What this calculator does
Acceleration is the rate at which velocity changes over time. The acceleration formula, a = (v − u) / t, takes an initial velocity, a final velocity and the time taken to go from one to the other, and returns how quickly that change happened.
This calculator applies that formula directly, without the braking-distance or reaction-time extras that a full stopping-distance calculation adds. Enter the starting speed, the ending speed and the time taken, and it returns the acceleration, along with the distance covered over that time as a cross-check.
The formula
Subtract the initial velocity from the final velocity to get the change in speed, then divide by the time taken. A positive result means the object sped up; a negative result means it slowed down. The distance covered over the same time comes from the average of the two velocities multiplied by the time.
| Term | Meaning |
|---|---|
| u | Initial velocity, the speed at the start of the time interval. |
| v | Final velocity, the speed at the end of the time interval. |
| a | Acceleration, the rate of change of velocity: a = (v − u) / t. |
| t | The time taken for velocity to change from u to v. |
The inputs explained
| Field | What to enter |
|---|---|
| Initial velocity (u) (m/s) | The speed at the start of the interval being measured. |
| Final velocity (v) (m/s) | The speed at the end of the interval. |
| Time taken (t) (s) | The time taken to go from the initial speed to the final speed. |
When to use it
Working a straightforward physics problem
When a problem gives a starting speed, an ending speed and a time, and asks only for the acceleration formula itself, this skips past the extra braking-distance and reaction-time inputs that a full vehicle stopping-distance calculator adds.
Checking how acceleration compares to g
Expressing the result as a multiple of g (9.80665 m/s²) gives an intuitive sense of how strong an acceleration is, since 1g is roughly what gravity alone produces.
Finding distance covered during acceleration
Once acceleration is known, the distance covered over that same interval follows from the average of the two speeds multiplied by the time, without needing a separate distance formula.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How acceleration changes with time taken, for a fixed speed change
Speeding up from 0 to 20 m/s, across a range of times taken to do it.
| Time taken | Acceleration | Distance covered over this time |
|---|---|---|
| 2 s | 10.000 m/s² | 20.00 m |
| 4 s | 5.000 m/s² | 40.00 m |
| 5 s | 4.000 m/s² | 50.00 m |
| 8 s | 2.500 m/s² | 80.00 m |
| 10 s | 2.000 m/s² | 100.00 m |
| 20 s | 1.000 m/s² | 200.00 m |
Questions
What is the acceleration formula?
a = (v − u) / t, where u is the initial velocity, v is the final velocity, t is the time taken, and a is the resulting acceleration.
How do you calculate acceleration?
Subtract the starting speed from the ending speed to find how much the speed changed, then divide that change by the time it took. A negative acceleration is a deceleration, meaning the object slowed down rather than sped up.
What are the units of acceleration?
Metres per second squared (m/s²) in SI units, which is a change of 1 metre per second in speed, for every second that passes. Acceleration is also often expressed as a multiple of g, standard gravity, about 9.80665 m/s².
Does this calculator include braking distance?
No, this page is deliberately limited to the bare acceleration formula. For braking distance, reaction time and total stopping distance from a vehicle speed, see the fuller acceleration and stopping distance calculator.
For braking distance and reaction time added to the same calculation, see the acceleration and stopping distance calculator. For a full five-variable solver covering displacement, velocity, acceleration and time together, see the SUVAT equations calculator.