Centripetal Acceleration Calculator Formula

Understand the math behind the centripetal acceleration calculator. Each variable explained with a worked example.

Formulas Used

Centripetal Acceleration

centripetal_accel = pow(velocity, 2) / radius

Variables

VariableDescriptionDefault
velocityTangential Velocity(m/s)10
radiusRadius(m)5

How It Works

Centripetal Acceleration

An object moving in a circle at constant speed still accelerates because its direction changes.

Formula

a_c = v² / r

This acceleration always points toward the center of the circular path.

Worked Example

A car travels at 10 m/s around a curve of radius 5 m.

velocity = 10radius = 5
  1. 01a_c = v² / r
  2. 02a_c = 100 / 5
  3. 03a_c = 20 m/s²

Frequently Asked Questions

Why is there acceleration if speed is constant?

Acceleration is the rate of change of velocity, which is a vector. Even at constant speed, the direction changes continuously, so the velocity vector changes.

What direction does centripetal acceleration point?

It always points radially inward, toward the center of the circular path.

How does centripetal acceleration relate to angular velocity?

Since v = omega * r, we can write a_c = omega² * r, where omega is the angular velocity in radians per second.