Centripetal Force Calculator

How to use the Centripetal Force Calculator

1. 1Enter the mass, the speed and the radius of the circle.
2. 2Pick the units or options from the menus if the centripetal force tool offers them.
3. 3Read the centripetal force in the large result box.
4. 4Look at the extra rows for related figures.
5. 5Press Copy result to keep the answer.

When you need the centripetal force

Road engineers use the formula to design bends and banking so that tyres can supply the needed force. Amusement park designers use it to find the g-forces on loops, and astronomers use it for orbits, where gravity supplies the inward force.

A quick use is to see why speed matters so much in a corner: doubling the speed needs four times the grip. Halving the radius, a tighter turn, doubles the force. That is why sharp bends need lower speed limits.

How the centripetal force is worked out

Centripetal acceleration = speed² ÷ radius. Centripetal force = mass × speed² ÷ radius. A 1,000 kg car going round a bend of radius 50 m at 20 m/s needs 1,000 × 20² ÷ 50 = 8,000 N of grip from the tyres. The acceleration is 8 m/s², about 0.82 g, and a lap would take 15.7 seconds.

Every answer on this page comes from that one rule, so you can check any result by hand with a calculator. The figures shown underneath, such as other units, are conversions of the same answer.

• Mass in kg or lb
• Speed in several units
• Shows g-force and lap time

Mistakes to avoid with centripetal force

Centripetal force is not a new force that pushes things; it is the name for whatever force, such as friction, tension or gravity, is already pointing to the centre. The outward feeling you get in a turn is inertia, not a real outward force.

On phone and computer

On a phone, type into the boxes one after another and read the centripetal force underneath; Copy result puts it on the clipboard for a message or a note. On a computer the inputs sit on the left and the answer on the right, so you can change one figure and watch the centripetal force move. The centripetal force calculator works the same on both. The force depends on speed and radius, so check the speed with Speed Calculator and the radius with Circle Calculator. Force Calculator covers the F = m × a case, and Kinetic Energy Calculator shows how much energy the moving object carries.

Features

• Double the speed, four times the force
• Smaller radius, larger force
• It is a role, not a new force
• Clear messages when the centripetal force inputs make no sense
• Copy the result with one tap
• Private: nothing is uploaded

Frequently asked questions