Acceleration Calculator
Find acceleration from a change in velocity over time, or rearrange for final velocity or time.
A negative acceleration means the object is slowing down (decelerating).
Acceleration is the change in velocity divided by the time taken: a = (v − u) ÷ t. A car going from 0 to 27 m/s in 9 seconds accelerates at (27 − 0) ÷ 9 = 3 m/s². A negative result means deceleration. Rearrange to get final velocity (v = u + at) or time.
What acceleration measures
Acceleration is how quickly an object’s velocity changes. Because velocity is measured in metres per second (m/s) and you divide by seconds, acceleration comes out in metres per second per second — written m/s². A value of 3 m/s² means the speed increases by 3 m/s every second. Acceleration is a vector, so a negative sign simply means the change points opposite to your chosen positive direction. To continue the motion into displacement and final velocity, use the SUVAT kinematics solver.
u = initial velocity (m/s), v = final velocity (m/s), t = time (s), a = acceleration (m/s²)
Worked example
A car merging onto a motorway speeds up from rest (u = 0) to v = 27 m/s in t = 9 s:
- 1 Find the change in velocity. Subtract initial from final velocity: v − u = 27 − 0 = 27 m/s.
- 2 Divide by the time taken. a = (v − u) ÷ t = 27 ÷ 9.
- 3 Read the result. a = 3 m/s² — the car gains 3 m/s of speed every second.
Typical accelerations
Approximate magnitudes for everyday and physical reference points.
| Situation | Acceleration | Note |
|---|---|---|
| Free fall near Earth | 9.81 m/s² | Standard gravity, g |
| Brisk car (0–27 m/s in 9 s) | 3 m/s² | Comfortable merging |
| Sprinter off the blocks | ≈ 2.5–4 m/s² | First few strides |
| Emergency car braking | ≈ −8 m/s² | Negative: slowing down |
| Passenger jet at takeoff | ≈ 3 m/s² | Along the runway |
Reading the sign and avoiding mistakes
A negative acceleration is deceleration. If you call the direction of motion positive, an object slowing down has a negative acceleration — there is no separate braking formula, just a negative number.
Velocity and acceleration are different. A fast object can have zero acceleration (cruising at constant speed), and a momentarily stationary object can have large acceleration (the top of a thrown ball’s flight).
This formula assumes constant acceleration. It gives the average acceleration over the interval; if the rate changes during the motion, split it into segments or use calculus.