Centripetal Force Calculator
Calculate centripetal force and acceleration for circular motion.
Enter mass, velocity, and radius to find the force keeping an object in its path.
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” — it is a net force, not a separate force in its own right.
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 be insufficient — 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)
Real-world examples of centripetal force:
- Moon orbiting Earth: gravity provides the force
- Washing machine spin cycle: drum wall provides the force (clothes feel pushed outward — that’s inertia, not a force)
- Banked highway curves: designed so normal force provides the centripetal force, reducing dependence on friction