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Centripetal force calculator

A-level Motion

The resultant force towards the centre that keeps an object moving at constant speed in a circle.

F = m 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

FCentripetal force to find 26.7 N

mMass

vSpeed

rRadius of the circle

Significant figures

Working

Write the equation
F = m v² / r
Substitute the values
F = 0.5 × 8² ÷ 1.2
Calculate
F = 26.6667 N
Give the answer to 3 significant figures
F = 26.7 N

Worked example

Find F, the centripetal force. Given: mass m = 0.500 kg; speed v = 8.00 m/s; radius of the circle r = 1.20 m.

Write the equation
F = m v² / r
Substitute the values
F = 0.5 × 8² ÷ 1.2
Calculate
F = 26.6667 N
Give the answer to 3 significant figures
F = 26.7 N

Symbols and units

Symbol	Quantity	SI unit
F	Centripetal force	N
m	Mass	kg
v	Speed	m/s
r	Radius of the circle	m

Centripetal force: rearranged

To find centripetal force: F = m v² / r
To find mass: m = F r / v²
To find speed: v = √(F r / m)
To find radius of the circle: r = m v² / F

Exam tip

Centripetal force is not an extra force. It is the name for the resultant force towards the centre, such as tension or friction.

Common questions

What is the formula for centripetal force?

The equation is F = m v² / r, where F is the centripetal force (N); m is the mass (kg); v is the speed (m/s); r is the radius of the circle (m).

What units should I use for centripetal force?

In SI units: centripetal force in N, mass in kg, speed in m/s, radius of the circle in m. The calculator also accepts common alternatives such as kilometres, grams or minutes, and converts them for you.

How do I rearrange F = m v² / r?

Rearranging gives these forms: to find centripetal force: F = m v² / r. to find mass: m = F r / v². to find speed: v = √(F r / m). to find radius of the circle: r = m v² / F.

Practise centripetal force questions

Include unit conversions (km, g, minutes…)

Press the button for a question with random numbers. Work it out on paper first, then type your answer.

Read the full explanation on the Centripetal force formula page. 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.