Acceleration Calculator
Acceleration is how quickly velocity changes. One subtraction and one division turn a starting speed, an ending speed and a time into the rate at which the motion is changing.
Acceleration
4
- Change in velocity
- 20
- Distance travelled
- 50
- Net force required
- 4,800
Values update as you type. This calculator covers the single scenario its formula assumes — see Common Mistakes for what it leaves out.
The formula this calculator uses
a = (v - u) / t
- a
- Acceleration, the rate at which velocity changes
- u
- Starting velocity, in metres per second
- v
- Final velocity, in metres per second
- t
- Time taken, in seconds
- m
- Mass, used only when you want the force involved
How to check the result by hand
- 1
Write down both velocities in the same unit
Convert anything in kilometres per hour to metres per second first, by dividing by 3.6. A single mixed unit turns the answer into nonsense that still looks plausible.
- 2
Subtract the starting velocity from the final one
For a car going from rest to 20 metres per second that is 20 minus 0, which is 20. If it were braking from 30 to a stop the answer would be -30, and the minus sign is the whole point.
- 3
Divide by the time taken
Twenty metres per second of change spread over 5 seconds is 4 metres per second squared. Doubling the time halves the acceleration for the same change in speed.
- 4
Take the average speed if you need the distance
Add the two velocities and halve them. Ten metres per second average over 5 seconds covers 50 metres. This midpoint rule only holds when the acceleration is steady.
- 5
Multiply by mass for the force
A 1200 kilogram car accelerating at 4 metres per second squared needs 4800 newtons. Remember that this is the net force, so the engine has to deliver more than this to also beat friction and drag.
For worked examples, common mistakes and the limits of this formula, read the full How To Calculate Acceleration page.