About the Centripetal Force Calculator
This centripetal force calculator works out the inward force needed to keep a mass moving in a circle, using F = m × v² ÷ r. You can enter the speed directly (in m/s, km/h or mph) or give the rotation rate in revolutions per minute, and it returns the force, the centripetal acceleration, the equivalent g-force, the angular velocity and the time for one lap.
It suits physics students solving circular-motion problems, drivers and engineers wondering how much grip a car needs on a curve, and anyone working with centrifuges, spinning rides, washing-machine drums or a ball on a string.
The calculation assumes uniform circular motion — constant speed on a circle of fixed radius. The force is not a new kind of force; it is supplied by tension, friction, gravity or a normal force pointing toward the centre.
With the default inputs, the centripetal force is 9,600 N. Change any value above to recalculate instantly.
How to use the centripetal force calculator
- 1Choose whether you know the linear speed or the RPM.
- 2Enter the mass in kilograms.
- 3Enter the radius of the circle in meters.
- 4Enter the speed (with its unit) or the rotation rate.
- 5Read the force, acceleration, g-force and time per revolution.
Formula and method
An object moving in a circle constantly changes direction, so it is accelerating toward the centre even at constant speed. That centripetal acceleration equals the speed squared divided by the radius, and Newton’s second law gives the required force as mass times that acceleration.
When you enter RPM, the calculator converts it to linear speed with v = 2πr × RPM ÷ 60. Angular velocity ω = v ÷ r in radians per second, the period is the circumference divided by speed, and g-force divides the acceleration by standard gravity (9.80665 m/s²).
- F
- Centripetal force (N)
- m
- Mass (kg)
- v
- Linear (tangential) speed (m/s)
- r
- Radius of the circular path (m)
- ω
- Angular velocity (rad/s)
Worked examples
1,200 kg car on a 50 m curve at 20 m/s
a = 20² ÷ 50 = 8 m/s² (about 0.82 g), so the tyres must provide F = 1200 × 8 = 9,600 N of sideways grip. A full lap of that circle would take 2π × 50 ÷ 20 ≈ 15.7 s.
0.5 kg ball on a 0.3 m string at 120 RPM
120 RPM is 12.57 rad/s, giving a speed of 12.57 × 0.3 = 3.77 m/s. Acceleration is 3.77² ÷ 0.3 = 47.4 m/s², so the string tension must be 0.5 × 47.4 ≈ 23.7 N.
1,500 kg car at 72 km/h on a 100 m radius bend
72 km/h is 20 m/s, so F = 1500 × 20² ÷ 100 = 6,000 N. That needs a friction coefficient of about 0.41, easily met on dry asphalt.
Frequently asked questions
What is the formula for centripetal force?+
Centripetal force F = mv²/r, where m is mass in kg, v is speed in m/s and r is the radius in meters. Equivalently F = mω²r using angular velocity in rad/s.
What provides centripetal force?+
Whatever pulls the object toward the centre: tension in a string, friction between tyres and road, gravity for orbiting planets and satellites, or the normal force from a banked track or spinning drum wall.
What is the difference between centripetal and centrifugal force?+
Centripetal force is the real inward force acting on the object. Centrifugal force is the apparent outward push felt in the rotating frame of reference; it is a fictitious force caused by inertia.
How do I convert RPM to g-force?+
Convert RPM to angular velocity ω = 2π × RPM ÷ 60, compute a = ω²r, then divide by 9.81. For a centrifuge this is the relative centrifugal force (RCF): about 1.118 × 10⁻⁵ × r(cm) × RPM².
Why does speed matter more than radius?+
Force grows with the square of speed but only inversely with radius. Doubling speed quadruples the force needed, which is why speeding into a bend is far more dangerous than taking a slightly tighter line.