This centripetal force calculator computes the inward force that keeps an object moving in a circle — from mass, speed (or RPM) and radius — plus the centripetal acceleration.
The Force That Is Always Pointing In
An object in a circle is perpetually falling toward the center — its velocity direction changes constantly even at constant speed, and that change is an acceleration: a = v²/r, aimed inward. Whatever supplies it — tension in a string, friction under tires, gravity holding an orbit, a wall of death’s normal force — plays the role of centripetal force: F = m·v²/r. Remove it and the object obeys Newton and leaves along the tangent, not “outward” (the outward sensation you feel is your own inertia; there is no centrifugal force in an inertial frame, a hill physics teachers will die on). Sibling of our Force Calculator, in our Physics Calculators collection.
Worked Example (Verified)
- 2 kg at 10 m/s on a 5 m circle: a = 100 ÷ 5 = 20 m/s²; F = 2 × 20 = 40 N — about 2 g of inward pull, like a firm car corner
- Same circle at 60 RPM (1 revolution/second): v = 2π × 5 = 31.4 m/s, a ≈ 197 m/s² ≈ 20 g — beyond human tolerance, which is why ultracentrifuges, not pilots, work there. Note the v²: tripling the speed multiplied the force ninefold.
Where You Meet This Force
- Driving: tire friction must supply m·v²/r on every curve — halving the corner’s radius doubles the demand, ice deletes the supply. The math behind every “reduce speed on ramps” sign.
- Orbits: gravity is the centripetal supplier — set G·M·m/r² = m·v²/r and orbital velocity v = √(GM/r) drops out (try it with the Gravitational Force Calculator).
- Loop-the-loops: at the top, gravity helps; minimum speed to stay on the track is v = √(g·r) — for a 10 m loop, ≈ 9.9 m/s at the crown.
- Washing machines & centrifuges: the drum wall pushes clothes inward; the water, unpushed, leaves through the holes on its tangent — spin-drying is selective centripetal failure.
Related Tools
- Gravitational Force Calculator — the orbital supplier
- Force Calculator
- Physics Calculators — the full collection
Frequently Asked Questions
What is the centripetal force formula?
F = m·v²/r — mass times speed squared, divided by the radius. Equivalently F = m·ω²·r from the angular speed ω, which the RPM mode converts for you.
Is centripetal force a real force?
It is a role, not a separate interaction: the net inward force, supplied by tension, friction, gravity or a normal force depending on the setup. The calculator computes how much inward force the motion demands.
What is the difference between centripetal and centrifugal?
Centripetal (center-seeking) is the real net force in an inertial frame. Centrifugal (center-fleeing) is a fictitious force that appears when you adopt the rotating frame — useful in engineering, nonexistent in Newton’s accounting.
Why does speed matter so much?
It is squared: double the speed, quadruple the required force. This is why a corner taken at 60 is not “a bit spicier” than at 30 but four times as demanding of the tires.
What happens if the required force exceeds what is available?
The circle widens or breaks: the string snaps, the car skids outward into a larger-radius path, the satellite leaves orbit. Circular motion persists only while supply meets the m·v²/r demand.
Is this centripetal force calculator free?
Yes — free, instant, no sign-up.