How to use this calculator
Enter the mass, slope angle and the friction coefficients (or pick surfaces). The calculator compares the downhill pull with the maximum static friction.
Formulas
Components of weightN = mg cos θ W∥ = mg sin θ
Slips ifW∥ > μsN ⇔ tan θ > μs
Slidinga = g(sin θ − μk cos θ) Pup = W∥ + μkN
Worked example
25 kg wooden block on a 30° wooden ramp (the default)
- W = 25 × 9.807 = 245.2 N; N = 245.2 cos 30° = 212.3 N; W∥ = 122.6 N.
- Maximum static friction = 0.5 × 212.3 = 106.2 N < 122.6 N, so it slides.
- a = (122.6 − 0.3 × 212.3)/25 = 2.36 m/s².
Check: tan 30° = 0.577 > μs = 0.5, so the block slips.
Frequently asked questions
Why does mass cancel in whether it slides?
Both the downhill pull and the friction limit are proportional to mg, so the test reduces to tan θ > μs.
What is the angle of repose?
The steepest slope a block (or pile of material) can rest on: θ = arctan μs.