Centripetal Force Calculator: Formula & Examples

A centripetal force calculator determines the inward force required to keep an object moving in a circular path. You enter the object’s mass, its speed, and the radius of the circle, and the calculator returns the force in newtons (or pounds-force). This page includes the formula, a worked example, and practical guidance for using it in physics problems or real-world applications.

Formula

The standard formula for centripetal force is:

F = m × v² / r

Where:

• F = centripetal force (newtons, N)
• m = mass of the object (kilograms, kg)
• v = speed of the object (meters per second, m/s)
• r = radius of the circular path (meters, m)

The related centripetal acceleration is a = v² / r, measured in m/s². Force and acceleration point toward the center of the circle at every instant.

Worked Example

Using the default values from the calculator above (mass = 2 kg, speed = 10 m/s, radius = 5 m):

1. Square the speed: v² = 10² = 100 (m/s)²
2. Multiply by mass: 2 × 100 = 200 kg·(m/s)²
3. Divide by radius: 200 / 5 = 40 N

The centripetal force is 40 newtons. The centripetal acceleration is 100 / 5 = 20 m/s², which is roughly 2 times the acceleration due to gravity (about 9.81 m/s²).

When to Use This Calculator

Use the centripetal force calculator whenever you need the inward force for uniform circular motion—motion at constant speed along a circular path. Common situations include:

• Physics homework: satellite orbits, conical pendulums, banked curves
• Engineering: tension in a string whirling a mass, forces on a rotating part
• Vehicle dynamics: required friction on a curve (with mass and speed known)
• Amusement park rides: forces on riders in a rotating ride

The result tells you the net inward force needed. If the actual available force (friction, tension, gravity component) is less than this value, the object will not stay on the circle—it will fly outward tangentially.

How to Read the Result

The calculator outputs force in newtons (SI). In US customary units, you might want pounds-force (lbf). One newton equals about 0.2248 pounds-force, so 40 N ≈ 9.0 lbf. The acceleration output helps you compare to gravity: 1 g ≈ 9.81 m/s². An acceleration of 20 m/s² means the object feels about 2 g of inward acceleration.

Remember that the force is always perpendicular to the velocity. It does no work on the object (speed stays constant), but it continuously changes the direction of motion.

Common Mistakes and Unit Mix-ups

The most frequent error is mixing units. The formula works only with consistent units: kilograms, meters, seconds. If you enter mass in grams or speed in km/h, the result will be off by factors of 1000 or 3.6. Convert first:

• 1 kg = 1000 g
• 1 m/s = 3.6 km/h (so divide km/h by 3.6 to get m/s)
• 1 m = 100 cm

Another common mistake is using diameter instead of radius. The radius is half the diameter. Also, ensure the speed is constant—if the object speeds up or slows down, there is also a tangential force, and the total force is not purely centripetal.

Rounding too early can cause small errors. Keep intermediate values with more digits and round only the final answer.

Limits of the Formula

The formula F = m·v²/r applies only to uniform circular motion (constant speed). It does not account for:

• Changing speed (tangential acceleration)
• Non-circular curved paths (use more general dynamics)
• Relativistic effects (speeds near the speed of light)
• Forces like gravity or friction that may provide the centripetal force—this calculator gives the required net force, not the source

Also, the formula assumes a point mass. For extended objects rotating about their own axis, use moment of inertia, not this simple form.

Frequently Asked Questions

What is the difference between centripetal and centrifugal force?

Centripetal force is a real, inward force acting on the object (e.g., tension, friction, gravity). Centrifugal force is a fictitious outward force experienced in a rotating reference frame. In an inertial frame, only centripetal force exists.

Can I use this calculator for a car turning a corner?

Yes, if you know the car’s mass, speed, and turn radius. The result is the total lateral force needed from friction or banking. If the tire-road friction cannot provide that force, the car will skid outward.

What if I only know the frequency or period of rotation?

Convert to speed first: v = 2Ï€r/T (T = period in seconds) or v = 2Ï€rf (f = frequency in Hz). Then use the calculator.

Why does the force increase with the square of speed?

Because acceleration is v²/r. Doubling speed quadruples the required force. That’s why sharp turns at high speed are so dangerous.

What are the units for the result in US customary?

If you use pounds-mass, feet, and seconds, the force will be in poundals. More commonly, convert to pounds-force: 1 N ≈ 0.2248 lbf. The calculator gives newtons; multiply by 0.2248 for lbf.

Is centripetal force a new kind of force?

No. It is a role that any existing force can play—tension, gravity, friction, or a normal force. The calculator tells you how much net inward force is needed, not what provides it.

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in m | Mass | kg | 2 | 0
in v | Speed | m/s | 10 | 0
in r | Radius | m | 5 | 0
out F | Centripetal force | N | m * v^2 / r | 2
out a | Centripetal acceleration | m/s² | v^2 / r | 2