Coefficient of Static Friction

What is the Coefficient Of Static Friction?

It is the “The maximum ratio of applied force to normal force with no motion” we all know Frictional force is a force which opposes motion. If we keenly observe, once you apply force to move a body from rest, there exist a point upto which the body resist to move. To move the body the applied force should be greater to overcome this resistance. This maximum resistive force offered by the body against the applied force to continue its state of motion is called Coefficient Of Static Friction.

Coefficient Of Static Friction Formula

Magnitude of frictional force depends on two factors

  • How heavy is the material
  • How rough is the surface

The roughness of the surface is often measured by a parameter called Coefficient Of Static Friction. It is mathematically expressed as the ratio of applied force to the normal reaction. Given by-

\(\mu _{s}=\frac{\vec{F}_{s}}{\vec{F}_{N}}\)

Coefficient Of Static Friction Symbol

It is represented by the greek alphabet \(\mu _{s}\)

Coefficient Of Static Friction units

It is a unit less quantity. As it is the ratio of two forces. The respective S.I units get cancelled. This also implies that, it is a dimensionless quantity.

Coefficient Of Static Friction Example


In the above illustration we can see a heavy wooden box placed on the floor. If you try to push the box away from you. Due to the presence of friction the box is going to say ‘No No I’m not going to go that way!’ The reason for this is, the roughness of surface/floor. If we see the point of contact between the box and the floor with higher resolution, we can see microscopic deformations.

These tiny imperfections present on the surface is going to resist the motion. How much resistance to the motion depends on the force of friction. To understand that, it is important to know about the forces that are acting on the box along with its directions.


  • Force of Gravity\(\left (\vec{F}_{g}\right )\): As a virtue of mass of the box, a force of \(\vec{F}_{g}=mg\) N will be acting downwards.
  • Normal force\(\left ( \vec{F}_{N}\right )\): The force pushing the box upwards, i.e., away from the gravity. Thus, we know that, \(\vec{F}_{N}=mg\) N
  • Applied force\(\vec{F}_{applied}\): The force you are applying on the object to move/push.
  • Frictional force\(\vec{F}_{s}\): A resistive force exerted by the object so as to oppose the motion.

The moment you start pushing the box away from you as shown in the figure(1). Initially it does not move, you push it and it pushes you back, eventually, strong enough, box does started to move. At this point, there exists a small interval between the moment you started pushing the box and the box just started to move, that is were coefficient of static friction comes into the picture. This value plays a crucial role in many applications.

Coefficient Of Static Friction value

This value is directly proportional to the applied force. To simplify the exercise and calculate the values precisely Coefficient Of Static Friction calculator is developed.