Friction is the force that resists sliding between two surfaces in contact, and its size follows a simple rule: f = μN. The friction force is the coefficient of friction μ — a number for that particular pair of materials — multiplied by the normal force N pressing them together. On a flat, level floor that normal force is just the object's weight, mg, so a heavier object grips harder. Remarkably, the contact area doesn't enter the formula at all; only the coefficient and the normal force matter.
Reviewed: June 20, 2026 · Author: Naveen P N, Founder — AI Calculator · Verified against: the Coulomb model of dry friction f = μN.
The friction equations
The coefficient μ is dimensionless, so the friction force comes out in the same unit as the normal force (newtons). To find the friction on a resting object, first get the normal force — weight on the level, or mg·cos θ on a slope — then multiply by the coefficient. Use the static coefficient for the maximum force before motion starts, and the kinetic coefficient for the steady force once it is sliding.
Worked example — a sliding block
Scenario: A 10 kg block sits on a level floor with a coefficient of kinetic friction of 0.3. What friction force resists its sliding?
The friction force is about 29.4 N. If the normal force were a round 100 N — say the block were pressed down slightly — the friction would be exactly 30 N. Double the coefficient to 0.6 and the friction doubles to roughly 59 N; widen the block's footprint and nothing changes, because area plays no part in f = μN. To start the block moving you would need to overcome the slightly larger static-friction maximum first.
Frequently Asked Questions
f = μ × N. e.g. 0.3 × 100 N = 30 N. On level ground N = mg, so a 10 kg block has N ≈ 98.1 N.
A dimensionless ratio μ = f/N. Rubber on concrete ≈ 1.0; ice on steel ≈ 0.03. Static > kinetic.
The perpendicular support force. On the level N = mg; on a slope N = mg·cos θ.
No — f = μN has no area term. Same weight, same friction, whatever the contact patch.
Static resists starting (up to μ_s·N); kinetic resists sliding (μ_k·N). Kinetic is usually a bit smaller.