600$ m/s). So 72 km/h $= 20$ m/s.
• m/s to km/h: multiply by 3.6.
• Minutes to seconds: multiply by 60; hours to seconds: multiply by 3,600.

Most mistakes come from mixing units, such as kilometres with seconds. The calculator converts everything to metres and seconds first and shows that step.

The AQA GCSE specification expects students to recall typical values: walking about 1.5 m/s, running about 3 m/s and cycling about 6 m/s, with the speed of sound in air about 330 m/s. These help you check whether an answer is sensible: a person walking at 150 m/s means a unit has gone wrong.

Speed is how fast something moves; velocity is speed in a given direction, so it can change even when speed doesn't (like a car going round a roundabout). Most journeys involve changing speed, so $d \div t$ gives the average speed. On a distance-time graph, the gradient is the speed. For more, see our guide to speed, distance and time.