Centripetal Force Calculator - F = mv²/r

Mass

0.01100,000

Velocity

0100,000

Radius

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.

Why Use a Centripetal Force Calculator?

Manually squaring velocity and dividing by radius is simple arithmetic, but doing it repeatedly for different masses, speeds, or radii, as when comparing scenarios for a physics problem or engineering design, is time-consuming and error-prone.

This calculator updates the result live as you adjust any input, and the step-by-step breakdown shows exactly how the centripetal acceleration and force were derived, which is useful for checking homework or verifying design assumptions quickly.

Because centripetal force scales with the square of velocity, small changes in speed produce large changes in the required force, a relationship that's easy to underestimate without running the actual numbers.

Who Should Use This Calculator?

Physics students solving circular motion problems and checking their algebra against a reliable reference.

Mechanical and automotive engineers estimating cornering forces, centrifuge loads, or rotating machinery stresses.

Amusement park and track designers calculating the forces experienced on curved tracks and loops.

Teachers demonstrating how mass, speed, and radius interact to determine circular-motion forces.

Hobbyist physicists and makers building or analyzing spinning mechanisms, slingshots, or rotational experiments.

What Insights Does This Calculator Give You?

Centripetal force, the primary result, in newtons, showing how much inward force is needed to sustain the given circular motion.

Centripetal acceleration, the rate of directional change in velocity (v² ÷ r), independent of mass, useful for understanding how sharp a turn "feels" regardless of the object's weight.

Sensitivity to speed, because force scales with velocity squared, this calculator makes it easy to see how quickly required force grows as speed increases, which matters for safety margins in vehicles and machinery.

How to use this Centripetal Force calculator

Enter the mass, the mass of the object moving in a circle, in kilograms.
Enter the velocity, the object's speed along its circular path, in meters per second.
Enter the radius, the radius of the circular path, in meters.
Read the centripetal force result, the highlighted result shows the force in newtons, with centripetal acceleration shown alongside.
Check the step-by-step breakdown, expand the calculation steps to see exactly how the acceleration and force were derived.

Show formula & methodology ↓Show less ↑

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

What is the formula for centripetal force?

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.

What is centripetal acceleration and how does it relate to 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.

Why does centripetal force always point toward the center?

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.

What provides centripetal force in real-world situations?

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.

How does increasing speed affect centripetal force?

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.

How does radius affect 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.

What is the difference between centripetal force and centrifugal force?

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.

Can I use this calculator for satellites and orbital motion?

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/).

What units should I use for mass, velocity, and radius?

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.

How is centripetal force used in engineering and design?

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.

What happens if the centripetal force suddenly disappears?

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.

How does this calculator relate to kinetic energy?

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