Centripetal Force Calculator
Centripetal Force12.500 N
Centripetal Acceleration6.250 m/s²
The Centripetal Force Calculator finds the inward force and acceleration required to keep an object moving along a circular path at constant speed. Enter the object mass in kilograms, its tangential speed in metres per second, and the radius of the circle in metres, and the tool returns the centripetal force in newtons and the acceleration in metres per second squared. It suits problems on cars on curves, spinning masses, and orbital motion.
Formula
F = m·v² / r ; a = v² / r
- F
- Centripetal force (N)
- a
- Centripetal acceleration (m/s²)
- m
- Mass of the object (kg)
- v
- Tangential speed (m/s)
- r
- Radius of the circular path (m)
How it works
- Enter the mass in kilograms, the tangential speed in metres per second, and the radius of the circular path in metres.
- The calculator computes the centripetal acceleration as a = v²/r, then multiplies by mass to get the force F = m·v²/r, which always points toward the centre of the circle.
- Because speed is squared, doubling the velocity quadruples the required force, while a larger radius reduces it.
Worked example
A 2 kg ball is whirled at 5 m/s on a string of radius 4 m.
- Acceleration = v² ÷ r = 25 ÷ 4 = 6.25 m/s².
- Force = m × a = 2 × 6.25 = 12.5 N.
- The force points toward the centre, supplied here by the string tension.
A centripetal force of 12.5 N and acceleration of 6.25 m/s².
Frequently asked questions
- What is the difference between centripetal and centrifugal force?
- Centripetal force is the real inward force that curves the path toward the centre. Centrifugal force is an apparent outward force felt only in the rotating reference frame; it is not a true force acting on the object.
- What provides the centripetal force in real situations?
- It depends on the setup. Friction holds a car on a curve, tension holds a whirled ball, and gravity holds a satellite in orbit. The calculator gives the magnitude regardless of the source.
- Why does speed have such a large effect on the force?
- Because the force depends on the square of the speed. Going twice as fast around the same curve needs four times the force, which is why high-speed cornering demands much more grip.
- Does centripetal force do any work on the object?
- No. For uniform circular motion the force is always perpendicular to the velocity, so it changes direction but not speed and performs zero net work over a full revolution.