Friction & Inclined Plane Calculator
Work out friction, normal force and whether an object slides on a flat surface or a slope.
About the Friction & Inclined Plane Calculator
Friction opposes motion and is proportional to the normal force: up to μs × N before something starts moving, then μk × N while sliding. On a slope at angle θ, gravity splits into mg sin θ along the slope and mg cos θ into it. An object starts to slide when tan θ exceeds μs.
The formula
N = mg cos θ; F_slope = mg sin θ; F_friction ≤ μs N (static), = μk N (sliding)
Typical friction coefficients (dry)
| Surfaces | μs | μk |
|---|---|---|
| Rubber on dry asphalt | 0.9 | 0.7 |
| Steel on steel | 0.74 | 0.57 |
| Wood on wood | 0.25–0.5 | 0.2 |
| Ice on ice | 0.1 | 0.03 |
| PTFE on PTFE | 0.04 | 0.04 |
Typical textbook values; real values vary with surface condition.
Worked example
Example: It stays put = friction holds 40.41 N
- Inputs: Mass: 11 kg; Slope angle: 22 °; Static friction coefficient μs: 0.55; Kinetic friction coefficient μk: 0.44; Extra force along the slope (up +): 0 N.
- Formula: N = mg cos θ; F_slope = mg sin θ; F_friction ≤ μs N (static), = μk N (sliding)
- Result: It stays put = friction holds 40.41 N
- Weight mg: 107.8731 N
- Normal force: 100.0182 N
- Along slope: 40.41 N
Questions people ask
Why is kinetic friction lower?
Once moving, surfaces have less time to interlock.
Use 0° for a flat floor?
Yes; then the push needed to start moving is μs × mg.