How to use this calculator
- Enter or choose solve for.
- Enter or choose mass.
- Enter or choose mass unit.
- Enter or choose radius unit.
- Enter or choose speed unit.
- The result updates as you type. Use Copy result or Share to keep it.
Method
F = m v² ÷ r = m ω² r; a = v² ÷ r; v = ω r; T = 2π ÷ ω
- F
- centripetal force in N
- m
- mass in kg
- v
- linear speed in m/s
- r
- radius in m
- ω
- angular velocity in rad/s (1 rpm = 2π/60 rad/s)
- T
- period of one revolution in s
Worked example
- 72 km/h ÷ 3.6 = 20 m/s.
- a = v² ÷ r = 400 ÷ 50 = 8 m/s² (about 0.82 g).
- F = m a = 1,000 × 8 = 8,000 N.
A 1,000 kg car taking a 50 m radius curve at 72 km/h needs 8 kN of sideways grip from its tyres.
What the result means
The force must come from something real: tyre friction, a string’s tension, a banked road or gravity. If that source cannot supply F, the object moves to a wider path. Solving for speed gives the fastest the curve can be taken with a known maximum force.
Assumptions and limits
- Uniform circular motion at constant speed.
- Does not model banking angles, tyre friction coefficients or changing speed.
Questions
What about centrifugal force?
Centrifugal force is the outward force you seem to feel in the rotating frame. It has the same size as the centripetal force calculated here.
Why does halving the radius double the force?
At the same linear speed, F = m v² ÷ r, so the force is inversely proportional to the radius. At the same rpm the opposite happens: F = m ω² r grows with radius.