Centripetal Force Calculator
Any object moving in a circle is constantly changing direction, and that change requires a force pointed toward the centre of the circle, the centripetal force. Enter the object's mass in kilograms, its speed in metres per second and the radius of its circular path in metres, and this calculator returns the centripetal force in newtons (N) and the centripetal acceleration in m/s². Use it for a car rounding a bend, a satellite in orbit, a ball on a string, or a rider on a fairground ride. The result updates instantly as you type.
How to use the calculator
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1
Enter mass and velocity
Type the object's mass in kilograms (kg) and its speed in metres per second (m/s).
-
2
Enter the radius
Type the radius of the circular path in metres (m). It must be greater than zero.
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3
Read the result
The centripetal force (N) and acceleration (m/s²) appear instantly.
The formula
For an object moving at constant speed in a circle, the centripetal force points toward the centre and equals:
F = m · v² / r
The centripetal acceleration is the same expression without the mass:
a = v² / r
Where:
F= centripetal force, in newtons (N).m= mass of the object, in kilograms (kg).v= linear (tangential) speed, in metres per second (m/s).r= radius of the circular path, in metres (m).a= centripetal acceleration, in m/s².
Notice that the speed is squared: doubling the speed quadruples the required force. Halving the radius doubles it.
Worked example
A 2 kg ball is whirled on a string in a circle of radius 3 m at a speed of 5 m/s. First find the acceleration:
a = v² / r = (5 m/s)² / 3 m = 25 / 3 ≈ 8.33 m/s²
Then the force the string must supply:
F = m · a = 2 kg × 8.33 m/s² ≈ 16.67 N
If the speed rises to 10 m/s, the force jumps to 2 × (100 / 3) ≈ 66.67 N, four times larger, because v is squared.
Quick reference
| Mass (kg) | Velocity (m/s) | Radius (m) | Acceleration (m/s²) | Force (N) |
|---|---|---|---|---|
| 2 | 5 | 3 | 8.33 | 16.67 |
| 2 | 10 | 3 | 33.33 | 66.67 |
| 1 | 4 | 2 | 8.00 | 8.00 |
| 1000 | 20 | 50 | 8.00 | 8000.00 |
| 0.5 | 3 | 1 | 9.00 | 4.50 |
Common pitfalls
- Speed is squared. A small increase in v has a big effect on the force. Always square the velocity before dividing by the radius.
- Radius cannot be zero. Division by zero is undefined; a real circular path always has r > 0. The calculator returns 0 when the radius is left at zero.
- Centripetal vs. centrifugal. Centripetal force is the real, inward force keeping the object on its path. The outward “centrifugal force” you feel is an apparent effect of being in a rotating frame, not a separate real force.
- Keep SI units. Mass in kg, speed in m/s and radius in m give force directly in newtons. Convert km/h, grams or centimetres first.
Frequently Asked Questions
Centripetal force is the net inward force that keeps an object moving along a circular path, always directed toward the centre of the circle. Without it the object would fly off in a straight line. It is given by F = m·v²/r.
Centripetal acceleration (a = v²/r) describes how quickly the velocity direction is changing and is measured in m/s². Centripetal force (F = m·a) is the force needed to produce that acceleration on a given mass, measured in newtons.
Because velocity is squared in the formula, doubling the speed multiplies the centripetal force by four (assuming the same mass and radius). This is why high-speed turns require much stronger forces.
The numbers you enter are sent to our server only to compute the result, which updates as you type. They are not stored, logged, or shared.
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