Centripetal force calculator

A centripetal force calculator works out the force needed to keep an object moving in a circle: F = mv²/r, or F = mω²r with the angular velocity. A 1,200 kg car going round a 50 m bend at 20 m/s needs 1,200 × 20² ÷ 50 = 9,600 N towards the centre. Our Circular Motion Calculator finds the force, speed, radius or mass, and gives the angular velocity, period, frequency and acceleration alongside.

It opens on that car: Force, From v, with 1,200 kg, 20 m/s and 50 m.

Try it

Circular Motion Calculator

Find centripetal force, acceleration and angular velocity

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How to use the centripetal force calculator

1. Under Calculate, choose a group: Force, Acceleration, Rotation or Period.
2. In the second row, choose what to find. Force has From v, From ω, Speed, Radius and Mass; Acceleration has From v, From ω, Speed and Radius.
3. Type the values you know, and pick units: speed in km/h or mph, angular velocity in rad/s, deg/s or rpm.
4. Read the answer and the working, then the extra readings: angular velocity, period, frequency and acceleration, as they apply.

Practice and help sets centripetal force, acceleration, angular velocity and period questions with worked solutions. Our centripetal force guide explains the physics behind the formula.

The circular motion formulas

The force always points towards the centre of the circle. It is not a new kind of force: friction, tension, gravity or a normal reaction provides it. Without it, the object would carry on in a straight line.

Worked examples you can check in the calculator

Example 1: a car on a bend

The calculator gives 9,600 N, with an angular velocity of 0.4 rad/s, a period of 15.708 s for a full circle and an acceleration of 8 m/s².

Example 2: a ball on a string, from ω

A 0.5 kg ball is whirled on a 1.2 m string at 6 rad/s. Choose Force, From ω:

That is the tension the string must supply. The calculator also gives a period of 1.05 s.

Example 3: the fastest speed round a bend

Friction between the tyres and a flat road can give at most 7,200 N to a 1,000 kg car on a 40 m bend. Choose Force, Speed:

Any faster and friction cannot supply the force needed, so the car slides outwards. The calculator gives 16.97 m/s, which is about 61 km/h.

Example 4: a spin dryer in rpm

A washing machine drum of radius 0.25 m spins at 1,200 rpm. Choose Acceleration, From ω, set the angular velocity unit to rpm and type 1200. In rad/s, ω = 1200 × 2π ÷ 60 = 125.7 rad/s:

That is about 400 times g, which is why the drum squeezes water out of the clothes so well. The calculator gives 3,947.8 m/s², with a period of 0.05 s.

Check yourself:

What the calculator does not do

• No banked tracks or vertical circles. For a banked curve, the horizontal part of the normal reaction gives the force; for a loop, weight and tension or the reaction combine. Work these out by hand, then use the calculator for F = mv²/r.
• No friction coefficient input. For a flat bend, find the maximum friction μmg first, then use it as F in the Speed mode, as in Example 3.
• Uniform circular motion only. It assumes a constant speed round the circle.

Common mistakes

• Drawing the force outwards. Centripetal force points towards the centre. The outward "push" you feel is your body trying to carry on in a straight line.
• Forgetting to square v or ω. F = mv²/r, so doubling the speed needs four times the force.
• Using rpm in mω²r. Convert to rad/s first: multiply rpm by 2π ÷ 60. The calculator does this if you set the unit.
• Using the diameter as r. r is the radius of the circle.
• Adding centripetal force to a free-body diagram. It is the resultant of the real forces, not an extra one.

Practise circular motion in a short timed paper

Circular motion comes up in A-level Physics: Year 2 practice in the UK, and in College Physics (Calculus Based) in the US. Each daily paper is a short timed paper of 8 questions worth 25 to 35 marks, and the papers mix topics. Our angular velocity guide covers ω, and the Orbit Simulator shows gravity providing the centripetal force for planets.

Read next

Physics · MechanicsCentripetal force: formula F = mv²/r, with examplesWhat centripetal force is, the formulas F = mv²/r and F = mω²r, centripetal acceleration, what provides the force, and examples from cars to satellites.