Physics overview
What is centripetal acceleration?
Centripetal acceleration is the inward net force that continually changes the direction of an object moving in a circle.
Formula
Centripetal acceleration formula
Centripetal Forceac = v² ÷ r
- Fc is centripetal force in newtons.
- v is tangential velocity in meters per second.
- r is radius in meters.
Worked example
A 4 kg object moves at 6 m/s in a 3 m radius circle
- Write the formula: ac = v² ÷ r.
- Substitute the values: Fc = 4 × 6² ÷ 3.
- Calculate the force: Fc = 48 N.
Rearranged equations
Solve for velocity or radius
Mass
m = Fc r ÷ v²
Multiply force by radius, then divide by velocity squared.
Velocity
v = √(Fc r ÷ m)
Take the square root after dividing force times radius by mass.
Radius
r = mv² ÷ Fc
Divide mass times velocity squared by force.
Velocity effect
Why velocity is squared
Centripetal acceleration is proportional to velocity squared. If velocity doubles, the required inward force becomes four times greater when mass and radius stay unchanged.
Units
Standard SI units
Use newtons for centripetal acceleration, kilograms for mass, meters per second for velocity, and meters for radius.
Real-world applications
Where centripetal acceleration is used
- Vehicles turning on curved roads.
- Objects rotating on strings.
- Roller coasters and amusement rides.
- Satellites and orbital motion.
- Laboratory circular-motion experiments.
Calculation limits
Important assumptions
- All entered values must be greater than zero.
- Velocity is tangential to the circular path.
- Radius is measured from the center of rotation.
- The result represents the net inward force, not a separate type of physical force.
- Units are not converted automatically.
Related tools
Continue your motion calculations
Use the Force Calculator to solve force, mass, or acceleration.
Use the Kinetic Energy Calculator to calculate energy from mass and velocity.
Questions and answers
Centripetal acceleration calculator FAQ
What formula does the centripetal acceleration calculator use?
It uses ac = v² ÷ r, where centripetal acceleration equals velocity squared divided by radius.
What is centripetal acceleration?
Centripetal acceleration is the inward net force that keeps an object moving along a circular path.
What is the SI unit of centripetal acceleration?
The SI unit of centripetal acceleration is the newton, written as N.
How does velocity affect centripetal acceleration?
Centripetal acceleration increases with the square of velocity, so doubling velocity produces four times the force when mass and radius remain constant.