Friction calculator

How do you calculate friction?

Friction = coefficient of friction × normal force: f = μN. On a level surface the normal force equals the weight, m × g. Static friction (μs) holds an object still up to a maximum; kinetic friction (μk) acts once it slides (OpenStax University Physics).

Example

OpenStax: a 20.0 kg crate with μs = 0.700 and μk = 0.600 weighs 196 N. It takes more than 137 N to start it moving; once it slides, friction is 118 N, so a 180 N push accelerates it at about 3.1 m/s².

Where do the coefficients come from?

OpenStax’s table of approximate values — for example wood on wood 0.5 static and 0.3 kinetic, shoes on ice 0.1 and 0.05, Teflon on steel 0.04. Real values depend on the surfaces’ condition, so they are given to only one or two digits.

Why is kinetic friction smaller than static?

For most surfaces it takes more force to start something sliding than to keep it sliding — that is why μk is usually lower than μs.

Does the contact area matter?

In this simple model, no — friction depends on the normal force and the coefficient, not on how large the contact area is.

At what angle does an object start sliding down a slope?

When tan θ equals the static coefficient, because the downhill component of weight, mg sin θ, then equals the maximum static friction, μs mg cos θ. For wood on wood with μs = 0.5 that is 26.6°. For forces on a slope in general, see the inclined plane calculator.

Is friction always equal to μ times the normal force?

Only for kinetic friction, and for static friction at the point of slipping. Below that point static friction matches whatever force is applied, up to the maximum μs N, and no more. A box that you push with less than that maximum does not move, and the friction force on it equals your push.

Static, kinetic and the normal force

The friction force opposes sliding. Static friction can take any value from zero up to its maximum, μs × N; once the object slides, kinetic friction is μk × N, usually smaller. N is the normal force, the push of the surface on the object perpendicular to the surface. On a level floor with no other vertical forces N = mg, but on a slope N = mg cos θ, and a push or pull at an angle changes N by its vertical component.

Worked example: a 50 kg wooden crate on a wooden floor

With g = 9.80665 m/s² the weight, and the normal force, is 490.3 N. Using μs = 0.5 and μk = 0.3 for wood on wood, the maximum static friction is 245.2 N and the kinetic friction is 147.1 N. A 200 N push does not move the crate, because it is below 245.2 N. A 300 N push does: the net force is 300 − 147.1 = 152.9 N, so the acceleration is 3.06 m/s². For comparison, with the coefficients 0.1 and 0.05 for shoes on ice, the maximum static friction on the same weight would be only 49.0 N.

Common mistakes

Using the weight as the normal force on an incline overstates friction, since N is only mg cos θ there. Another is treating μ as a fixed property of a material: the table gives approximate values for specific pairs under typical conditions, and moisture, roughness, speed and temperature all change it. Reading the static friction as always equal to μs N is the third, and the fourth is mixing mass with force: N is in newtons, so a mass in kilograms must be multiplied by g first.

Sources: OpenStax University Physics, Volume 1, section 6.2 (friction, including the table of approximate coefficients). Related: inclined plane calculator, force calculator, stopping distance calculator and terminal velocity calculator.