Centripetal Force Calculator — F = mv²/r
Calculate centripetal force for circular motion. Covers F = mv²/r, centripetal acceleration, banking angles, and examples from cars to satellites.
Anything moving in a circle is constantly accelerating — even if its speed is constant. That sounds contradictory until you remember that acceleration is a change in velocity, and velocity includes direction. Circular motion means direction is always changing, so there must be a force pulling the object toward the center. That's centripetal force.
Use the CalcHub centripetal force calculator to find the force required for any circular motion scenario.
The Formula
F = m × v² / rOr in terms of angular velocity (ω in rad/s): F = m × ω² × r
- F = centripetal force (Newtons, N)
- m = mass (kg)
- v = linear speed (m/s)
- r = radius of circular path (m)
What Provides the Centripetal Force?
This is the key conceptual point. "Centripetal force" isn't a new type of force — it's a label for whatever force is acting toward the center:
| Situation | What provides F_c |
|---|---|
| Car in a turn | Road friction on tires |
| Satellite orbiting | Gravity |
| Ball on a string | Tension in string |
| Clothes in a spin dryer | Normal force from drum wall |
| Banked curve | Normal force component |
Worked Example
A 1200 kg car takes a flat circular turn of radius 80 m at 54 km/h (15 m/s). What centripetal force does friction need to provide?
F = mv²/r = 1200 × 15² / 80 = 1200 × 225 / 80 = 3375 N
Required friction force ≈ 3375 N. The maximum static friction for a car with μ = 0.7 on dry concrete:
f_max = μ × mg = 0.7 × 1200 × 9.81 ≈ 8239 N
The required force (3375 N) is well within the available friction (8239 N), so the car safely holds the corner.
What is centrifugal force?
In an inertial (non-rotating) reference frame, centrifugal force doesn't exist. In a rotating reference frame, it appears as a "fictitious" outward force — equal in magnitude to centripetal force but pointing outward. When you feel pushed to the side in a turning car, that sensation is centrifugal force in your rotating reference frame.
How does centripetal force relate to orbital mechanics?
For a satellite, gravity provides centripetal force: GMm/r² = mv²/r. This gives orbital velocity v = √(GM/r). Larger orbit → lower speed. This is Kepler's third law in action — outer planets orbit slower than inner ones.
Why does the radius matter so much?
Speed appears squared in F = mv²/r, but radius is in the denominator. Doubling speed quadruples the required force. Halving the radius also doubles the required force. This is why tight corners at speed are much more demanding on tires than wide, gradual bends.