What is the difference between centripetal and centrifugal force?

Centripetal force is the real inward force that keeps an object moving in a circular path (e.g., tension in a string, friction on a road). Centrifugal force is the apparent outward force felt in the rotating reference frame. They are equal in magnitude: F = mω²r = mv²/r.

What does the formula F = mω²r mean?

F is the centripetal/centrifugal force in Newtons, m is the mass in kilograms, ω (omega) is the angular velocity in radians per second, and r is the radius of the circular path in meters. Multiplying ω²r gives the centripetal acceleration, which is then multiplied by mass to yield force.

How do I convert RPM to rad/s?

Multiply the RPM value by 2π/60 (≈ 0.10472). For example, 1000 RPM × 0.10472 ≈ 104.72 rad/s. This calculator performs the conversion automatically when you choose the RPM input unit.

How is linear velocity related to angular velocity?

Linear (tangential) velocity v = ω × r. If you know the linear velocity, you can rearrange to get ω = v/r. When you choose the linear velocity input mode, this calculator derives ω internally before applying F = mω²r.

What units does this calculator output?

Results are shown in Newtons (N), kilonewtons (kN), and pound-force (lbf). 1 kN = 1000 N; 1 lbf ≈ 4.44822 N.

Why does force increase so quickly with speed?

Because force is proportional to ω² (or v²). Doubling the angular velocity quadruples the centripetal force, while doubling the radius only doubles it. This quadratic relationship is why high-speed rotors must be very precisely balanced.

Centrifugal Force Calculator

Name: Centrifugal Force Calculator
Availability: InStock
Author: Nham Vu

Compute centrifugal or centripetal force from mass, radius, and angular velocity (or linear velocity) using F = mω²r.

Input Parameters

Velocity Input Mode

Mass (m)

Radius (r)

Angular Velocity (ω)

Results

Enter values and click Calculate

Common Centripetal Force Examples

Scenario	Mass	Radius	Speed	Force
Car in a curve	1500 kg	50 m	60 km/h	~8333 N
Lab centrifuge	0.01 kg	0.1 m	3000 RPM	~987 N
Roller coaster loop	70 kg	10 m	50 km/h	~2700 N
Spinning flywheel	2 kg	0.3 m	1500 RPM	~14804 N

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Summary

Compute centrifugal or centripetal force from mass, radius, and angular velocity (or linear velocity) using F = mω²r.

How it works

Select your input mode: Angular Velocity (ω) or Linear Velocity (v).
Enter the mass of the rotating object and choose its unit.
Enter the radius of the circular path and choose its unit.
Enter the angular velocity (rad/s or RPM) or linear velocity (m/s or km/h).
Click Calculate — force results appear instantly in N, kN, and lbf.
Use Reset to start a new calculation.

Use cases

Designing centrifuges and determining required motor torque.
Analyzing forces on rotating machinery components such as flywheels and pulleys.
Calculating the lateral force on a vehicle cornering at a given speed and radius.
Estimating g-forces experienced on amusement park rides.
Verifying structural loads on rotating parts in engineering design.
Teaching circular motion and Newton's second law in physics courses.
Computing satellite orbital mechanics and required centripetal force.
Determining belt tension and bearing loads in rotational assemblies.

Frequently Asked Questions

Last updated: 2026-06-10 · Reviewed by Nham Vu