Last updated: 2026-06-15

Friction Force

Friction is the force that resists sliding between two surfaces in contact. It is what lets you walk without slipping, what brings a rolling ball to rest, and what a car's brakes rely on. For dry surfaces it follows a strikingly simple rule: the friction force is proportional to how hard the surfaces are pressed together, $f = \mu N$. This calculator finds the maximum static friction and the kinetic friction from the normal force and the two friction coefficients, and tells you whether a given push is enough to make the object slide.

Two kinds of friction

Friction comes in two flavours. Static friction acts before anything moves. It is not a fixed number — it grows to match whatever force is trying to start the motion, up to a ceiling of $\mu_s N$. Kinetic friction takes over once sliding begins and stays roughly constant at $\mu_k N$. Because the kinetic coefficient is usually a little smaller than the static one, an object is harder to get going than to keep going; this is why a stuck drawer suddenly jerks loose.

Formula

On a level surface the normal force equals the weight, $N = mg$. On a slope it is smaller — only the component of weight perpendicular to the surface.

Worked example

A 100 N normal force presses a steel block onto a steel surface with $\mu_s = 0.6$ and $\mu_k = 0.4$. The friction limits are:

Push with 50 N and nothing moves — static friction quietly rises to 50 N to cancel it. Push with 80 N and you exceed the 60 N limit, so the block breaks free; once it is sliding only 40 N of kinetic friction acts, leaving a net driving force of $80 - 40 = 40\ \text{N}$ to accelerate it.

Typical coefficients

Friction coefficients depend on the materials and their condition, so treat these as rough guides for the static coefficient: rubber on dry concrete ≈ 1.0, steel on steel ≈ 0.6, wood on wood ≈ 0.4, and steel on ice ≈ 0.03. Lubricated surfaces fall well below 0.1. Kinetic coefficients are usually somewhat lower. Because real surfaces vary, use measured values whenever the answer needs to be reliable.

Limitations

This is the simple Coulomb model of dry friction. It assumes the friction force is independent of the contact area and of sliding speed, which holds well for ordinary solid surfaces but breaks down for lubricated, very smooth, or very fast-moving contacts. It does not cover rolling resistance, fluid drag, or the deformation of soft materials. For an object on a slope, work out the normal force from the perpendicular component of weight first, then apply $f = \mu N$.