Centripetal Force Calculator
Calculate the centripetal force required to keep an object moving in a circular path from its mass, velocity, and radius.
Enter the object's mass, its tangential velocity, and the radius of the circular path to calculate the centripetal force in Newtons, kilonewtons, and pound-force.
Centripetal Force Calculator
Calculate the centripetal force required to keep an object moving in a circular path from its mass, velocity, and radius.
About the Centripetal Force Calculator
Centripetal force, from the Latin meaning 'centre-seeking,' is the net force directed toward the centre of a circular path that is required to keep an object moving in that path at constant speed. Without a centripetal force, an object in motion would travel in a straight line according to Newton's first law of motion. Any time you observe an object moving in a curve — a car turning a corner, a planet orbiting a star, a ball on a string, or a satellite circling Earth — a centripetal force is acting.
The centripetal force formula is F = mv²/r, where F is the centripetal force in Newtons, m is the mass of the object in kilograms, v is the tangential speed (the speed along the circular path) in metres per second, and r is the radius of the circular path in metres. This formula shows that centripetal force increases linearly with mass, increases with the square of velocity (doubling speed quadruples the required force), and decreases as the radius increases (a tighter curve requires more force at the same speed).
Centripetal force is not a new or separate type of force — it is simply the name given to whatever force happens to be acting toward the centre of the circular path in a specific scenario. For a satellite in orbit, gravity provides the centripetal force. For a car turning a corner, friction between the tyres and the road provides the centripetal force. For a ball on a string, the tension in the string provides the centripetal force. For a charged particle in a magnetic field, the magnetic force provides the centripetal force. The physics is the same in all cases; only the source of the force differs.
A frequent source of confusion is the distinction between centripetal force and centrifugal force. Centripetal force is a real force directed inward toward the centre of the circle — it is what keeps the object on its circular path. Centrifugal force is an apparent or fictitious force that seems to push the object outward from the centre — it is the effect of inertia as experienced by an observer in the rotating reference frame of the object itself. In a car turning left, the centripetal force (friction) pushes the car left; the occupants feel pushed to the right by what feels like centrifugal force, but that sensation is actually their inertia resisting the leftward change in direction.
Banked road curves are an engineering application of centripetal force principles. On a banked curve, the road is tilted so that the normal force from the road surface has a horizontal component directed inward. This horizontal component contributes to the centripetal force, supplementing friction and allowing vehicles to navigate the curve at the design speed with less reliance on tyre friction. Banked curves in racetracks allow cars to corner at much higher speeds than flat curves would permit.
Orbital mechanics is another direct application. A satellite in circular orbit must have exactly the right speed for its altitude so that gravitational centripetal force equals the centripetal acceleration needed for the orbit. At lower altitudes, a satellite needs more speed to stay in orbit; at higher altitudes, less speed is needed. The International Space Station orbits at about 400 km altitude with an orbital speed of roughly 7660 m/s, completing one orbit every 92 minutes. This calculator supports multiple unit options for mass (kg, g, lb), velocity (m/s, km/h, mph, ft/s), and radius (m, km, ft, miles) to handle diverse engineering and physics scenarios.
Centripetal Force Examples
Real-world scenarios demonstrating centripetal force calculations.
| Inputs | Centripetal Force | Application |
|---|---|---|
| m = 1500 kg, v = 15 m/s, r = 50 m | F = 6,750 N | Car on a 50 m radius turn at 15 m/s (54 km/h). The road friction must supply 6750 N (0.46 g) to keep the car on the curve. |
| m = 500 kg, v = 7600 m/s, r = 6,800 km | F ≈ 4,247 N | Simplified satellite orbit model. Gravity provides ~4247 N of centripetal force to keep the 500 kg satellite in circular orbit at 6800 km radius. |
| m = 40 kg, v = 3 m/s, r = 2 m | F = 180 N | Child on a merry-go-round. The structure must provide 180 N toward the centre to keep the child on the circular path at 3 m/s. |
| m = 0.5 kg, v = 4 m/s, r = 1.2 m | F ≈ 6.67 N | Ball swung on a 1.2 m string. The string tension equals the centripetal force of 6.67 N directed toward the hand at the centre of rotation. |
How to Use the Centripetal Force Calculator
- Enter the mass of the object and select its unit (kg, g, or lb). For a vehicle, this is the total vehicle mass; for a ball on a string, the ball's mass.
- Enter the tangential velocity — the object's speed along its circular path — and select the unit (m/s, km/h, mph, or ft/s).
- Enter the radius of the circular path and select the unit (m, km, ft, or miles). This is the distance from the object to the centre of the circle.
- Click Calculate. The result shows the centripetal force in Newtons, kilonewtons, and pound-force simultaneously for convenient comparison.
- Click Reset to clear all fields and start a new calculation with different inputs.
Centripetal Force FAQ
What provides centripetal force in different situations?
Centripetal force is always provided by an existing physical force or combination of forces. For a planet orbiting a star, gravity provides the centripetal force. For a car rounding a corner, static friction between the tyres and road provides it. For a ball on a string, string tension provides it. For a charged particle in a magnetic field, the magnetic (Lorentz) force provides it. For a roller coaster at the top of a loop, the normal force plus gravity provides it. Centripetal force is never a new fundamental force — it is just the name for the net inward-directed component of the forces already present.
Why does doubling speed quadruple the required centripetal force?
The centripetal force formula F = mv²/r contains velocity squared. When you double the speed while keeping mass and radius constant, the force increases by a factor of 2² = 4. This quadratic relationship has important engineering implications: a car travelling at 60 km/h around a curve requires four times the friction force compared to 30 km/h. It also explains why high-speed racing cars need enormous downforce to increase the normal force and thereby the maximum available friction force for cornering.
Is centripetal force the same as centrifugal force?
No. Centripetal force is a real force directed inward toward the centre of the circular path — it is what causes the circular motion and must be supplied by some physical agent (friction, gravity, tension, etc.). Centrifugal force is an apparent or fictitious force that appears only in a rotating (non-inertial) reference frame, directed outward. The two forces are equal in magnitude but opposite in direction. In an inertial frame, only centripetal force exists. In the rotating frame, both appear, but they cancel, leaving the object in apparent equilibrium.
What happens if the centripetal force is insufficient?
If the available centripetal force is less than what is required to maintain the circular path, the object cannot complete the curve and will move outward in a curved trajectory that deviates from the intended circle. For a car, this means skidding outward — the tyres lose grip because friction cannot provide sufficient centripetal force. For a satellite, insufficient orbital speed means the satellite will spiral inward toward Earth. In both cases, the object follows a path with a larger radius (lower curvature) than the intended path.
How do banked curves reduce the need for friction?
On a banked curve, the road is tilted so the normal force (perpendicular to the road surface) has a horizontal component pointing inward toward the centre of the curve. This horizontal component of the normal force acts as centripetal force, supplementing or even replacing the need for tyre friction. At the optimal banking angle for a given speed (called the design speed), no friction is needed at all — the horizontal component of the normal force alone provides the exact centripetal force required. Banking is calculated using tan(θ) = v²/(rg).
How is centripetal force related to orbital mechanics?
For a satellite in circular orbit, the centripetal force equals the gravitational force: mv²/r = GMm/r², where G is the gravitational constant and M is Earth's mass. Solving for orbital speed gives v = √(GM/r). This means the orbital speed depends only on the orbital radius — not on the satellite's mass. At 400 km above Earth (r ≈ 6778 km), the required orbital speed is about 7660 m/s. At a higher orbit, the required speed is lower, which is why geostationary satellites at 42,164 km altitude orbit at only 3070 m/s.