Friction Force Calculator — Static and Kinetic Friction
Calculate friction force using the coefficient of friction and normal force. Covers static vs kinetic friction, common materials, and inclined plane problems.
Friction is everywhere, and it's not always the villain. Without friction, you couldn't walk, drive, or pick anything up. Cars steer and brake because of friction between tires and road. But the same force that lets you grip a jar lid also causes energy loss in engines and wear in machinery.
The CalcHub friction calculator computes friction force and helps you find the minimum force needed to move an object.
The Formulas
Friction force: f = μ × N- f = friction force (Newtons, N)
- μ (mu) = coefficient of friction (dimensionless)
- N = normal force (force perpendicular to surface, in Newtons)
Static vs. Kinetic Friction
| Type | When | Coefficient |
|---|---|---|
| Static (μₛ) | Object at rest, trying to move | Higher |
| Kinetic (μₖ) | Object already sliding | Lower |
Common Coefficients
| Surfaces | μₛ | μₖ |
|---|---|---|
| Rubber on dry concrete | 0.6–0.8 | 0.5–0.6 |
| Steel on steel | 0.74 | 0.57 |
| Wood on wood | 0.25–0.5 | 0.2 |
| Ice on ice | 0.1 | 0.03 |
| PTFE (Teflon) on steel | 0.04 | 0.04 |
Worked Example
A 60 kg box sits on a wooden floor (μₛ = 0.4). What force is needed to start sliding it?
N = mg = 60 × 9.81 = 588.6 N
f_static_max = μₛ × N = 0.4 × 588.6 = 235.4 N
So you need to push harder than 235.4 N to get it moving. Once it's moving (μₖ = 0.3), kinetic friction is:
f_kinetic = 0.3 × 588.6 = 176.6 N
Does friction depend on surface area?
For standard dry surfaces: no, surprisingly. The friction force only depends on the normal force and the coefficient, not the contact area. This counterintuitive result comes from the microscopic contact area actually scaling with load regardless of macroscopic contact area. Exceptions apply for very soft or adhesive materials.
What is rolling friction?
Rolling friction (rolling resistance) is much lower than sliding friction. That's why wheels and ball bearings are used in machinery. Typical rolling resistance coefficients are 0.001–0.01, compared to 0.1–0.8 for sliding friction. Pneumatic tires on concrete are around 0.01–0.015.
How does friction work on an incline?
On a slope at angle θ, the component of gravity pulling along the slope = mg sin(θ), and normal force = mg cos(θ). The object starts sliding when mg sin(θ) > μₛ × mg cos(θ), which simplifies to tan(θ) > μₛ. The critical angle is called the angle of repose.