Friction is the force that resists two surfaces sliding past each other, and it comes down to just two numbers: how rough the contact is (μ) and how hard the surfaces are pressed together (N). This calculator applies f = μN directly, extends it to an object on a slope, and lets you rearrange the formula to solve for any missing piece.
How the Friction Calculator works
The core relationship is f = μN: friction force equals the coefficient of friction times the normal force. μ is a property of the two materials in contact (rubber on asphalt, steel on ice, and so on) and doesn't depend on the size of the contact area in the idealized model used here. N is whatever perpendicular force is holding the surfaces together — on flat ground that's just weight; on a slope it's the perpendicular component of gravity, N = mg·cosθ.
Inputs and what they mean
The coefficient of friction (μ) is unitless and typically falls between about 0.04 (ice on ice) and 1+ (rubber on dry concrete) — look up a reference table for your specific materials if you need a precise value. The normal force (N) is in newtons; if you only know a mass, convert with N = mg using g = 9.81 m/s². On the incline tab, mass (m) and angle (θ) combine with μ to find both the normal force and the force pulling the object down the slope.
Limits and edge cases
This calculator uses the simple Coulomb friction model, which assumes friction is independent of contact area and sliding speed — real materials deviate from this at very high speeds, very high pressures, or with lubrication. It also doesn't distinguish a static coefficient from a kinetic one; enter whichever value matches your situation (static to check if something starts moving, kinetic if it's already sliding). For a precise engineering calculation, consult a materials reference for the actual μ of your surfaces.