What is the Centripetal Force?
Centripetal force is the force that acts on any object moving along a curved path, directed toward the center of curvature. In circular motion — the most common case — centripetal force always points toward the center of the circle, keeping the object on its circular trajectory.
Without centripetal force, a moving object would travel in a straight line (Newton's first law). The centripetal force continuously redirects the velocity vector inward, producing circular motion without changing the object's speed.
Centripetal Force Equation
The centripetal force formula can be expressed in two equivalent ways:
- F = m × v² / r — using linear velocity
- F = m × ω² × r — using angular velocity
Where:
- F — centripetal force (N or lbf)
- m — mass of the object (kg or lb)
- v — linear velocity (m/s or ft/s)
- ω — angular velocity (rad/s)
- r — radius of circular path (m or ft)
The centripetal acceleration is: a = v² / r (m/s² or ft/s²)
Centripetal Force Units
Because centripetal force is a force, it uses the same units as all other forces:
- SI unit: Newton (N)
- Imperial unit: pound-force (lbf)
- CGS unit: dyne (1 N = 100,000 dyne)
- Engineering unit: kilogram-force (kgf)
Our calculator automatically shows results in N, lbf, and kgf simultaneously.
Centripetal vs. Centrifugal Force: What Is the Difference?
Centripetal and centrifugal force use the same formula (F = mv²/r), but they represent different perspectives on the same phenomenon:
- Centripetal force — observed from an inertial (non-rotating) reference frame. A parent watching a child on a merry-go-round sees only one force: the centripetal force directed toward the center, which keeps the child moving in a circle.
- Centrifugal force — observed from a non-inertial (rotating) reference frame. The child on the merry-go-round feels pushed outward. This apparent outward push is the centrifugal force — a pseudo-force that appears only in the rotating frame of reference.
In short: centripetal force is real and acts in all frames; centrifugal force is a fictitious force that exists only in rotating (non-inertial) frames.
How to Use the Centripetal Force Calculator
This calculator can solve for any one of the four main variables:
- Find Force (F) — enter mass, velocity (linear, angular in rad/s, or RPM), and radius. The calculator computes the centripetal force in N and lbf.
- Find Mass (m) — enter force, velocity, and radius. Useful when you know the required force and need the object mass.
- Find Velocity (v) — enter force, mass, and radius. Solves v = √(F × r / m).
- Find Radius (r) — enter force, mass, and linear velocity. Solves r = m × v² / F.
Both metric (kg, m, m/s → N) and imperial (lb, ft, ft/s → lbf) unit systems are supported. Results are always shown in both unit systems for easy comparison.
Centripetal Force and the Conservation of Energy
A key property of centripetal force: it is always perpendicular to the velocity. This means it does no work on the object — it changes the direction of motion but not the speed. Therefore, in uniform circular motion, the kinetic energy and speed remain constant even though centripetal force is continuously applied.
This is why planets maintain stable orbits: gravitational force provides the centripetal force, continuously curving their path without altering their orbital speed (in the idealized circular case).
Practical Examples
- Car turning on a road: Friction between tires and road provides the centripetal force.
- Satellite in orbit: Earth's gravity acts as the centripetal force keeping the satellite in a circular orbit.
- Ball on a string: Tension in the string provides the centripetal force.
- Electron in an atom: Electrostatic attraction to the nucleus acts as centripetal force (in the Bohr model).
- Roller coaster loop: Normal force from the track provides centripetal force at the top of the loop.
FAQs
Is centripetal force a real force?
Yes. Centripetal force is a real net force directed toward the center of circular motion. It is always provided by some physical interaction — gravity, tension, friction, or normal force.
What is the difference between centripetal force and centripetal acceleration?
Centripetal acceleration is a = v²/r (the rate of change of velocity direction). Centripetal force is simply F = m × a = m × v²/r — mass times centripetal acceleration.
Can centripetal force be negative?
In physics, centripetal force has a defined positive direction (toward the center), so its magnitude is always positive. A negative result in a calculation would indicate an error in the input values.
What happens if centripetal force disappears?
If the centripetal force suddenly vanishes (e.g., a string breaks), the object continues in a straight line tangent to the circular path at the point of release — as dictated by Newton's first law.