Engineering Mechanics

Centripetal Force Calculator

Calculate centripetal force, mass, radius, tangential speed, or angular speed for uniform circular motion.

Formula Fc = m v² / rReviewed Sep 8, 2026

Centripetal force is the inward net force needed to keep an object moving along a circular path. This calculator supports both common forms: Fc = m v² / r when tangential speed is known, and Fc = m r ω² when angular speed or RPM is known. It also reports centripetal acceleration so the result is easier to connect back to Newton's second law.

Calculation Bench

Solve for

01Mass

m · Mass of the object moving in the circular path.

02Radius

r · Radius of the circular path measured from the center of curvature.

03Tangential Speed

v · Speed along the circular path, tangent to the circle at each instant.

This calculator uses magnitudes. The force direction is inward toward the center of the circular path.

Solution

Enter the known values to calculate centripetal force.

Fc = m v² / r

Formula Sheet

F_c=\dfrac{m v^2}{r}

F_c=m r \omega^2

m=\dfrac{F_c r}{v^2}

m=\dfrac{F_c}{r\omega^2}

r=\dfrac{m v^2}{F_c}

r=\dfrac{F_c}{m\omega^2}

v=\sqrt{\dfrac{F_c r}{m}}

\omega=\sqrt{\dfrac{F_c}{m r}}

a_c=\dfrac{v^2}{r}

a_c=r\omega^2

FcCentripetal Force
mMass
rRadius
vTangential Speed
ωAngular Speed
acCentripetal Acceleration

Variables & Units

Symbol	Variable	Description	Common Units
Fc	Centripetal Force	Magnitude of the inward net force required for circular motion.	N, kN, lbf
m	Mass	Mass of the object moving in the circular path.	kg, g, lb
r	Radius	Radius of the circular path measured from the center of curvature.	m, cm, ft
v	Tangential Speed	Speed along the circular path, tangent to the circle at each instant.	m/s, km/h, mph
ω	Angular Speed	Rate of rotation in radians per second or equivalent rotational-speed units.	rad/s, rpm, Hz
ac	Centripetal Acceleration	Inward radial acceleration caused by the direction change of velocity.	m/s², ft/s², g

How to Use This Calculator

01Choose Tangential Speed mode if you know speed along the path, such as a car speed in m/s or mph.
02Choose Angular Speed / RPM mode if you know rotational speed, such as rad/s, rpm, hertz, or revolutions per second.
03Select the variable you want to solve for: centripetal force, mass, radius, tangential speed, or angular speed.
04If a problem gives diameter, divide by 2 before entering radius. If it gives period, convert to angular speed with ω = 2π/T first.
05Enter the known values with units. Mass and radius must be positive; force and speed are treated as magnitudes.
06Calculate to see the result plus the derived centripetal acceleration and related speed/angular-speed conversion.

How the Formula Works

Uniform circular motion has a radial acceleration toward the center of the path. With tangential speed v and radius r, that acceleration is ac = v² / r.

Newton's second law then gives Fc = m ac, so substituting ac = v² / r gives Fc = m v² / r.

Angular speed is related to tangential speed by v = ωr. Substituting that into v²/r gives ac = rω² and Fc = m r ω².

Centripetal force is not a new kind of force. It is the inward net force supplied by something physical, such as tension, gravity, friction, or a normal-force component.

Worked Example 01

Car moving through a circular curve

Known

Mass (m): 900 kg
Speed (v): 25 m/s
Radius (r): 500 m

Formula

Fc = m v² / r

Substitution

Fc = 900 × 25² / 500

Result

Fc = 1,125 N

This is the inward net force required to keep the car on the 500 m radius path. On a flat road, static friction would need to supply that force.

Worked Example 02

Small mass spinning at known angular speed

Known

Mass (m): 2 kg
Radius (r): 0.5 m
Angular speed (ω): 10 rad/s

Formula

Fc = m r ω²

Substitution

Fc = 2 × 0.5 × 10²

Result

Fc = 100 N

The same result could be found by first converting angular speed to tangential speed: v = ωr = 5 m/s, then Fc = mv²/r.

Applications

01Finding required inward force for a car, bike, or object moving around a curve
02Checking rotating machinery or centrifuge loads from RPM and radius
03Solving physics homework involving uniform circular motion
04Comparing how force changes when speed doubles or turn radius changes

Assumptions

01Motion is treated as uniform circular motion over the instant being calculated.
02Inputs are magnitudes. The centripetal force direction is inward toward the center of curvature.
03Radius is measured from the center of the circular path to the moving object's path.
04Angular speed is converted internally to rad/s before using Fc = m r ω².

Where This Model Stops

01Does not identify which physical force supplies the centripetal force; tension, friction, gravity, and normal force must be analyzed from the actual free-body diagram.
02Does not model changing radius, changing speed, tangential acceleration, non-circular paths, banked-road friction limits, or structural stress from rotation.
03Does not check human comfort, tire grip coefficient, bearing load rating, rotor balance, material stress, or safety containment for rotating equipment.
04For vehicle cornering, the result is the required inward force, not proof that tire friction, banking, or road conditions are sufficient.

References

[1]
6.3 Centripetal Force
OpenStax University Physics Volume 1
Reference for ac = v²/r, ac = rω², Fc = mv²/r, and Fc = mrω².
[2]
6.2 Uniform Circular Motion
OpenStax Physics
Reference for the direction and interpretation of centripetal force as the inward net force in circular motion.

Frequently Asked Questions

Is centripetal force a separate kind of force?

No. Centripetal force is the inward net force required for circular motion. In a real problem it may be supplied by tension, gravity, friction, a normal force component, or another physical interaction.

Why does speed get squared in Fc = mv²/r?

Because centripetal acceleration is v²/r. Doubling speed makes the required inward force four times larger if mass and radius stay the same.

Can I use rpm instead of rad/s?

Yes. Select Angular Speed / RPM mode and choose rpm as the angular-speed unit. The calculator converts rpm to rad/s internally before applying Fc = mrω².

Is this the same as the Force Calculator?

It is related but more specific. The Force Calculator uses F = ma for any one-dimensional acceleration. This calculator uses the circular-motion acceleration ac = v²/r or rω² before applying F = ma.

Why does the force point inward if the object moves forward?

The velocity is tangent to the path, but the acceleration is caused by the velocity direction changing. That required acceleration points toward the center, so the net force must point inward too.

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