Centripetal Acceleration Calculator

How it works

1. 1Choose whether you know the linear speed (v) or the angular speed (ω), then enter that value with the radius of the circular path.
2. 2The calculator converts inputs to SI and applies a = v²/r (from linear speed) or a = ω²r (from angular speed).
3. 3The result is shown in your chosen unit (m/s² or ft/s²), always in m/s², and as a g-force (a ÷ 9.80665).

Use cases

• Rotating machinery — the inward acceleration on a flywheel rim or centrifuge rotor.
• Vehicle dynamics — the lateral acceleration a car feels on a curved road at a given speed.
• Amusement rides and sports — the g-force in banked turns and loops.

Frequently asked questions

What formula does this calculator use?

Two equivalent forms: a = v²/r when you know the linear speed v, and a = ω²r when you know the angular speed ω. They agree because v = ωr. A car at v = 10 m/s on r = 50 m feels a = 100 ÷ 50 = 2 m/s² ≈ 0.20 g.

In which direction does centripetal acceleration act?

It always points radially inward, toward the centre of the circular path. It is not a new force — it is the net inward component of the real forces (tension, gravity, normal force) that keep the object on its curved path.

Can you show a worked example?

A ball on a string moves in a circle of radius 5 m at 10 m/s. a = v²/r = 100 ÷ 5 = 20 m/s², or about 2.04 g. With ω = 2 rad/s and r = 5 m, a = ω²r = 4 × 5 = 20 m/s² — the same result.