THE NUMORIX GUIDE
How to use the Centripetal Force Calculator
Last reviewed September 14, 2026
What this calculator does
The engine first computes inward centripetal acceleration a_c = v^2 / r and then applies Newton's second law: F_c = m a_c = m v^2 / r.
Formula and method
The engine first computes inward centripetal acceleration a_c = v^2 / r and then applies Newton's second law: F_c = m a_c = m v^2 / r.
Variables and inputs
Mass m is in kilograms, velocity v in m/s, and circular-path radius r in meters. The default values are 2 kg, 10 m/s, and 5 m; the UI requires positive mass and radius, while velocity may be signed because it is squared.
Worked example
For m = 2 kg, v = 10 m/s, and r = 5 m: a_c = 10^2 / 5 = 20 m/s^2 and F_c = 2(20) = 40 N toward the center.
How to interpret the result
Centripetal force is the net inward force required for curved motion; it is not a separate physical force. Friction, tension, gravity, a normal force, or their combination can supply it.
Common mistakes to avoid
Square the speed before dividing by radius, use the radius from the center of curvature rather than a diameter, and do not report the inward force as tangential motion. A negative velocity has the same centripetal-force magnitude as the corresponding positive speed.
Assumptions and limitations
The formula describes the instantaneous radial requirement for circular motion and omits tangential acceleration, changing radius, friction details, and nonuniform paths. The engine returns zero when radius is nonpositive, although the UI blocks such input.
Practical use and checks
The Centripetal Force Calculator estimates the inward net force required for circular motion using F = m*v^2/r. Enter mass 2 kg, speed 10 m/s, and radius 5 m as a check; centripetal acceleration should be 20 m/s^2 and force should be 40 N. Doubling speed to 20 m/s with the other inputs fixed should raise force to 160 N, demonstrating the square dependence. The force points toward the center and is not a separate interaction. Use the result to check whether friction, tension, gravity, or a normal force could supply the required inward net force. Radius means the distance from the center of curvature, not the diameter or the distance traveled around the circle. A signed velocity has the same squared magnitude as its opposite direction, so direction must be handled separately if the motion is part of a vector analysis. The model describes an instantaneous circular requirement and omits tangential acceleration, changing radius, slip, surface banking, drag, and nonuniform paths. Zero or negative radius is an invalid edge, and a very small radius can make an otherwise modest speed require an impractical force. Compare the computed demand with contact, tire, cable, or structural limits rather than interpreting it as a guarantee that circular motion will occur.