Centripetal Acceleration Calculator
Find the centripetal acceleration of an object moving in a circle using a = v^2 / r. Enter tangential speed in m/s and radius in metres. Essential for circular motion, car cornering, and satellite orbit analysis.
How to use this tool
- Enter tangential speed (v) and radius (r) in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your centripetal acceleration and the full breakdown beneath it.
Formula
a = v^2 / r
How it works
An object travelling in a circle of radius r at speed v experiences centripetal (centre-seeking) acceleration a = v²/r directed toward the centre.
Worked examples
Car on roundabout
Low Earth orbit satellite
Common mistakes to avoid
- Using angular velocity omega in place of tangential speed v — the formula a = v^2/r requires linear (tangential) speed in m/s, not rad/s.
- Entering the diameter of the circular path instead of the radius, halving the denominator and doubling the computed acceleration.
- Forgetting that centripetal acceleration always points toward the centre of the circle, not in the direction of motion — direction matters in vector problems.
Key terms
Frequently asked questions
- What is the difference between centripetal and centrifugal acceleration?
- Centripetal acceleration is a real inward acceleration directed toward the centre of curvature. Centrifugal acceleration is a fictitious outward term that appears only in a rotating reference frame. In an inertial frame, only centripetal acceleration exists.
- How do I convert from angular velocity to use this formula?
- Tangential speed v = omega * r, where omega is in rad/s and r is the radius. Substitute into a = v^2/r to get a = omega^2 * r.
- Why does centripetal acceleration increase with the square of speed?
- The direction of velocity changes continuously in circular motion. At higher speeds the direction changes more rapidly for the same radius, so more acceleration is needed. Doubling speed quadruples the required centripetal acceleration.