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Physics

Calculator Use

The friction calculator solves for the unknown variable using the friction equation f = μN. Calculate friction f, coefficient of friction μ or normal force N. Enter two values to calculate the third.

You can enter numbers, decimals or scientific notation as in 3.45e22.

Friction is the force that resists motion when two surfaces come into contact with each other. If the two surfaces do not move with respect to one another it is called static friction. When the two surfaces move and slide against each other it is called kinetic friction.

The Friction Equation

Variables in the Friction Equation

• \( f \) = friction force, in newtons
• \( \mu \) = coefficient of friction
• \( N \) = normal force, in newtons

Friction can be described as the coefficient of friction multiplied by the normal force. The Friction Calculator uses the formula f = μN, or friction f is equal to the coefficient of friction μ times the normal force N.

Note that the standard units for the friction equation is newtons. If you enter other units of measure for your calculation the calculator will do the units conversion for you. The coefficient of friction is a multiplying factor and does not have a unit.

Friction Formulas

Solve for friction, coefficient of friction or normal force using the following formulas:

Calculate f Given μ and N
Calculate friction force given coefficient of friction and normal force:

Calculate μ Given f and f
Calculate coefficient of friction given friction force and normal force:

Calculate N Given μ and f
Calculate normal force given coefficient of friction and friction force:

Normal Force as a Function of Mass and Gravity

A simple form of the normal force equation is N = mg where the normal force N is equal to mass m times gravity g. This calculator allows you to enter mass and gravity instead of the normal force which is then also calculated.

Solve for friction force and coefficient of friction where the normal force equation is:

Variables in the Normal Force Equation

• \( N \) = normal force
• \( m \) = mass
• \( g \) = gravity

Calculate f Given μ, m and g
Calculate friction force given coefficient of friction, mass and gravity:

Calculate μ Given f, m and g
Calculate coefficient of friction given friction force, mass and gravity:

Example: Compare Friction Forces - Rubber vs. Banana Peel on Linoleum

You and a friend have decided to compare the frictional forces of rubber versus banana peel on linoleum flooring material. You can use the first Normal Force Equation above to calculate f Given μ, m and g.

After doing some research you and your friend have found that the coefficient of friction for the soles of his sneakers against lineoleum is 0.53. And the coefficient of friction for the inside of a banana peel against linoleum is 0.07. Your friend weighs 65 kg, and you can see from the Planetary Gravity Table below that standard gravity on Earth is 9.81 m/s^2.

First, set up your equation to find the friction force of rubber on linoleum. You want to use the formula f = μmg.

f_rubber = 0.53 * 65 kg * 9.81 m/s²

f_rubber = 337.95

So the frictional force of your friend wearing sneakers on lineoleum is 337.95 newtons. Note that your use of kg and m/s² is standard for the equation to result in some number of newtons. If you want to use other units of measure be sure to convert your units to kg, m/s², and newtons before pluging your numbers into the equations.

Next, set up your equation to find the friction force of the slippery inside of a banana peel on linoleum:

f_{banana peel} = 0.07 * 65 kg * 9.81 m/s²

f_{banana peel} = 44.64 N

So the frictional force of your friend stepping on a banana peel on lineoleum is 44.64 newtons.

What does this mean? A newton is defined as the force required to move a mass of 1 kg at a speed of 1 m/s². Looking at the friction force of your friend wearing his sneaker on lineoleum, it would take 337.95 newtons to start your friend sliding across the linoleum floor (wearing his sneaker, standing on one leg).

If your friend was standing on a banana peel, slippery side down, it would take 44.64 newtons to start your friend sliding. If you divide 337.95 by 44.64 you can see it would take about 7.5 times more force to slide your friend across the lineoleum via sneaker vs. banana peel.

If you were on a different planet the force of gravity would be different than it is on Earth. This reference table provides the gravitational force for the sun, moon and each planet in our solar system.

Table source: Planetary Fact Sheet - NASA

Standard gravity (g_n): 1.00g_n is equal to 9.80665 m/s² gravity on Earth.