Circular motion tool

Centripetal Acceleration Calculator

Solve centripetal acceleration, velocity, or radius using ac = v² ÷ r.

Enter two known values

Solve a centripetal acceleration problem

Free tool
m/s²

This is the value being calculated.

m/s

Positive tangential speed of the moving object.

m

Positive radius of the circular path.

Use meters per second squared for acceleration, meters per second for velocity, and meters for radius.

Try an example:

Your centripetal acceleration result will appear here

Choose the missing variable and enter the other two known values.

Calculator guide

How this calculator works

Centripetal Acceleration Calculator determines the inward acceleration required for an object moving along a circular path. It helps physics students, engineers, and laboratory users analyze rotating systems, vehicles, machines, and circular motion experiments using velocity and radius relationships.

Formula explanation

Centripetal acceleration describes the inward acceleration required for circular motion.

Formula

Centripetal Acceleration = Velocity² ÷ Radius

Worked example

Example: A car moving around a curve experiences centripetal acceleration toward the center of the path.

Assumptions

  • Velocity and radius measurements are accurate.
  • The object follows circular motion principles.
  • Input values use compatible units.
  • The calculated acceleration represents ideal inward acceleration.

Examples

  • Example: Calculate centripetal acceleration when velocity and radius are known.
  • Example: Engineers analyze rotating machinery, vehicles, and mechanical systems using circular motion calculations.

Common mistakes

  • Using diameter instead of radius.
  • Ignoring velocity changes.
  • Incorrect unit conversion.

Variables

  • Object velocity
  • Radius of circular path
  • Centripetal acceleration
  • Circular motion conditions
  • Rotation speed
  • Measurement units

Limitations

  • Results assume ideal circular motion conditions.
  • Complex rotating systems with changing forces may require advanced dynamics analysis.

Scientific references

  • OpenStax University Physics: Circular Motion
  • NIST SI Units and Measurement References
  • Classical mechanics principles

Content review

Reviewed by: ScienceCalcHub Physics Review Team | Last reviewed: 2026-08-30

Applications

  • Physics education
  • Circular motion analysis
  • Engineering rotating system studies
  • Vehicle turning and dynamics analysis
  • Robotics and mechanical systems
  • Laboratory circular motion experiments

Frequently asked questions

How is centripetal acceleration calculated?

Centripetal acceleration is calculated by dividing the square of velocity by the radius of the circular path using the relationship ac = v² ÷ r.

What factors affect centripetal acceleration?

Centripetal acceleration increases with higher velocity and decreases when the radius of the circular path becomes larger.

What is the SI unit of centripetal acceleration?

The SI unit of centripetal acceleration is meters per second squared (m/s²), representing acceleration toward the center of rotation.

What is the difference between centripetal and tangential acceleration?

Centripetal acceleration changes the direction of velocity toward the center of rotation, while tangential acceleration changes the magnitude of rotational speed.

Accuracy and transparency

Created and maintained by our editorial team

This physics calculator is maintained by the ScienceCalcHub Editorial Team. Its calculation logic is tested with representative inputs, while the supporting guidance is checked for formula clarity, units, assumptions, and common mistakes.

Written by
ScienceCalcHub Editorial Team
Reviewed by
ScienceCalcHub Scientific Review Team
Review standard
Formula accuracy, units, examples, and educational clarity

Learn more about our formula-review and correction process, explore our calculation methodology, or view our scientific references.

  • Calculation logic tested
  • Variables and units explained
  • Assumptions stated clearly
  • Corrections handled transparently

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

  1. Write the formula: ac = v² ÷ r.
  2. Substitute the values: Fc = 4 × 6² ÷ 3.
  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

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

Calculator FAQ

How is centripetal acceleration calculated?

Centripetal acceleration is calculated by dividing the square of velocity by the radius of the circular path using the relationship ac = v² ÷ r.

What factors affect centripetal acceleration?

Centripetal acceleration increases with higher velocity and decreases when the radius of the circular path becomes larger.

What is the SI unit of centripetal acceleration?

The SI unit of centripetal acceleration is meters per second squared (m/s²), representing acceleration toward the center of rotation.

What is the difference between centripetal and tangential acceleration?

Centripetal acceleration changes the direction of velocity toward the center of rotation, while tangential acceleration changes the magnitude of rotational speed.