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Centripetal acceleration calculator

A-level Motion

The acceleration towards the centre of a circle for an object moving at constant speed.

a = v² / r

This free calculator is for A-level physics. Choose the quantity you want to find, enter the other values with their units, and it shows the working in the layout used in exams, with the answer to the number of significant figures you choose. The values shown are an example. Change them to your own.

Quantity to find

aCentripetal acceleration to find 4.50 m/s² m/s²

vSpeed

rRadius

Significant figures

Working

Write the equation
a = v² / r
Substitute the values
a = 15² ÷ 50
Calculate
a = 4.5 m/s²
Give the answer to 3 significant figures
a = 4.50 m/s²

Worked example

Find a, the centripetal acceleration. Given: speed v = 15.0 m/s; radius r = 50.0 m.

Write the equation
a = v² / r
Substitute the values
a = 15² ÷ 50
Calculate
a = 4.5 m/s²
Give the answer to 3 significant figures
a = 4.50 m/s²

Symbols and units

Symbol	Quantity	SI unit
a	Centripetal acceleration	m/s²
v	Speed	m/s
r	Radius	m

Centripetal acceleration: rearranged

To find centripetal acceleration: a = v² / r
To find speed: v = √(a r)
To find radius: r = v² / a

Exam tip

The speed is constant but the velocity is changing, so there is an acceleration.

Common questions

What is the formula for centripetal acceleration?

The equation is a = v² / r, where a is the centripetal acceleration (m/s²); v is the speed (m/s); r is the radius (m).

What units should I use for centripetal acceleration?

In SI units: centripetal acceleration in m/s², speed in m/s, radius in m. The calculator also accepts common alternatives such as kilometres, grams or minutes, and converts them for you.

How do I rearrange a = v² / r?

Rearranging gives these forms: to find centripetal acceleration: a = v² / r. to find speed: v = √(a r). to find radius: r = v² / a.

Practise centripetal acceleration questions

Include unit conversions (km, g, minutes…)

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More motion equations: Speed, distance and time, Acceleration, Final velocity, Velocity squared, Displacement under constant acceleration, Displacement from average velocity, Momentum, Force and change in momentum. See the full list on the a-level physics equation calculator page.