Centripetal force calculator
Enter the mass, the radius of the circle and how fast the object goes round, as a speed, a period or revolutions per minute. The calculator gives the centripetal force in newtons, the acceleration in m/s² and in g, and the angular velocity.
Runs in your browser: nothing you enter is sent anywhere.
How to use it
- Choose whether you know the speed, the time for one turn or the rpm.
- Enter the mass and the radius and pick their units.
- Enter the speed, period or rpm.
- Read the force, the acceleration (also in g) and the angular velocity, period and rpm.
- Acceleration: a = v² ÷ r = ω² × r.
- Force: F = m × a.
- From a period: v = 2πr ÷ T. From rpm: ω = 2π × rpm ÷ 60, v = ω × r.
- Period and rpm: T = 2π ÷ ω, rpm = ω × 60 ÷ 2π.
Worked example
A 1200 kg car takes a curve of radius 50 m at 20 m/s: a = 20² ÷ 50 = 8 m/s² (8 ÷ 9.80665 = 0.816 g) and F = 1200 × 8 = 9,600 N. The tyres must supply this much sideways grip. The angular velocity is 20 ÷ 50 = 0.4 rad/s.
A 1 kg mass spun on a 10 cm arm at 600 rpm: ω = 2π × 600 ÷ 60 = 62.8319 rad/s, a = 62.8319² × 0.1 = 394.7842 m/s² (40.257 g) and F = 394.7842 N.
Tips
- Speed counts twice. Doubling the speed makes the force four times larger; halving the radius only doubles it.
- Use metres. A radius in centimetres must be converted, or the result is 100 times off. Pick the unit instead.
- Real turns may need more grip if the road is banked the wrong way or the surface is wet.
Frequently asked questions
What is the centripetal force formula?
F = m × v² ÷ r, where m is the mass, v the speed and r the radius. The same force can be written F = m × ω² × r with the angular velocity ω in radians per second.
How do I use the period or rpm instead of speed?
One turn covers the circumference 2πr, so v = 2πr ÷ T for a period T. For revolutions per minute, ω = 2π × rpm ÷ 60 and v = ω × r. The calculator does this for you.
What does the result in g mean?
It is the centripetal acceleration divided by standard gravity, 9.80665 m/s². A value of 0.82 g in a turn means the sideways push is 82% of your weight.
Is centripetal force a separate force?
No. It is the name for whatever net force points to the centre, such as friction on car tyres, tension in a string or gravity for a satellite. The calculator tells you how large that force has to be.