Friction Calculator (f = μN)
Solve f = μN for friction force, the coefficient, or the normal force.
Force in newtons (N); the coefficient μ is dimensionless.
Friction force is found with f = μN — multiply the coefficient of friction by the normal force. With μ = 0.5 and a normal force N = 200 N, the friction force is f = 0.5 × 200 = 100 N. Rearrange to μ = f ÷ N or N = f ÷ μ to solve for the others.
What the friction equation means
Friction is the force that resists sliding between two surfaces in contact. Its size is modelled as f = μN: the friction force equals a dimensionless coefficient of friction (μ) times the normal force (N) pressing the surfaces together. A rougher pairing has a larger μ, and pushing the surfaces together harder (more N) raises the friction proportionally. Notice that contact area does not appear — for ordinary dry surfaces it cancels out.
f = friction force (N), μ = coefficient of friction (dimensionless), N = normal force (N)
Worked example
A crate sits on a floor with coefficient of friction μ = 0.5, pressed down by a normal force of N = 200 N. How much friction force resists sliding it?
- 1 Write the friction equation. f = μ × N, with the normal force in newtons and μ dimensionless.
- 2 Substitute the known values. f = 0.5 × 200 N.
- 3 Compute the friction force. f = 100 N — the maximum friction available to resist sliding.
Typical coefficients of friction
Approximate dry textbook values; real surfaces vary with finish, lubrication, and load.
| Surface pair | Static μₛ | Kinetic μₖ |
|---|---|---|
| Rubber on dry concrete | ≈ 1.0 | ≈ 0.7 |
| Rubber on wet concrete | ≈ 0.7 | ≈ 0.5 |
| Steel on steel (dry) | ≈ 0.74 | ≈ 0.57 |
| Glass on glass | ≈ 0.94 | ≈ 0.4 |
| Wood on wood | ≈ 0.25–0.5 | ≈ 0.2 |
| Waxed ski on snow | ≈ 0.1 | ≈ 0.05 |
| Ice on ice | ≈ 0.1 | ≈ 0.03 |
| Teflon on steel | ≈ 0.04 | ≈ 0.04 |
Static vs kinetic friction
Static friction acts while the surfaces are still locked together. It adjusts itself to match whatever push you apply, up to a maximum of f = μₛN — so the equation gives the largest force the surfaces can resist before they break free, not the friction at every instant.
Kinetic friction takes over once sliding begins and is usually a bit smaller, f = μₖN, which is why an object lurches forward the moment it starts to move. Use the static coefficient to find whether something will budge, and the kinetic coefficient to find the resisting force while it slides.
The normal force is not always the weight. On a flat surface N equals mg, but on an incline only the component perpendicular to the slope counts, and pushing down or pulling up changes N too. Get the normal force right first, then apply f = μN.