Engineering ToolBox - Resources, Tools and Basic Information for Engineering and Design of Technical Applications!

Centripetal and Centrifugal Acceleration Force

Forces due to circular motion and centripetal / centrifugal acceleration.

Sponsored Links

Centripetal and Centrifugal Force are the action-reaction force pair associated with circular motion.

Centripetal acceleration - forces due to circular motion

Centripetal Acceleration

Velocity is a vector - specifying how fast (or slow) a distance is covered and the direction of the movement. Since the velocity vector (the direction) of a body changes when moved in a circle - there is an acceleration.

This  acceleration is named the centripetal acceleration - and can be expressed as

ac = v2 / r  

    = ω2

    = (2 π nrps)2 r   

    = (2 π nrpm / 60)2 r   

    =  (π nrpm / 30)2 r                      (1)


ac = centripetal acceleration (m/s2, ft/s2)

v = tangential velocity (m/s, ft/s)

r = circular radius (m, ft)

ω = angular velocity (rad/s)

nrps = revolutions per second (rev/s, 1/s)

nrpm = revolutions per min (rev/min, 1/min)

Centripetal Force

According Newton's second law the centripetal force can be expressed as

Fc = m ac

    = m v2 / r  

    = m ω2 r        

    = m (2 π ns)2

    = m (2 π nrpm / 60)2

    =  m (π nrpm / 30)2 r                             (2)


Fc = centripetal force (N, lbf)

m = mass (kg, slugs)

According to Newton's Third Law the centripetal force acting on the object has a centrifugal force of the same magnitude acting in the opposite direction.

Example - the Centripetal Acceleration and Force acting on a Car through a Curve

road banked turn

Metric Units

A car with mass 1000 kg drives through a curve with radius 200 m at speed 50 km/h. The centripetal acceleration can be calculated as

ac = ((50 km/h) (1000 m/km) (1/3600 h/s))2 / (200 m)

   = 0.965 m/s2

   = 0.1 g


1 g = acceleration of gravity (9.81 m/s2)

The centripetal force can bee calculated as

Fc = (1000 kg) (0.965 m/s2)

    = 965 N

    = 0.97 kN 

Related to the gravity force - weight:

Fg = (1000 kg) (9.81 m/s2)

    = 9810 N

    = 9.8 kN

Imperial Units

A car with weight (gravity force) 3000 lb travels through a curve with radius 100 ft with speed 15 miles/h.

The mass of the car can be calculated as

m = (3000 lb) / (32 ft/s2)

   = 94 slugs

The centripetal acceleration can be calculated as

ac = ((15 miles/h)(5280 ft/mile) / (3600 s/h))2 / (100 ft)

   = 4.84 ft/s2

The centripetal force can bee calculated as

Fc = (94 slugs) (4.84 ft/s2)

    = 455 lbf

Centripetal (Centrifugal) Calculator - velocity

This calculator can be used if the velocity of an object is known - like a car in a turning curve.

m - mass of object (kg)

v - velocity of object (m/s)

r - radius of curve (m)

Centripetal force acting on a car in a curve

Centripetal (Centrifugal) Force - rpm

Equation (2) can be modified to express centripetal or centrifugal force as a function of revolution per minute - rpm - as

Fc = 0.01097 m r nrpm2                              (3)


nrpm = revolution per minute (rpm)

Centripetal (Centrifugal) Calculator - rpm

This calculator can be used if revolution speed of an object is known - like a turning bowl in a lathe.

m - mass (kg)

nrpm - revolutions per minute (rpm)

r - radius (m)

Centrifugal Force

Force is an abstraction representing the push and pull interaction between objects.  Newton's third law states that 

  • for every acting force there is an equal and opposite reaction force

Therefore there must be an equal and opposite reaction force to the Centripetal Force - the Centrifugal Force.

Sponsored Links

Related Topics

  • Dynamics

    Motion - velocity and acceleration, forces and torque.
  • Mechanics

    Forces, acceleration, displacement, vectors, motion, momentum, energy of objects and more.

Related Documents

Sponsored Links

Engineering ToolBox - SketchUp Extension - Online 3D modeling!

3D Engineering ToolBox Extension to SketchUp - add parametric components to your SketchUp model

Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your Sketchup model with the Engineering ToolBox - SketchUp Extension - enabled for use with older versions of the amazing SketchUp Make and the newer "up to date" SketchUp Pro . Add the Engineering ToolBox extension to your SketchUp Make/Pro from the Extension Warehouse !

Translate this Page

Translate this page to Your Own Language .

About the Engineering ToolBox!

Privacy Policy

We don't collect information from our users. More about


This page can be cited as

  • The Engineering ToolBox (2009). Centripetal and Centrifugal Acceleration Force. [online] Available at: [Accessed Day Month Year].

Modify the access date according your visit.


3D Engineering ToolBox - draw and model technical applications! 2D Engineering ToolBox - create and share online diagram drawing templates! Engineering ToolBox Apps - mobile online and offline engineering applications!

Unit Converter


Sponsored Links