Centripetal Force Calculator
Centripetal force F = m v² ÷ r and centripetal acceleration from mass, speed (or angular speed, rpm or period) and radius, or solve for any one of them.
Result…
How it's calculated
F = m v² ÷ r = m ω² r a = v² ÷ r = ω² r ω = 2π × rpm ÷ 60 = 2π ÷ period v = ω r
An object moving in a circle at steady speed is always changing direction, so it accelerates toward the centre at v² ÷ r. By Newton's second law that needs a net inward force of m v² ÷ r. Speed can be given along the path, or as angular speed, revolutions per minute or the time for one turn, which are converted with v = ω r. Unit factors are exact: 1 lb = 0.45359237 kg, 1 lbf = 4.4482216152605 N, 1 mph = 0.44704 m/s, 1 ft = 0.3048 m.
Your numbers, step by step
About the Centripetal Force calculator
This centripetal force calculator works out the inward force F = m v² ÷ r that keeps something moving in a circle, along with its centripetal acceleration in m/s² and in g. Give the motion as a speed along the path in m/s, km/h, mph or ft/s, or as angular speed, revolutions per minute or the time for one turn. You can also solve for the mass, the speed or the radius when you know the force. Mass works in kg, g or lb, force in N, kN or lbf, and radius in metres, centimetres, feet or inches, all with exact conversion factors. It suits physics homework, checking a car taking a bend, a ball on a string, a centrifuge or a fairground ride. Every step is shown with your numbers, including the check that F = m × a.
How to use it
- Choose what to “Solve for”: force, mass, speed or radius.
- Enter the known values, such as “Mass” and “Radius”, and pick each unit.
- Pick how the “Motion given as” is known: speed, angular speed, revolutions per minute or period.
- Read the answer, the centripetal acceleration and the speed, rpm and time per turn underneath.
Worked example
A 1200 kg car takes a bend of radius 40 m at 54 km/h. 54 km/h is 15 m/s, so the centripetal force is 1200 × 15² ÷ 40 = 6750 N. The acceleration is 15² ÷ 40 = 5.625 m/s², about 0.57 g, and the friction between the tyres and the road has to supply all of that force.
Updated
Questions people ask
How do I calculate centripetal force?
Multiply the mass by the speed squared and divide by the radius: F = m v² ÷ r, with mass in kg, speed in m/s and radius in metres to get newtons. With angular speed ω in rad/s, use F = m ω² r instead.
What is the formula for centripetal acceleration?
a = v² ÷ r, or a = ω² r. It points toward the centre of the circle, and dividing it by 9.80665 m/s² gives it in g.
How do I convert rpm to speed for a spinning object?
Angular speed ω = rpm × 2π ÷ 60 in rad/s, and the speed at radius r is v = ω × r. The calculator does this for you when you choose revolutions per minute.
Is centripetal force a real force?
It is the name for the net inward force, not an extra one. Tension in a string, friction on a tyre, gravity on a satellite or the push of a wall supplies it. A common mistake is to add it to a force diagram as well as the force that provides it.
Why does going twice as fast need four times the force?
Speed is squared in the formula, so doubling it multiplies the force by 2² = 4. Halving the radius at the same speed only doubles it. For the force needed to speed something up in a straight line, use the force calculator.
What does the centripetal force calculator not cover?
It assumes steady circular motion at constant speed. It does not tell you whether tyres or a rope can actually supply the force, which depends on friction, banking and material strength, so do not use it alone for safety-critical design.