Home›Calculators›Physics›Centripetal Force Calculator

Centripetal Force Calculator

Physics

Calculate centripetal force using F = mv²/r. Enter mass, velocity, and radius to instantly get the force keeping an object in circular motion.

0.01100,000
0100,000
0.01100,000

Centripetal Force

125
Centripetal Acceleration
12.5

This calculator computes your Centripetal Force, Centripetal Acceleration from the values you enter.

Inputs
MassVelocityRadius
Outputs
Centripetal ForceCentripetal Acceleration

What is a Centripetal Force?

The Centripetal Force Calculator computes the inward force required to keep an object moving along a circular path, using the formula F = mv² ÷ r. Enter the object's mass, its velocity, and the radius of its circular path, and the calculator instantly returns the centripetal force in newtons along with the centripetal acceleration.

Centripetal force is a foundational concept in classical mechanics, describing everything from a ball swung on a string to a car rounding a curve to a satellite orbiting a planet. Related concepts like the actual speed of that motion can be explored with the Velocity Calculator.

How to use this Centripetal Force calculator

  1. Enter the mass — the mass of the object moving in a circle, in kilograms.

  2. Enter the velocity — the object's speed along its circular path, in meters per second.

  3. Enter the radius — the radius of the circular path, in meters.

  4. Read the centripetal force result — the highlighted result shows the force in newtons, with centripetal acceleration shown alongside.

  5. Check the step-by-step breakdown — expand the calculation steps to see exactly how the acceleration and force were derived.

Formula & Methodology

Centripetal force formula:
F = m × v² ÷ r

Centripetal acceleration:
a = v² ÷ r

Variable definitions:
- m — mass (kilograms)
- v — velocity (meters per second)
- r — radius (meters)
- F — centripetal force (newtons)
- a — centripetal acceleration (meters per second squared)

Worked example:

A 10 kg object moves in a circle of radius 2 m at a velocity of 5 m/s.

Step 1 — Acceleration: a = 5² ÷ 2 = 12.5 m/s²

Step 2 — Force: F = 10 kg × 12.5 m/s² = 125 N

Note: This formula assumes uniform circular motion (constant speed along the circular path). For non-uniform circular motion, where speed also changes, additional tangential force components apply beyond what this calculator computes.

Frequently Asked Questions

Centripetal force is calculated as F = mv² ÷ r, where m is the mass of the object in kilograms, v is its tangential velocity in meters per second, and r is the radius of the circular path in meters. The result is expressed in newtons (N), the SI unit of force.
Centripetal acceleration is a = v² ÷ r, the rate at which an object's velocity direction changes as it moves in a circle. Centripetal force is simply mass times this acceleration (F = ma), which is why this calculator shows both values together.
An object moving in a circle is constantly changing direction, and any change in velocity requires acceleration in that direction — toward the center of the circle. Without this inward force, the object would move in a straight line (Newton's first law), so something must always supply center-directed force to maintain circular motion.
Centripetal force isn't a new fundamental force — it's supplied by whatever physical force is available: tension in a string for a swung ball, gravity for orbiting satellites and planets, friction between tires and road for a car turning a corner, or the normal force on a rider in a curved amusement park track.
Because velocity is squared in the formula (F = mv² ÷ r), doubling the speed quadruples the required centripetal force for the same radius and mass. This is why high-speed turns require much more grip or tension than slow ones, and why racetrack curves are banked to help supply extra centripetal force.
Centripetal force is inversely proportional to radius, so a tighter turn (smaller radius) at the same speed requires more force, while a wider turn (larger radius) requires less. This is why sharp corners feel more forceful than gentle curves at the same speed.
Centripetal force is the real, inward-directed force that keeps an object moving in a circle, observed from a stationary (inertial) reference frame. Centrifugal force is a fictitious outward-feeling force experienced only inside a rotating reference frame — like feeling pushed outward in a spinning car — and doesn't actually exist as a physical force acting on the object.
Yes — for an object in a stable circular orbit, gravity supplies the exact centripetal force needed to maintain that path, so you can use this formula with the satellite's orbital velocity and orbital radius. For computing the actual orbital velocity or escape speed of a body, see the [Escape Velocity Calculator](/escape-velocity-calculator/).
Use kilograms (kg) for mass, meters per second (m/s) for velocity, and meters (m) for radius to get a result directly in newtons (N). If your data is in other units (grams, km/h, centimeters), convert to SI units first for an accurate result.
Engineers use centripetal force calculations to design safe curve banking angles on roads and racetracks, size the tension needed in centrifuges and rotating machinery, calculate loads on roller coaster tracks, and determine the minimum friction needed for vehicles to safely navigate a turn at a given speed.
If the centripetal force is removed (a string snaps, friction is lost, etc.), the object stops moving in a circle and instead travels in a straight line tangent to the circle at the point where the force was lost, consistent with Newton's first law of motion.
Both centripetal force and kinetic energy depend on mass and velocity, but kinetic energy (KE = ½mv²) measures the energy of motion regardless of direction, while centripetal force measures the inward force needed to keep that motion curved. Use the [Kinetic Energy Calculator](/kinetic-energy-calculator/) to compute the energy of the same moving object.
Also known as
F = mv2/r calculatorcircular motion force calculatorcentripetal acceleration calculatorradial force calculator