Centripetal Force Calculator
Centripetal force is the inward pull that keeps a mass moving on a circular path, equal to mass times v squared over the radius. Enter the mass, the radius of the path and either a linear speed or an angular velocity, and the calculator returns both the centripetal force in newtons and the centripetal acceleration in m/s^2. It suits classroom mechanics problems, orbit and curve questions, and quick engineering sanity checks.
How to use the centripetal force calculator
- Open the 'Speed input' menu and choose 'Linear speed (v)' or 'Angular velocity (omega)'.
- Type the mass in the 'Mass (m)' field, measured in kilograms.
- Type the path radius in the 'Radius (r)' field, measured in metres.
- Enter the speed value: metres per second for linear speed, or radians per second for angular velocity.
- Read the centripetal force in newtons and the centripetal acceleration in m/s^2 in the result cards.
- Click Copy to grab both figures as text.
Examples
From linear speed
m = 2 kg, v = 5 m/s, r = 0.5 m
a = 50 m/s^2, F = 100 N
From angular velocity (same motion)
m = 2 kg, omega = 10 rad/s, r = 0.5 m
a = 50 m/s^2, F = 100 N
Car rounding a curve
m = 1000 kg, v = 20 m/s, r = 50 m
a = 8 m/s^2, F = 8000 N
Frequently asked questions
What is the centripetal force formula?
Centripetal force is F = m x v^2 / r, where m is mass, v is linear speed and r is the radius. It always points toward the centre of the circle, along the radius.
How does angular velocity change the formula?
With angular velocity omega the acceleration is omega^2 x r, so the force is F = m x omega^2 x r. For the same physical motion, v equals omega times r, so both forms give the identical answer. That is why 5 m/s at r = 0.5 m and 10 rad/s at r = 0.5 m both return 100 N.
What is centripetal acceleration?
Centripetal acceleration is the inward acceleration that keeps an object turning instead of flying off in a straight line. It equals v^2 / r or omega^2 x r and is reported in m/s^2. The force is simply this acceleration times the mass.
Is centripetal force a separate kind of force?
No. It is the name for the net inward force, supplied by tension, gravity, friction or a normal force depending on the setup, not a new force of its own. The calculator tells you how large that net inward force must be, whatever provides it.
What units does the calculator use?
Mass in kilograms, radius in metres, linear speed in metres per second and angular velocity in radians per second. Force comes out in newtons and acceleration in m/s^2. Convert other units first, for example rpm to rad/s by multiplying by 2 pi divided by 60.
Do the inputs have to be positive?
Mass and radius must both be greater than zero, or the tool shows an error. Speed can be any finite number, though a negative or zero speed simply reflects no net turning, so the force works out to zero or the same magnitude as the positive value.
How precise are the results?
The engine computes with full floating point and rounds the displayed force and acceleration to nine decimal places, so rounding never changes a normal answer. Very large or very small inputs stay exact to that precision.
Can I use it for satellite orbits or spinning objects?
Yes, for a point mass on a circular path. Give the orbital radius and the orbital speed, or the spin rate as angular velocity, and read the required inward force. For a rigid spinning body the mass is not at a single radius, so treat each part separately.
Is my data private?
Yes. The calculation runs entirely in your browser with no numbers sent to a server, so your figures never leave your device.
Learn more
- Centripetal vs centrifugal force explained
Why centripetal force points inward, what the centrifugal effect really is, and how to pick the right speed form when solving circular motion problems.
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