Acceleration Calculator — change in velocity over time

How it works

Acceleration measures how quickly velocity changes. Average acceleration is the change in velocity divided by the time over which it happens:

a = (v − u) ÷ t

where u is the initial velocity, v is the final velocity and t is the elapsed time. In SI units, velocities in metres per second and time in seconds give an acceleration in metres per second squared (m/s²) — a change of one m/s of speed every second.

Acceleration can be negative. If the final velocity is smaller than the initial one — braking, for instance — the result comes out negative, meaning the object is slowing down (sometimes called deceleration). This calculator is unit-agnostic: use any consistent velocity and time units and read the acceleration in velocity-unit-per-time-unit.

Worked example

OpenStax's racehorse leaves the gate from rest (u = 0) and reaches 15 m/s in 1.8 s, so its average acceleration is (15 − 0) ÷ 1.8 = 8.33 m/s². A car that brakes from 27 m/s to a stop in 3 s has (0 − 27) ÷ 3 = −9 m/s² — negative because it is slowing. And a sprinter reaching 12 m/s in 4 s accelerates at 12 ÷ 4 = 3 m/s².

Frequently asked questions

What is the formula for average acceleration?

Average acceleration is the change in velocity divided by the time taken: a = (v − u) ÷ t, where u and v are the initial and final velocities. It tells you how many units of speed the object gains (or loses) each unit of time.

What is the difference between velocity and acceleration?

Velocity is how fast something moves (and in which direction); acceleration is how fast that velocity is *changing*. A car cruising at a steady 100 km/h has a high velocity but zero acceleration, because its velocity is not changing.

Can acceleration be negative?

Yes. A negative acceleration means the velocity is decreasing — braking or slowing down — or that it points opposite to the direction you chose as positive. Enter a final velocity lower than the initial one and the result is negative.

What units does acceleration use?

The SI unit is metres per second squared (m/s²): a change of one metre per second of velocity every second. This calculator uses whatever consistent velocity and time units you enter, so km/h per second or mph per second work too, as long as you stay consistent.

Is this average or instantaneous acceleration?

It is **average** acceleration over the time interval you enter. Instantaneous acceleration — the value at a single moment — requires the rate of change at that instant (calculus). For constant acceleration the two are equal.

How is acceleration related to force?

By Newton's second law, force = mass × acceleration, so acceleration = force ÷ mass. A given force produces more acceleration on a lighter object. This calculator finds acceleration from a change in velocity; the force calculator finds it from mass and force.