What is the formula for centripetal force?

The formula is Fc = mv²/r. Multiply mass by the square of tangential speed and divide by the circular radius.

What unit is used for centripetal force?

Centripetal force is measured in newtons, abbreviated as N.

Does the calculator automatically convert units?

Yes. It converts supported mass, speed, and radius units into standard SI units before calculating the results.

Circular Motion Physics Tool

Centripetal Force Calculator

Q: What happens when an object's speed doubles?

The required centripetal force becomes four times larger because speed is squared in the formula.

Calculate the inward force required to keep an object moving in a circular path. Enter mass, tangential speed, and radius to find force, acceleration, angular velocity, period, frequency, and RPM.

Calculate Centripetal Force

Enter three values and select the appropriate units.

Calculator Ready

Motion Parameters

Object Mass Amount of matter in the rotating object

Mass must be greater than zero.

Tangential Speed Speed along the circular path

Tangential speed acts perpendicular to the radius.

Circular Radius Distance from the center of rotation

Use the radius, not the complete diameter.

Calculation Results

Your result will appear here

Enter the object's mass, tangential speed, and circular radius, then select “Calculate Force.”

Simple Three-Step Process

How the Centripetal Force Calculator Works

The calculator converts every value into standard SI units before applying the circular motion equations.

Enter the Object's Mass

Provide the mass of the rotating object and select kilograms, grams, pounds, ounces, milligrams, or metric tonnes.

Add Speed and Radius

Enter the object's tangential speed and its distance from the center of the circular path.

Review the Physics Results

Get centripetal force, acceleration, angular velocity, orbital period, frequency, and rotational speed.

What Is Centripetal Force?

Centripetal force is the net inward force that keeps an object moving along a circular path. The word “centripetal” means center-seeking, which describes the direction of this force.

Although an object may move at a constant speed, its velocity continually changes because its direction changes. This change in velocity creates centripetal acceleration directed toward the center of the circle.

F_c = mv² ÷ r

F_c is centripetal force measured in newtons.
m is the object's mass measured in kilograms.
v is tangential speed measured in metres per second.
r is the circular radius measured in metres.

How Speed Affects Centripetal Force

Speed has a squared relationship with centripetal force. Doubling the speed increases the required force by a factor of four. Tripling the speed increases it by a factor of nine. This is why high-speed turns require much greater inward force.

How Radius Affects Centripetal Force

Centripetal force is inversely proportional to radius. A smaller circular path requires more force when mass and speed remain unchanged. A wider circular path requires less force.

Real-World Sources of Centripetal Force

Centripetal force is not usually a separate physical force. It is the name given to the net inward force produced by tension, gravity, friction, electrical attraction, or another interaction.

Examples include tire friction while a car turns, gravitational attraction holding a satellite in orbit, tension in a string attached to a rotating object, and normal force acting on a roller coaster.

Key Physics Relationships

Greater mass produces proportionally greater centripetal force.
Greater speed produces a much larger force because speed is squared.
A smaller turning radius increases the required inward force.
The force always points toward the center of the circular path.

Example Calculation

Suppose a 10 kg object moves at 20 m/s in a circle with a radius of 5 m.

F_c = 10 × 20² ÷ 5

Centripetal Force = 800 N

Common Applications

Vehicles travelling around curved roads
Satellites and planets in circular orbits
Rotating machines, wheels, and turbines
Athletes running around curved tracks
Roller coasters and amusement rides

Frequently Asked Questions

Centripetal Force Calculator FAQs

Find answers to common questions about circular motion, centripetal acceleration, units, and calculation results.

The formula is F_c = mv²/r. Multiply the object's mass by the square of its tangential speed, then divide the result by the circular radius.

The standard SI unit is the newton, written as N. One newton is equal to one kilogram metre per second squared.

Centripetal force is always directed inward toward the center of the circular path. The apparent outward effect experienced in a rotating reference frame is commonly described as centrifugal force.

Centripetal force becomes four times larger because speed is squared in the formula. This assumes that mass and radius remain unchanged.

Yes. When mass and speed remain constant, increasing the radius decreases the required centripetal force. Doubling the radius reduces the force by half.

Yes. A speed of zero produces zero centripetal force, acceleration, frequency, and RPM because the object is not moving around the circular path.

Centripetal acceleration is the inward acceleration that changes the direction of an object's velocity. It is calculated using a_c = v²/r.

Yes. The calculator converts supported mass, speed, and radius units into kilograms, metres per second, and metres before performing the calculation.

Note: This calculator assumes uniform circular motion and treats the provided radius as the distance from the center of rotation to the object's center of mass.