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
Centripetal force is the net force directed toward the center of a circular path, keeping an object moving in a circle.
F = m × v² / r
Centripetal acceleration:
a = v² / r
Where:
- F = centripetal force (N)
- m = mass (kg)
- v = velocity/speed (m/s)
- r = radius of circular path (m)
- a = centripetal acceleration (m/s²)
Alternative with angular velocity (ω):
F = m × ω² × r
a = ω² × r
Practical examples:
| Scenario | Typical Force |
|---|---|
| Car turning (1000 kg, 60 mph, 100m radius) | ~7,200 N |
| Merry-go-round (50 kg child, 2 m/s, 3m) | ~67 N |
| Satellite in orbit | Equals gravitational pull |
Key concepts:
- Centripetal = “center-seeking” — always points inward
- Centrifugal force is the “apparent” outward force felt in the rotating frame
- At any speed, a tighter radius requires more force
- This is why banked curves help cars turn at speed