Centripetal Force Calculator
Force from mass, velocity, and radius.
About this calculator
This calculator models the force needed to keep an object moving on a circular path — not a separate outward "centrifugal" force, but the real, center-pointing pull (gravity, tension, friction, or normal force) required to bend a straight-line path into a circle. It computes force directly from F = mv²/r, then derives centripetal acceleration a = v²/r, and expresses that acceleration as a multiple of Earth's gravity (g-force) by dividing by 9.80665 m/s² — useful for judging how a roller coaster curve or aircraft turn will feel to a rider. Angular velocity (ω = v/r), RPM, period, and frequency are all just alternate ways of describing the same rotation rate, derived from the geometric relationship between tangential speed and radius: a smaller radius at the same speed means a higher angular velocity and more revolutions per minute.
The calculator assumes uniform circular motion — constant speed along a fixed-radius circle — so it won't capture the changing forces in an elliptical orbit or a car accelerating through a curve. A frequent mixup: velocity here means tangential (linear) speed along the path, not angular velocity, and force scales with the square of that speed, so doubling speed quadruples the force needed to hold the same radius, which is why tight, fast turns demand so much more grip or structural strength than gentle ones.
Inputs
Results
Centripetal Force (N)
20
Centripetal Acceleration (m/s²)
20
How to Use This Calculator
- Enter mass (kg), tangential velocity (m/s), and radius (m) of the circular path.
- Read centripetal force (N) and centripetal acceleration (m/s2).
- Review G-force to assess the acceleration relative to Earth gravity.
- Check angular velocity (rad/s), RPM, period (s), and frequency (Hz) for the rotation.
How the result changes with Tangential Velocity (m/s)
| Tangential Velocity (m/s) | Centripetal Force (N) | Centripetal Acceleration (m/s²) |
|---|---|---|
| 5 | 5 | 5 |
| 7.5 | 11.25 | 11.25 |
| 15 | 45 | 45 |
| 25 | 125 | 125 |
What each input means
- Mass (kg)
- Mass of the rotating object in kilograms.
- Tangential Velocity (m/s)
- Speed along the circular path.
- Radius (m)
- Radius of the circular path.
What each result means
- Centripetal Force (N)
- F = mv²/r. Force directed toward the center.
- Centripetal Acceleration (m/s²)
- a = v²/r.
- G-Force
- Acceleration relative to Earth gravity (9.81 m/s²).
- Angular Velocity (rad/s)
- ω = v/r.
- RPM
- Revolutions per minute.
- Period (s)
- Time for one complete revolution.
- Frequency (Hz)
- Revolutions per second.
How this is calculated
Worked example, using the default values
- Identify Input ParametersMass (kg) = 1, Tangential Velocity (m/s) = 10, Radius (m) = 5 = 3 input(s) provided
- Calculate Centripetal ForceCentripetal Force = massKg * velocityMs * velocityMs / radiusM20 = 20
- Calculate Centripetal AccelerationCentripetal Acceleration = velocityMs * velocityMs / radiusM20 = 20
- Calculate G-ForceG-Force = accelerationMs2 / 9.806652.039 = 2.039
- Calculate Angular VelocityAngular Velocity = velocityMs / radiusM2 = 2
Engine last updated . Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.
Frequently Asked Questions
Is centripetal force a real, separate force I need to add to a free-body diagram?
No — this calculator isn't computing some extra force alongside gravity, tension, or friction; F = mv²/r is the net inward force those real forces must already add up to for an object to hold a circular path. If you're analyzing a specific situation, the centripetal force is whichever real force (or combination) is providing that net pull toward the center, not something separate to sum in.
Why does halving the radius at the same speed increase both the force and the RPM?
Force scales as v²/r, so at fixed velocity, cutting the radius in half doubles the force needed to hold that tighter circle. Angular velocity ω = v/r also doubles for the same reason, and since RPM is derived directly from ω, the rotation rate doubles too — a tighter circle at the same tangential speed means the object sweeps around it twice as often.
What does the g-force output actually mean here?
It's the centripetal acceleration (v²/r) expressed as a multiple of standard Earth gravity, 9.80665 m/s², rather than in raw m/s². A g-force of 2 means the object experiences twice the acceleration you'd feel from gravity alone — a useful gut-check for how a turn or curve would feel, since human tolerance to sustained g-force is a well-known reference point.
Why do I need to enter tangential velocity instead of RPM or angular velocity?
The calculator's core formula, F = mv²/r, is built around linear (tangential) speed along the circular path, not rotation rate — RPM, angular velocity, and period are all derived outputs computed afterward from that velocity and radius, not separate inputs. If you only know RPM, you'd need to convert it to tangential velocity (v = ωr) yourself before entering it.
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