Friction Coefficient Calculator

Background.

Hook a spring scale to a loaded crate and pull it level across the floor. The reading climbs while the crate stays put, then the crate jerks free and the reading drops back to a steadier value as it slides. Those two readings, each divided by the force pressing the crate onto the floor, are the crate's two coefficients of friction: static from the peak just before it moved, kinetic from the steady pull while it was moving.

The climb before breakaway is worth understanding. Static friction is not a fixed force; it rises to match whatever you apply, up to a ceiling of μₛ × N. A reading taken while the crate is still resting a light push tells you only how hard you happened to be pulling. That is why the friction input here asks for the limiting force, the value at the moment of slip, or the sustained force during sliding.

The coefficient belongs to a pair of surfaces in a particular state, never to one material. OpenStax's table of approximate values gives rubber on dry concrete 1.0 static and 0.7 kinetic, falling to 0.5–0.7 and 0.3–0.5 when the concrete is wet. Steel on dry steel is listed at 0.6 and 0.3; oil it and the figures collapse to 0.05 and 0.03, which is the whole purpose of lubrication. Teflon on steel sits at 0.04 either way.

Because μ is a ratio of two forces it has no unit, and once you have it the friction for any other load follows from multiplying by the new normal force — provided the surfaces, their condition and the sliding speed stay much the same.

What is friction coefficient calculator?

The coefficient of friction is the ratio of the friction force acting along a contact to the normal force pressing the two surfaces together, μ = F_f ÷ N. The static coefficient μₛ describes the largest friction force the contact can supply before sliding starts, so static friction obeys f ≤ μₛN; the kinetic coefficient μₖ describes the friction while sliding continues and is usually the smaller of the two. Both are dimensionless and describe a specific surface pair under specific conditions, not a property of either material alone.

How to use this calculator.

1. 01Enter the friction force in newtons. For a static coefficient, use the peak pull at the instant the object starts to move; for a kinetic coefficient, use the steady pull that keeps it sliding at constant speed. Pull parallel to the surface.
2. 02Enter the normal force. On level ground with a level pull it equals the weight, mass × 9.81 m/s². On a slope it is weight × cos θ, and anything clamping or pressing the object down adds to it.
3. 03Watch the pull angle. Pulling upward at angle α lifts part of the load and reduces the normal force by F × sin α, so either keep the rope level or subtract that share before entering N.
4. 04If your scale reads in pounds-force or kilograms-force, enter both forces in that same unit. The units cancel, so the coefficient comes out identical.
5. 05Write down the regime and the conditions with the result: static or kinetic, the surface finish, whether it was clean, dry, wet or lubricated.

The formula.

μ = F_f ÷ N, where F_f is the friction force along the contact and N is the normal force perpendicular to it, both in newtons. The relation behind it, F_f = μN, is empirical rather than derived. Guillaume Amontons stated its two surprising parts in 1699: friction is proportional to the load, and it does not depend on the apparent area of contact. Coulomb later added that kinetic friction is roughly independent of sliding speed, and OpenStax confirms it is nearly so at small but nonzero speeds.

The same ratio gives a way to measure μ with no force gauge at all. On a ramp the gravity component along the slope is mg sin θ and the normal force is mg cos θ, so at the angle where an object just begins to slide, μₛ = tan θ; at the angle where it slides down at constant speed, μₖ = tan θ.

The model weakens where its assumptions fail: at high sliding speeds, for soft or sticky materials such as rubber whose contact area spreads with pressure, and for very clean metals that bond on contact. In those cases μ can depend on load and area, and values above 1 are perfectly possible.

A worked example.

Frequently asked questions.

References& sources.

1. [1]OpenStax, University Physics Volume 1, section 6.2, Friction.
2. [2]ASTM G115, Standard Guide for Measuring and Reporting Friction Coefficients (bibliographic standard).
3. [3]BIPM, The International System of Units (SI Brochure), 9th ed., version 3.01, coherent derived units and quantity equations.