Mechanics
Centripetal Force
Net force required for circular motion.
Variables
FcN
Centripetal force
Force toward center
In SI units: kg·m/s²
Allowed values: 0 or more
mkg
Mass
Object mass
Allowed values: 0 or more
vm/s
Tangential velocity
Speed along circle
rm
Radius
Radius of path
Allowed values: greater than 0
Derivation
F = ma with a = a_c: F_c = mv²/r.
Your notes
0/5000
Check value
Round inputs run through this page's calculator. Use it to test your own working or a rearranged form. It is a test case, not a real-world example.
- m = 2 kg (Mass)
- v = 3 m/s (Tangential velocity)
- r = 4 m (Radius)
Result: Fc = 4.5 N
Other mechanics formulas with the same quantities
- Linear-Angular Velocity Relation (Rotational Motion) shares Radius
- Moment of Inertia (Point Mass) (Rotational Motion) shares Mass
- Rolling Kinetic Energy (Rotational Motion) shares Mass
Where this formula is listed
- Mechanics formulas, under Rotational Motion, alongside Angular Velocity, Angular Acceleration, Torque, Newton's Second Law (Rotation) and Rotational Kinetic Energy.
- In the mechanics list it comes after Centripetal Acceleration and before Torque.
- Mechanics formula sheet, one of 58 formulas printed with symbol keys and SI units.
- The full formula index, grouped by category and topic.
Common questions
What is the Centripetal Force formula?
Centripetal Force is written F_c = mv²/r = mω²r. Net force required for circular motion. It belongs to Mechanics, under Rotational Motion.
What are the units in F_c = mv²/r = mω²r?
In SI units, F_c is centripetal force, measured in kg·m/s²; m is mass, measured in kg; v is tangential velocity, measured in m/s; r is radius, measured in m.
How is the Centripetal Force formula derived?
F = ma with a = a_c: F_c = mv²/r. The result is F_c = mv²/r = mω²r.