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Centripetal Force Calculator

With assumed mass 1,200 kilograms, speed 20 meters per second and turn radius 50 meters, the required net inward force is 9,600 newtons. The corresponding centripetal acceleration is 8 meters per second squared. These outputs do not predict available tire grip or a safe driving speed.

Doubling speed while holding mass and radius fixed multiplies the required force by four.

Centripetal Force Calculator: inputs

Calculated result
Centripetal force (N)9,600
Centripetal acceleration (m/s²)8

Centripetal Force Calculator: Mass (kg) sensitivity

Centripetal Force Calculator: Mass (kg) and Centripetal force (N)5 calculations vary the “Mass (kg)” input while holding the other entered inputs constant.9607,6801,0808,6401,2009,6001,32010,5601,44011,520

Centripetal Force: formula

Centripetal acceleration = v² ÷ r; force = m × v² ÷ r

NIST Physical Measurement Laboratory · OpenStax: Centripetal force

Enter the mass in kilograms, the speed in meters per second and the radius of the turn in meters. The centripetal acceleration is the speed squared divided by the radius, and the force is the mass times that. It is the net inward force needed to keep an object on a circular path, supplied by tire friction, a rope, gravity or a banked road.

Use the radius of the path, not the diameter.

Centripetal Force: worked example

Mass (kg)1,200
Speed (m/s)20
Turn radius (m)50
Centripetal force (N)9,600
Centripetal acceleration (m/s²)8

The equation describes constant-speed circular motion. Banking, friction and other forces must combine to provide the calculated net inward force. In a rotating reference frame an inertial centrifugal force can be included; in an inertial frame it is not an additional physical interaction.

Centripetal Force: changing Mass (kg)

Mass (kg)Centripetal force (N)Centripetal acceleration (m/s²)
9607,6808
1,0808,6408
1,200 (example)9,6008
1,32010,5608
1,44011,5208

Centripetal Force: compare input ranges

InputTested fromToCentripetal force (N): low inputCentripetal force (N): high inputSwing
Speed (m/s)18227,77611,6163,840 (40%)
Turn radius (m)455510,666.78,727.31,939.4 (20%)
Mass (kg)1,0801,3208,64010,5601,920 (20%)

Centripetal Force: individual input comparisons

InputValueCentripetal force (N)Centripetal acceleration (m/s²)
Mass (kg)9607,6808
1,0808,6408
1,2009,6008
1,32010,5608
1,44011,5208
Speed (m/s)166,1445.1
187,7766.5
209,6008
2211,6169.7
2413,82411.5
Turn radius (m)4012,00010
4510,666.78.9
509,6008
558,727.37.3
608,0006.7

Centripetal Force: combined input changes

Mass (kg) / Speed (m/s)162024
9604,915.27,68011,059.2
1,0805,529.68,64012,441.6
1,2006,1449,60013,824
1,3206,758.410,56015,206.4
1,4407,372.811,52016,588.8

Centripetal Force: which assumptions move the result?

Centripetal Force: Centripetal force (N) as Speed (m/s) changesCentripetal force (N) starts at 6,144. Moving Speed (m/s) from 16 to 24 changes it to 13,824, with Mass (kg) 1,200; Turn radius (m) 50 kept fixed.166,144187,776209,6002211,6162413,824
Chart quantityDisplayed settings
Speed (m/s)16 → 24
Centripetal force (N)6,144 → 13,824
Mass (kg)1,200
Turn radius (m)50
Centripetal Force: Centripetal force (N) as Turn radius (m) changesCentripetal force (N) starts at 12,000. Moving Turn radius (m) from 40 to 60 changes it to 8,000, with Mass (kg) 1,200; Speed (m/s) 20 kept fixed.4012,0004510,666.7509,600558,727.3608,000
Chart quantityDisplayed settings
Turn radius (m)40 → 60
Centripetal force (N)12,000 → 8,000
Mass (kg)1,200
Speed (m/s)20

Centripetal Force: values and definitions

Quantity and definitionValue used
Mass (kg)1,200
Speed (m/s)20
Turn radius (m)50
Centripetal force (N)9,600
Centripetal acceleration (m/s²)8

Centripetal Force: half and double Speed (m/s)

Speed (m/s)Centripetal force (N)
102,400
209,600
4038,400

Common error: Treating the outward push as a real force. What you feel is inertia, and the only real force in the turn points inward toward the center.

Physics & Mechanics calculators: Pendulum Period Calculator, Horsepower Calculator, Speed, Distance and Time Calculator, Kinetic Energy Calculator, Newton's Second Law Force Calculator, Uniform Acceleration Calculator.

Moving in a curve needs a force pointing toward the center, and the force grows with the square of the speed. A 1,200 kilogram car at 20 meters per second in a 50 meter turn needs 9,600 newtons, an acceleration of 8 meters per second squared, or about 0.8 g. Tires provide that force through friction, so a tighter curve or a higher speed can exceed what the road offers.

Compare the required force with the friction available. A wet or icy road provides much less than a dry one, at the same speed.

See the general force on the force calculator, the energy on the kinetic energy calculator and the speed relations on the uniform acceleration calculator. The pendulum period and projectile motion pages cover related motion, and the circle circumference calculator handles the geometry.

What provides the centripetal force on a car in a curve?

Friction between the tires and the road supplies it, supplemented by banking when the road surface is tilted toward the inside.

How does speed affect the force needed in a turn?

Force grows with the square of the speed, so doubling the speed needs four times the inward force.

Is centrifugal force real?

In an inertial frame, an object released from circular motion initially follows the tangent if no other force acts.