Calculators
Centripetal Force Calculator
Solve force, acceleration, speed, mass, or radius for circular motion.
Solve ideal uniform circular motion using centripetal acceleration a = v²/r and force F = mv²/r.
Calculated force
40 N
F = mv²/r
This ideal model assumes constant speed around a circular path. It calculates the inward net force required for circular motion, not friction limits or structural safety margins.
About This Tool
Centripetal force is the inward net force needed to keep an object moving along a circular path. This calculator uses a = v²/r and F = mv²/r to solve common uniform circular motion questions: required force, centripetal acceleration, mass, speed, or turn radius. It is useful for physics homework, lab checks, and quick estimates where speed is constant and the path radius is known. All calculations run locally in your browser.
How To Use It
- Choose whether to solve for force, acceleration, mass, speed, or radius.
- Enter the known positive values and choose matching units.
- Use radius as the distance from the centre of the circular path to the moving object.
- Read the result as an ideal uniform-circular-motion value and compare it with the stated assumptions.
Examples
Force for a 2 kg object
A 2 kg object moving at 10 m/s around a 5 m radius circle needs F = mv²/r = 40 N of inward net force.
Centripetal acceleration
At 10 m/s with a 5 m radius, a = v²/r = 20 m/s², which is a little over 2 g.
Find the radius
If a 2 kg object moving at 10 m/s has 40 N of inward net force, r = mv²/F = 5 m.
Find speed
With 40 N of centripetal force, 2 kg of mass, and a 5 m radius, v = √(Fr/m) = 10 m/s.
Useful Notes
Core formulas
Centripetal acceleration is a = v²/r. Multiplying by mass gives the inward net force F = ma = mv²/r. Rearranging those equations gives m = Fr/v², v = √(Fr/m), and r = mv²/F.
Direction of the force
Centripetal force points toward the centre of the circular path. It is not an extra type of force by itself; it is the net inward effect of forces such as tension, gravity, friction, or a normal force.
Speed and radius assumptions
The calculator assumes a constant speed along a circular path. The radius should be the actual turn radius or distance from the rotation centre to the object's centre of mass.
Units
Inputs can use kilograms, grams, pounds, metres per second, kilometres per hour, miles per hour, feet per second, metres, centimetres, millimetres, feet, newtons, kilonewtons, and pounds-force. Calculations convert through SI units internally.
Limits of the model
This educational calculator does not determine whether tyres, ropes, tracks, structures, or real materials can safely provide the force. Real systems can involve changing speed, banking, drag, deformation, and safety constraints.
FAQ
Is centripetal force a separate physical force?
No. It is the net inward force required for circular motion. Depending on the situation, that inward force may come from tension, friction, gravity, a normal force, or a combination of forces.
Can centripetal acceleration be larger than gravity?
Yes. The acceleration v²/r can be much larger than standard gravity when speed is high or radius is small. The g output unit shows that comparison directly.
What happens if speed doubles?
Force and acceleration scale with speed squared. Doubling speed makes the required centripetal force four times larger if mass and radius stay the same.
Can I use this for a banked road or roller coaster?
Use it only for the basic inward force or acceleration calculation. Banked turns, friction limits, vertical loops, and safety checks need additional equations and assumptions.
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