Centripetal Force Calculator
Choose what to solve for and enter the rest. Speed can be linear (m/s, km/h, mph) or angular (rad/s, rpm). The calculator also gives the centripetal acceleration and the period.
Updated
Report a problem
Formula
F = m × v² ÷ r or, with angular velocity, F = m × ω² × r (since v = ω × r)
Centripetal acceleration a = v² ÷ r; period T = 2π ÷ ω. Conversions: 1 rpm = 2π ÷ 60 rad/s, 1 mph = 0.44704 m/s, 1 km/h = 1 ÷ 3.6 m/s.
Worked example
A 1000 kg car at 20 m/s on a bend of 50 m radius:
- Force:
1000 × 20² ÷ 50 = 8000 N - Acceleration:
20² ÷ 50 = 8 m/s² - Angular velocity:
20 ÷ 50 = 0.4 rad/s, so one lap takes2π ÷ 0.4 = 15.71 s
From angular velocity: 2 kg, 3 rad/s, 0.5 m gives 2 × 3² × 0.5 = 9 N. For 1 kg at 60 rpm on a 1 m radius, ω = 2π rad/s and F = 4π² = 39.478 N.
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 of the circle. A 1000 kg car at 20 m/s on a 50 m radius bend needs 1000 × 400 ÷ 50 = 8000 N toward the centre.
How do I calculate centripetal force from angular velocity?
Use F = m × ω² × r, because v = ω × r. A 2 kg mass on a 0.5 m string turning at 3 rad/s needs 2 × 9 × 0.5 = 9 N. To convert rpm to rad/s multiply by 2π ÷ 60, so 60 rpm is 6.283 rad/s.
What happens if the speed doubles?
The force needed grows with the square of the speed, so doubling it multiplies the force by four. The 1000 kg car at 40 m/s on the same bend needs 32,000 N.
Is centripetal force the same as centrifugal force?
No. Centripetal force is the real inward force, such as tension, friction or gravity, that keeps an object on a circular path. Centrifugal force is the apparent outward push felt in the rotating frame of reference. Their sizes are equal in that frame.