Compute centripetal force and acceleration for circular motion from mass, radius and speed, period or angular velocity.
Enter mass, radius and any one of speed, angular velocity or period.
About this tool
Centripetal Force & Acceleration Calculator is a free, in-browser tool for uniform circular motion. Enter the mass and radius plus any one of speed, angular velocity or period, and it returns the centripetal force and acceleration together with the other motion quantities. Nothing leaves your browser.
It uses a = v²/r = ω²r = 4π²r/T² for the centripetal acceleration and F = m·a = m·v²/r for the force. The angular velocity relates to the others by ω = 2π/T = v/r, and the speed by v = ωr, so from any single rotational input the tool derives the complete set. Priority is given to angular velocity, then period, then speed.
Use it for objects on a string, cars rounding a bend, satellites or centrifuges. Enter mass in kilograms and radius in metres; speed is in m/s, angular velocity in rad/s and period in seconds, giving force in newtons and acceleration in m/s².
Frequently asked questions
What inputs do I need?
Always the mass and radius, plus exactly one of speed, angular velocity or period. From that single rotational quantity the tool computes the others, then the acceleration a = ω²r and force F = ma.
What are the formulas?
Centripetal acceleration is a = v²/r = ω²r = 4π²r/T², and centripetal force is F = ma = mv²/r. Angular velocity is ω = 2π/T = v/r and tangential speed is v = ωr.
Which way does the centripetal force point?
Always toward the centre of the circle. It is the net inward force required to keep the object on its circular path; the value here is its magnitude. Its source (tension, friction, gravity) depends on the situation.
What if I fill in more than one rotational quantity?
The tool uses one, in priority order: angular velocity, then period, then speed. Make sure the values you enter are consistent for that radius. All math runs locally in your browser.