Centripetal Force Calculator

Centripetal force is the inward-directed force required to keep an object moving in a circular path. Without this force, the object would fly off in a straight line (Newton’s first law). The word “centripetal” means “center-seeking”, and it names a net force rather than a separate force in its own right. Gravity, tension, friction, or a wall supplies it; nothing new is added to the free-body diagram.

Centripetal Force Formula:

F = m × v² / r

Alternatively, using angular velocity:

F = m × ω² × r

• F = Centripetal force (Newtons)
• m = Mass of the object (kg)
• v = Linear velocity (m/s)
• r = Radius of circular path (meters)
• ω = Angular velocity (radians/second)

Worked example — car rounding a curve: Mass: 1,200 kg Speed: 25 m/s (90 km/h) Curve radius: 150 meters F = 1,200 × 25² / 150 = 1,200 × 625 / 150 = 5,000 N

This force is provided by friction between the tires and road. If the road is wet or the curve is tighter, friction may run out, and then the car slides.

Maximum safe speed for a curved road:

v_max = sqrt(μ × g × r)

Where μ is the coefficient of friction (dry asphalt ≈ 0.7, wet ≈ 0.4) and g = 9.81 m/s².

Example: Curve of radius 150 m, wet road (μ = 0.4): v_max = sqrt(0.4 × 9.81 × 150) = sqrt(588.6) = 24.3 m/s (87 km/h)

Pick a road surface in the dropdown and the calculator runs that check against the speed you entered. Notice that mass cancels out of v_max entirely: a loaded truck and a small hatchback slide at the same speed on the same curve, which surprises most people. Mass raises the force needed and the friction available in equal measure.

Real-world examples of centripetal force:

• Moon orbiting Earth: gravity provides the force
• Washing machine spin cycle: the drum wall provides it, and the clothes only feel pushed outward because inertia carries them into the wall
• Banked highway curves: designed so the normal force provides the centripetal force, reducing dependence on friction