Centripetal Force Calculator

Calculate the force required to keep an object moving in a circular path.

Centripetal Force (F)
8,000N
r=50m1,000kgvF
How is this calculated?
Formula: F = (m × v²) / r
F = (1,000 kg × (20 m/s)²) / 50 m
F = (1,000 × 400) / 50
F = 8,000 N

About the Centripetal Force Calculator

Any object moving in a circle is constantly changing direction, which means it is accelerating toward the center. The force causing this acceleration is called centripetal force.

Mathematical Formula & Logic

Centripetal Force (Velocity) F_c = (m * v^2) / r - F_c = Centripetal Force (N) - m = Mass (kg) - v = Tangential Velocity (m/s) - r = Radius (m) Centripetal Force (Angular Velocity) F_c = m * omega^2 * r - F_c = Centripetal Force (N) - m = Mass (kg) - omega = Angular Velocity (rad/s) - r = Radius (m)

Step-by-Step Example

A 1,000 kg car taking a 50-meter radius curve at 20 m/s requires (1000 × 400) / 50 = 8,000 Newtons of friction force to not slip. Swinging a 0.5 kg ball on a 1-meter string at 10 m/s requires 50 Newtons of tension force.

Reference Data & Values

massvelocityradiuscentripetal force
1052125
100020508000
0.510150
500100
10-52125

Frequently Asked Questions

Centripetal force is the net inward force that keeps an object moving in a circular path. It is always directed toward the center of the circle.
The formula is F = mv²/r, where m is mass, v is tangential velocity, and r is the radius of the circular path.
Centripetal force is the actual inward force keeping the object in a circle. Centrifugal force is the 'apparent' outward force you feel when you are inside the turning object (like being pushed against a car door).
Centripetal force isn't a 'new' force. It is provided by other forces depending on the situation: friction for a turning car, tension for a swinging string, or gravity for an orbiting satellite.
In the formula F = mv²/r, velocity is squared. If you go from 10 m/s to 20 m/s, the velocity part goes from 100 to 400, multiplying the total required force by four.
Due to Newton's First Law (inertia), the object will immediately stop curving and fly off in a straight line tangent to the circle at the exact moment the force is removed.
Yes. Because radius is in the denominator of the formula (F = mv²/r), dividing by a smaller radius results in a larger required force for the same speed.
Yes, force is a vector. The magnitude is mv²/r, and the direction is always continuously changing to point toward the center of the circular path.