Centripetal Force Calculator: F = mv^2 / r

The inward force needed to keep an object moving in a circle.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Choose which quantity you want to find.

Enter the other values in the units shown.

The calculator gives the answer with the formula, the substituted numbers, and the answer in other units.

Formulas used

  • F = \frac{m\,v^2}{r}
  • v = \sqrt{\frac{F\,r}{m}}

Worked example

With the default numbers in the calculator above:

  1. The formula, arranged to find the centripetal force: centripetal force = (mass x speed^2) / (radius)
  2. Put the values in (every value in its SI unit): centripetal force = (1000 x 20^2) / (50)
  3. The answer: centripetal force: 8000 N
  4. The same answer in other units: 8 kN; 815.773 kgf; 1798.47 lbf

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: What do you want to find? Speed; Centripetal force (leave it as it is if this is what you are finding) 8000 N; Mass (leave it as it is if this is what you are finding) 1000 kg; Radius (leave it as it is if this is what you are finding) 50 m.

  1. The formula, arranged to find the speed: speed = square root of ((centripetal force x radius) / (mass))
  2. Put the values in (every value in its SI unit): speed = square root of ((8000 x 50) / (1000))
  3. The answer: speed: 20 m/s
  4. The same answer in other units: 72 km/h; 44.7387 mph

Common questions

What is the formula for centripetal force?

Mass times speed squared divided by the radius. A 1000 kg car at 20 m/s round a 50 m bend needs 8000 N.

What provides the force for a car on a bend?

Friction between the tyres and the road, or the banking of the road.

What happens if the force is too small?

The object moves in a wider circle or goes off in a straight line, as when a car skids on a bend.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Any school physics text (circular motion).

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