Centripetal Force Calculator

Anything moving in a circle needs a constant inward force to keep curving rather than flying off in a straight line — this is that force, and it grows fast with speed since it depends on velocity squared.

Inputs

Result

5,400 N

Acceleration 4.5 m/s²

How it works

F = mv²/r

How the centripetal force calculator works

F = mv² ÷ r, where r is the radius of the circular path.

Centripetal acceleration = v² ÷ r, independent of mass.

Worked example: 1,200 kg car cornering at 15 m/s, 50 m radius

  1. F = 1,200 × 15² ÷ 50 = 1,200 × 225 ÷ 50 = 5,400 N.
  2. Acceleration = 15² ÷ 50 = 4.5 m/s² — nearly half of standard gravity, sideways.

Common mistakes to avoid

Assuming doubling speed doubles the required force

Because velocity is squared, doubling cornering speed actually quadruples the centripetal force needed — this is a major reason why exceeding a curve's safe speed by even a modest margin dramatically increases the risk of losing grip.

Confusing centripetal force with 'centrifugal force'

Centripetal force is the real inward force causing circular motion (like tyre friction on a curve); the outward 'centrifugal force' passengers feel is a perceived effect of inertia in a rotating reference frame, not a real force acting on the object.

Frequently asked questions

What provides the centripetal force for a car going around a curve?

Friction between the tyres and the road — if the required centripetal force exceeds the maximum friction available (a wet or icy road, or too high a speed), the car skids outward rather than following the curve.

Why does a smaller radius require more force at the same speed?

The formula has r in the denominator — a tighter curve at the same speed demands proportionally more centripetal force, which is why sharp turns feel more forceful than gentle ones at equal speed.

Is centripetal force a completely separate force from gravity or friction?

No — centripetal force is a description of the net inward force required for circular motion, which in practice is provided by an existing force like friction, tension, or gravity, not a distinct new force of its own.

How does this relate to satellites orbiting a planet?

For an orbiting satellite, gravity itself provides exactly the centripetal force needed to maintain its circular (or elliptical) path — no other explicit force is needed for a stable orbit.

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