Circular Motion Calculator
Work out circular motion instantly with clear inputs, formula shown and shareable results.
About Circular Motion Calculator
Motion in a circle at constant speed still involves acceleration, because the direction keeps changing. That acceleration points inward with magnitude v^2/r, and the force needed is m v^2/r. A 2 kg mass at 8 m/s on a 4 m radius needs 32 N inward, supplied by whatever is doing the holding - string tension, friction or gravity.
Formulas
Centripetal acceleration
a = v^2 / r
Centripetal force
F = m v^2 / r
Worked example
With the default values below, Circular Motion Calculator returns Centripetal Force of 32.000. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Mass of the bodyminimum 0 kg
- 2 kg
- Tangential speedminimum 0 m/s
- 8 m/s
- Radius of the circular pathminimum 0 m
- 4 m
Results
- Centripetal Force
- 32.000 N
- Centripetal Acceleration
- 16.000 m/s2
- Angular Velocity
- 2.0000 rad/s
- Time For One Revolution
- 3.1416 s
Step by step
- 1Values used
- 2Centripetal acceleration
- 3Centripetal force
- 4Centripetal Force= 32.000 N
- 5Centripetal Acceleration= 16.000 m/s2
- 6Angular Velocity= 2.0000 rad/s
- 7Time For One Revolution= 3.1416 s
Assumptions and limits
- The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
Is centrifugal force real?
Not in an inertial frame. What you feel is your own inertia resisting the inward push; the only real force acts towards the centre.
What happens if the force disappears?
The body leaves along the tangent, not radially outward - Newton's first law taking over the instant the constraint is removed.