Circular motion calculator

Formula

How it works

Moving at constant speed around a circle still means constantly changing direction, which is an acceleration pointed toward the centre. Its size is speed squared divided by the radius, and the matching force follows from Newton's second law.

Worked example

The same calculation with the default values:

• Mass 1.5
• Radius 2
• Speed 4

1. a = 4² ÷ 2 = 8
2. F = 1.5 × 8 = 12
3. T = 2 × π × 2 ÷ 4 = 3.141593

Result: Centripetal acceleration: 8 · Centripetal force: 12 · Period (time per revolution): 3.14159265

Common mistakes

• Confusing centripetal force with a separate outward "centrifugal force" - in an inertial reference frame, the only real force is the centripetal force pointing inward, which is what keeps the object on the circular path.
• Using diameter instead of radius in the formulas - a = v²/r needs the radius, not the diameter; using diameter halves the correct acceleration.
• Forgetting that centripetal acceleration points toward the center at every instant, not in the direction of the velocity - velocity is tangent to the circle, acceleration is perpendicular to it.