What is the formula for acceleration?

Acceleration equals the change in velocity divided by time: a = (v - u) / t, where u is initial velocity, v is final velocity, and t is the time interval. Rearranging gives v = u + at to find final velocity, u = v - at to find initial velocity, and t = (v - u) / a to find time.

What are the units of acceleration?

The SI unit of acceleration is metres per second squared, written m/s2. This means for every second that passes, velocity changes by that many metres per second. Gravitational acceleration on Earth is approximately 9.81 m/s2.

Can acceleration be negative?

Yes. Negative acceleration, sometimes called deceleration, means the object is slowing down. If a car goes from 30 m/s to 0 m/s in 10 seconds, the acceleration is (0 - 30) / 10 = -3 m/s2. The negative sign indicates the velocity decreased over the time interval.

Acceleration Calculator

This calculator solves the linear acceleration equation, a = (v - u) / t, for any one of the four variables when you know the other three. Acceleration describes how quickly an object's velocity is changing and is one of the core quantities in Newtonian mechanics. You select the variable you want to find, enter the remaining values, and the calculator applies the appropriate rearrangement. When solving for acceleration, you enter the initial velocity u, the final velocity v, and the time t, and the result is in metres per second squared. A positive value means the object is speeding up; a negative value means it is slowing down. When solving for initial velocity, you provide the final velocity, acceleration, and time. When solving for final velocity, you provide the initial velocity, acceleration, and time. When solving for time, you provide both velocities and the acceleration. In each mode the calculator also shows the change in velocity and the distance covered during the interval, using the kinematic relationship d = ut + half a t squared. This tool is useful for physics students, engineers analysing vehicle performance, and coaches examining sprint mechanics. The formula assumes constant (uniform) acceleration throughout the time interval; if acceleration varies, the result is an average only.

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Solve for

Initial velocity (u)

m/s

Final velocity (v)

m/s

Time (t)

Acceleration (a)

m/s²

3.00 m/s²

acceleration

Change in velocity30.00 m/s

Distance covered150.00 m

How it works

The four rearrangements of the acceleration equation are: a = (v - u) / t, v = u + at, u = v - at, and t = (v - u) / a. Select what you want to find, enter the remaining values, and the calculator applies the correct formula. Distance during the interval uses the kinematic equation d = ut + ½at², which assumes constant acceleration. Change in velocity is simply v minus u.

Worked example

A car starts from rest (u = 0 m/s) and reaches 30 m/s in 10 seconds. Acceleration = (30 - 0) / 10 = 3.00 m/s². The change in velocity is 30 m/s and the distance covered during those 10 seconds is 0 × 10 + 0.5 × 3 × 100 = 150.00 m. These match the defaults pre-filled above.

Related calculators

Velocity Calculator: solve v = d / t for constant-speed problems.
SUVAT Calculator: solve for any two unknowns given three of the five kinematic variables.
Force Calculator: find the force required to produce a given acceleration using F = ma.
Free Fall Calculator: acceleration under gravity from a known height.

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