Centripetal Force Calculator
Calculate the centripetal force required to keep an object moving in a circular path using F = mv^2 / r. Enter mass, speed, and radius to find the inward force in newtons needed to maintain circular motion.
How to use this tool
- Enter mass (m), tangential speed (v) and radius (r) in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your centripetal force and the full breakdown beneath it.
Formula
F = m * v^2 / r
How it works
Centripetal force F is the net inward force needed to maintain circular motion. It equals mass times centripetal acceleration: F = m × v²/r.
Worked examples
Car cornering
Ball on string
Common mistakes to avoid
- Entering angular speed in rad/s for v instead of linear (tangential) speed in m/s — convert first with v = omega * r.
- Using diameter instead of radius for r, which halves the denominator and doubles the computed force.
- Treating centripetal force as a separate force type rather than recognising it as the net inward force provided by tension, gravity, friction, or another real force.
Key terms
Frequently asked questions
- What physical force provides centripetal force in real situations?
- Centripetal force is not a new type of force — it is the name for the net inward force. For a car rounding a bend, friction provides it. For a satellite, gravity provides it. For a ball on a string, string tension provides it.
- What happens if the centripetal force is too small?
- If the available inward force (e.g., friction) is less than the required centripetal force mv^2/r, the object cannot maintain the circular path and moves outward — a car skids, or a satellite drifts to a higher orbit.
- How does doubling the speed affect the required centripetal force?
- Because F = mv^2/r, doubling speed v quadruples the required centripetal force. This is why high-speed cornering or tight turns demand much more traction or structural strength.