Speed formula: distance = speed × time
Distance travelled = speed × time. In symbols, s = v t, where s is distance in metres (m), v is speed in metres per second (m/s) and t is time in seconds (s). Rearranged, speed = distance ÷ time. AQA, Edexcel and OCR each put the relationship on their recall list, and each board's exam sheet prints it.
Equation
s = v t
| Symbol | Quantity | Unit |
|---|---|---|
s | distance | m |
v | speed | m/s |
t | time | s |
What each specification says
| Exam board | Status | Equation |
|---|---|---|
| AQA Physics (8463) | Recall | s = v t |
| AQA Combined Science (8464) | Recall | s = v t |
| Edexcel Physics (1PH0) | Recall | distance travelled = average speed × time |
| Edexcel Combined Science (1SC0) | Recall | distance travelled = average speed × time |
| OCR Gateway Physics A (J249) | Recall | s = v t |
| OCR Twenty First Century Physics B (J259) | Recall | v = s/t |
Calculator: s = v t
Speed in everyday terms
Speed tells you how much distance you cover each second. If you walk at 1.5 m/s, you move one and a half metres in every second. After a minute you are 90 m down the road.
Most journeys speed up and slow down, so the equation gives the average speed over the whole trip. A bus might stop at lights and then race along a clear stretch. Divide the total distance by the total time and you get one number for the whole ride.
Physics uses the letter v for speed, from velocity. The letter s stands for distance. Take care not to mix up the symbol s, a distance, with the unit s, which means seconds.
For more practice with this equation, our sister site has a Speed Distance Time game where you drive a delivery van and set the missing value.
Three boards, three ways of writing it
This is one equation where the printed form really does differ. Use the one your board prints:
- AQA (8463 and 8464): s = v t, in words distance travelled = speed × time.
- Edexcel (1PH0 and 1SC0): words only, distance travelled = average speed × time. There is no symbol version.
- OCR Gateway (J249): s = v t.
- OCR Twenty First Century (J259): v = s/t, in words average speed = distance ÷ time.
All of them are the same physics, and all are recall equations in their specifications. Since 2025 the equation sheet in every physics paper includes the recall list as well as the given one. You can compare the AQA list with the OCR Twenty First Century list.
Rearranging for speed or time
- v = s ÷ t
- t = s ÷ v
Always turn the time into seconds and the distance into metres before you divide.
This equation only works when the speed is steady, or when you want the average. If the speed changes at a steady rate, use the acceleration equation. The same idea also turns up for waves, since the wave speed equation is another way of saying how far something travels each second.
Worked examples
v
- Change the time to seconds: 1 minute 20 s = 60 + 20 = 80 s
- v = s ÷ t
- v = 400 ÷ 80
- v = 5 m/s
5 m/s
s
- Change the time to seconds: 3 × 60 = 180 s
- s = v × t
- s = 50 × 180
- s = 9000 m
9000 m
t
- Change the distance to metres: 1.7 km = 1700 m
- t = s ÷ v
- t = 1700 ÷ 340
- t = 5 s
5 s
Common mistakes
- Typing 1 minute 20 seconds as 1.20 minutes. There are 60 seconds in a minute, so it is 80 s, or about 1.33 minutes.
- Dividing time by distance. A sprinter who runs 100 m in 10 s is doing 10 m/s, and 10 ÷ 100 would give a crawl of 0.1 m/s.
- Leaving the distance in kilometres while the speed is in m/s. The answer comes out 1000 times too small.
- Treating an average speed as the top speed. A car that averages 15 m/s on a town trip may have hit 20 m/s on the open stretches.
Swap between s, v and t as the subject in the Equation Rearranger to get quick at it.
Questions people ask
What is the difference between speed and velocity?
Speed is how fast. Velocity is speed in a stated direction, so a car going round a roundabout at a steady 10 m/s has a changing velocity.
How do I change km/h into m/s?
Divide by 3.6. The reason: 1 km/h is 1000 m in 3600 s, and 1000 ÷ 3600 is 1 ÷ 3.6. So 72 km/h is 20 m/s.
How far away is a thunderstorm?
Count the seconds between the flash and the thunder. Sound covers about 340 m each second, so a 3 second gap puts the storm roughly 1 km away.