Friction Force and Coefficient Calculator

How is friction force calculated?

When two surfaces are pressed together, the force resisting sliding is proportional to the normal force: F = μ × N. Here μ is the coefficient of friction and N is the force pressing at right angles to the surface. For an object resting on a level surface N = m × g. On a slope it is N = m × g × cos θ.

Static and kinetic friction

Starting an object moving is harder than keeping it sliding, so there are two coefficients: static (μ_s) and kinetic (μ_k). While the object is at rest, static friction matches the applied force up to a maximum of μ_s × N. Once sliding starts the force drops to μ_k × N.

How do you measure the coefficient?

There are two easy ways. Pull the object across a level surface with a spring scale: μ = F / N. Or tilt the surface slowly. The angle at which the object starts to slide gives the static coefficient: μ_s = tan θ.

Example

A 50 kg crate rests on a level floor with a coefficient of 0.3. The normal force is 50 × 9.80665 = 490.3 N and the friction force is 0.3 × 490.3 = 147.1 N. On a 30 degree ramp the normal force is reduced by cos 30°.

Limits

The coefficient belongs to the pair of surfaces, not to one material, and can change several times over with cleanliness, roughness, oil and moisture. The listed values are approximate textbook figures. For brakes, clutches, clamped joints and similar work, use manufacturer data or a measurement.