Centripetal Force Calculator

The formula and what it means physically

Centripetal force is the net force required to keep an object moving along a circular path instead of flying off in a straight line — it always points toward the center of the circle. The formula is F = mv²/r, where m is mass in kilograms, v is velocity in meters per second, and r is the radius of the circular path in meters. Doubling the velocity quadruples the required force (v² term), while doubling the radius halves it.

Worked example (the calculator's default values)

With mass = 10 kg, velocity = 15 m/s, radius = 5 m:

F = m·v²/r = 10 × 15² / 5 = 10 × 225 / 5 = 450 N

The tool also derives three related quantities from the same inputs:

• Centripetal acceleration: a = v²/r = 225/5 = 45 m/s²
• Angular velocity: ω = v/r = 15/5 = 3 rad/s
• Period: T = 2πr/v = 2π(5)/15 ≈ 2.09 seconds — the time for one full revolution

Input constraints

Mass and radius must both be positive numbers (zero or negative values are rejected, since a radius of 0 makes the formula divide by zero). Velocity can technically be entered as negative — the calculator takes the absolute value of the final force, since force magnitude doesn't have a sign in this context, only the direction (always inward) matters.

Typical use

This maps directly to problems like a car rounding a banked curve, a ball on a string being swung in a circle, or a satellite in circular orbit — anywhere a mass moves at constant speed along a fixed-radius circular path.