Acceleration Calculator

Acceleration is the rate at which velocity changes: not how fast something moves, but how quickly speed or direction changes. Car road tests quote it, lift engineers certify by it, and textbooks open motion with it. Two velocities and a duration are enough to calculate it — and the same three inputs also reveal the ground covered while changing speed, plus whether it was actually slowing down.

Enter values

Results

Acceleration: 4 m/s²
In km/h per second: 14.4 km/h/s
Distance covered: 50 m
Motion: Accelerating

How is the Acceleration calculated?

Three number fields: the initial velocity u, the final velocity v, both in metres per second, and the time t in seconds taken to get from one to the other. The calculator subtracts u from v and divides by t for the acceleration in m/s², restates it in the friendlier km/h per second, and computes the distance covered with the average-speed formula. The sign of the change decides the motion label: speeding up, slowing down, or holding constant.

Formula

a = (v − u) ÷ t gives acceleration in m/s² from initial velocity u, final velocity v and time t. Multiplying by 3.6 restates it in km/h per second. The distance covered is s = ½ (u + v) × t, the average velocity times the time. A positive a means speeding up, a negative a means decelerating, and a equal to zero means the velocity never changed.

Example

A hatchback pulls from 0 to 20 m/s in 5 seconds: a = (20 − 0) ÷ 5 = 4 m/s², which is 4 × 3.6 = 14.4 km/h per second, and it covers ½ × (0 + 20) × 5 = 50 m along the way. Braking the same car from 20 back to 0 m/s in 5 s gives −4 m/s² — the magnitude identical, the sign reporting deceleration — over the same 50 m. Hold 7 m/s for 3 s and the acceleration is 0 with 21 m travelled.

Things to remember

Velocity change over time is the whole definition, and the sign carries real meaning: negative acceleration is not an error but braking. The km/h per second row speaks road-test language, and the distance row reuses the same data. For speed conversions without the time component, the speed converter has its own page.

Frequently Asked Questions

What is the formula for acceleration?

a = (v − u) ÷ t — the final velocity minus the initial, divided by the time taken. Going from 0 to 20 m/s in 5 s gives (20 − 0) ÷ 5 = 4 m/s², meaning four metres per second of speed gained every second.

What is the difference between m/s² and km/h per second?

Only the scaling: multiply m/s² by 3.6 to get km/h per second. An acceleration of 4 m/s² is 14.4 km/h per second, which is how car reviews usually phrase it because the second unit matches the speedometer.

What does negative acceleration mean?

That velocity decreased — deceleration, or braking. Sliding from 20 to 0 m/s in 5 s yields −4 m/s². Direction decides the sign, so the same physical effort accelerating one way would read positive the other; the magnitude tells you how hard the speed changed.

How far does an object travel while accelerating?

Use s = ½ (u + v) × t, the average velocity over the time. From 0 to 20 m/s in 5 s the average is 10 m/s, so 10 × 5 = 50 m. It holds for slowing down too: the same 50 m is covered braking back from 20 to 0.