Solve centripetal force, mass, velocity, or radius for circular motion using F = mv²/r, with matching acceleration and angular-velocity context. Use it to test different inputs quickly, compare outcomes, and understand the main factors behind the result before moving on to related tools or deeper guidance.
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Solve the circular-motion variable you are missing Use the centripetal-force relationship to solve for force, mass, velocity, or radius,
then read the matching acceleration and angular-velocity context from the same setup.
Circular motion result
250 N
Solved centripetal force from F = mv² / r.
Force
250 N
Mass
5 kg
Velocity
10 m/s
Radius
2 m
Centripetal acceleration
50 m/s²
Angular velocity
5 rad/s
Interpretation
Higher speed raises force with the square of velocity, so doubling speed quadruples the
centripetal force when mass and radius stay fixed. A larger turning radius reduces the
force needed to keep the same object in circular motion.
Centripetal force calculator: solve force, mass, velocity, or radius for circular motion
A centripetal force calculator helps you solve the circular-motion relationship F = mv² / r in the direction you actually need. Instead of only returning force, this version can also solve for mass, velocity, or radius, then show the matching centripetal acceleration and angular-velocity context so the result is easier to interpret in real turning-motion problems.
What centripetal force is actually describing
Centripetal force is not a separate kind of force in the way weight or tension is. It is the inward net force required to keep an object moving in a circular path. That inward force can come from tension, gravity, friction, the normal force, or a combination of forces depending on the situation.
The important idea is direction: the required force always points toward the center of the circle. Without that inward force, the object would continue in a straight-line path rather than curve around the circle.
How the centripetal-force formula works
The circular-motion relationship is F = mv² / r. Mass increases the force requirement directly, radius reduces it, and velocity has the strongest effect because it is squared. That means even a modest speed increase can produce a large increase in the force required to maintain the same turn radius.
This is why solve-for mode matters. In some problems you know the turning radius and speed and need the force. In others you know the safe force limit and want the largest possible radius or the speed that stays within that force. The same formula supports all of those workflows.
F = mv² / r
Core centripetal-force relationship for uniform circular motion.
a_c = v² / r
Centripetal acceleration derived from the same circular-motion setup.
ω = v / r
Angular velocity for the same motion when linear speed and radius are known.
Worked example
Suppose a 5 kg object moves at 10 m/s around a 2 m radius circle. The required centripetal force is 5 × 10² / 2 = 250 N. The matching centripetal acceleration is 10² / 2 = 50 m/s², and the angular velocity is 10 / 2 = 5 rad/s.
Now reverse the question. If the force limit is 250 N, the mass is 5 kg, and the radius is 2 m, the maximum speed is √(Fr / m) = √(250 × 2 / 5) = 10 m/s. That is why the same page is useful as both a direct force calculator and a circular-motion constraint solver.
What this calculator does not cover
This page assumes uniform circular motion. It does not model changing speed around the path, tangential acceleration during spin-up or braking, or full dynamics where multiple forces need to be resolved component by component.
It is also a scalar solver. It gives the magnitude of the inward force required for circular motion, but it does not draw free-body diagrams or determine which specific real-world force provides that inward component in a more complex system.
Usually no. It is the inward net force needed for circular motion. Depending on the situation, that inward force may be supplied by gravity, friction, tension, the normal force, or another real force.
Why does speed affect centripetal force so strongly?
Because velocity is squared in F = mv² / r. If speed doubles while mass and radius stay the same, the required centripetal force becomes four times larger.
Can this calculator solve for speed instead of force?
Yes. This page supports solve-for modes for force, mass, velocity, and radius so you can rearrange the same relationship without doing the algebra manually.
Does this work for non-uniform circular motion?
Only partly. The centripetal-force magnitude still describes the inward component required for curvature, but non-uniform motion also introduces tangential acceleration and may need a fuller dynamics treatment.
