How to Calculate Friction

This finds the friction acting on an object resting on a surface. Friction is proportional to how hard the surfaces are pressed together.

$\mu$ is the coefficient of friction and $N$ is the normal force. On a level floor the normal force is simply the weight of the object, $N = mg$.

Static and kinetic friction

Friction before movement starts is static; friction while sliding is kinetic. Static friction matches whatever force is applied, up to a ceiling of $\mu_s N$, and beyond that the object breaks away. That ceiling is the maximum static friction. Once it is sliding the friction settles a little lower, at $\mu_k N$. This is why something feels heavy to start and lighter once it is going.

Example

A 10 kg object sits on a floor with a static coefficient of 0.5 and a kinetic coefficient of 0.3. The normal force is $10 \times 9.8 = 98$ N. The maximum static friction is $0.5 \times 98 = 49$ N, so a push above 49 N sets it moving. After that the friction is $0.3 \times 98 = 29.4$ N.

Notes

Friction does not depend on the area of contact. Spreading the load over a wider area lowers the pressure by the same factor, and the two effects cancel.

On a slope the normal force is less than $mg$. Use the slope calculator for that case.