Quick answer
Centripetal force is F = mv² ÷ r, with acceleration v² ÷ r. A 1,000 kg car at 20 m/s around a 50 m radius curve needs 8,000 N, an acceleration of 8 m/s².
Enter mass, speed and radius. The calculator returns the force and acceleration.
Related tools: Force Calculator: Force from mass and acceleration (Newton's second law). Normal Force Calculator: Normal force on an object resting on a flat or inclined surface. Net Force Calculator: Resultant of several forces at different angles.
How to use the Centripetal Force Calculator
- Enter mass (kg) (above 0).
- Enter speed (m/s).
- Enter radius (m) (above 0).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Mass | A number, in kg | > 0 |
| Speed | A number, in m/s | — |
| Radius | A number, in m | > 0 |
Formula and method
Formula
F = m v² ÷ r; a = v² ÷ r
IEEE-754 double precision; shown to the decimals indicated.
Directed toward the center of the circle.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Mass = 1000; Speed = 20; Radius = 50.
| Result | Value |
|---|---|
| Centripetal force | 8,000 N |
| Centripetal acceleration | 8 m/s² |
Example 2
Inputs: Mass = 0.5; Speed = 4; Radius = 0.8.
| Result | Value |
|---|---|
| Centripetal force | 10 N |
| Centripetal acceleration | 20 m/s² |
Example 3
Inputs: Mass = 70; Speed = 8; Radius = 25.
| Result | Value |
|---|---|
| Centripetal force | 179.2 N |
| Centripetal acceleration | 2.56 m/s² |
The first line is the headline result (centripetal force). Below it the centripetal Force Calculator lists centripetal acceleration, which describe the same case from other angles. IEEE-754 double precision; shown to the decimals indicated.
Speed is squared
Doubling the speed quadruples the force: at 40 m/s the same curve would need 32,000 N. That is why high speeds cause skids on tight bends.
Where the force comes from
For a car it comes from tyre friction: it must satisfy F ≤ μmg, so on a 50 m curve with μ = 0.8 the maximum speed is √(0.8 × 9.81 × 50) = 19.8 m/s. Banking the road reduces the friction needed.
How the result changes with mass
Holding every other input at the first worked example, this table changes only mass. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Mass | Centripetal force | Centripetal acceleration |
|---|---|---|
| 500 | 4,000 N | 8 m/s² |
| 1000 | 8,000 N | 8 m/s² |
| 2000 | 16,000 N | 8 m/s² |
| 4000 | 32,000 N | 8 m/s² |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Mass: entering "0" shows "Mass must be greater than 0." beside that field and no result.
- Radius: entering "0" shows "Radius must be greater than 0." beside that field and no result.
Choosing between the Centripetal Force Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Force Calculator](/science/force-calculator/) | mass and acceleration | Force |
| [Normal Force Calculator](/science/normal-force/) | mass, incline angle and gravitational acceleration | Normal force |
| [Net Force Calculator](/science/net-force-calculator/) | force magnitudes and direction of each force | Net force |
| [Friction Force Calculator](/science/friction-force-calculator/) | coefficient of friction μ and normal force | Friction force |
| [Momentum Calculator](/science/momentum-calculator/) | mass and velocity | Momentum |
Background: motion and mechanics
For constant acceleration the standard relations are v = u + at, s = ut + ½at², v² = u² + 2as and s = ½(u + v)t. Pick the equation that contains your three known quantities and the one you want. Use SI units (metres, seconds, kilograms, newtons, joules) throughout or the answer will be off by a factor.
These equations stop applying when acceleration changes during the motion, as with a rocket burning fuel; that needs calculus or numerical methods.
Assumptions and limitations
- Speed is squared
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for mass and radius to confirm this.
Frequently asked questions
Is centripetal force a real force?
It's the net inward force, supplied by friction, tension or gravity.
What is centrifugal force?
An apparent outward force in a rotating frame.
How does radius change the force?
A smaller radius needs a larger force.
What does the Centripetal Force Calculator calculate?
Force and acceleration for circular motion. It returns Centripetal force and Centripetal acceleration.
What formula does the Centripetal Force Calculator use?
F = m v² ÷ r; a = v² ÷ r. Directed toward the center of the circle.
What do I need to enter in the centripetal Force Calculator?
You enter Mass (kg), Speed (m/s) and Radius (m).
How is the result rounded or limited?
IEEE-754 double precision; shown to the decimals indicated. Speed is squared.
What is an example of a centripetal Force result?
With mass 1000, speed 20 and radius 50, the centripetal force is 8,000 N.
Related calculators
- Force Calculator — Force from mass and acceleration (Newton's second law).
- Normal Force Calculator — Normal force on an object resting on a flat or inclined surface.
- Net Force Calculator — Resultant of several forces at different angles.
- Friction Force Calculator — Friction force from the coefficient of friction and the normal force.
- Momentum Calculator — Linear momentum from mass and velocity.
- Coefficient of Friction Calculator — Coefficient of friction from friction and normal forces.
- Impulse Calculator — Impulse from force and time, and the change in velocity if the mass is known.
Sources
- OpenStax, University Physics Volume 1 (Rice University): mechanics
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.