Friction Calculator
Calculate the friction force on an object from its mass, the coefficient of friction and the slope angle — and whether it slides.
The grip holding an object still, and whether the slope beats it.
How the friction calculator works
Friction resists motion in proportion to the normal force pressing the surfaces together: F = μN. On level ground the normal force is the weight, mg. On a slope of angle θ it drops to mg cos θ while gravity pulls mg sin θ down the slope; the object slides once that pull exceeds the maximum friction, which happens when tan θ > μ.
Use the static coefficient to find what starts motion and the (lower) kinetic coefficient for what keeps it going. Typical values: rubber on dry concrete 0.7–1.0, wood on wood 0.25–0.5, steel on ice 0.03.
Formula: F = μ N · N = m g cos θ · pull down slope = m g sin θ
Worked examples
| Inputs | Maximum friction force | Note |
|---|---|---|
| 20 kg box, μ 0.4, flat | 78.45 N | 78.5 N to start it moving |
| 20 kg box, μ 0.4, 15° slope | 75.78 N | holds — 21.8° is the limit |
| 20 kg box, μ 0.4, 30° slope | 67.94 N | slides |
FAQFrequently asked questions
Static or kinetic coefficient?
Static (higher) for what it takes to start moving; kinetic for sliding. Car tyres rely on static friction — a skidding tyre has already dropped to the kinetic value.
Why does the slide angle not depend on mass?
Both the friction and the pull down the slope scale with mg, so it cancels: sliding starts when tan θ = μ, whatever the mass.
What are typical coefficients?
Rubber on dry road 0.7–1.0, wet road 0.4–0.5, wood on wood 0.25–0.5, steel on steel (dry) 0.5–0.8, steel on ice 0.03, Teflon on steel 0.04.
Does surface area matter?
Not in the simple model — friction depends on the normal force and the materials, not the contact area. Real tyres are wider for heat and wear reasons.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G, g₀, R, c
- NIST Special Publication 811 — Guide for the use of the International System of Units — unit conversions
- The Engineering ToolBox — material properties — specific heats, expansion coefficients, densities
- National Physical Laboratory — the UK's national measurement institute
Last checked: September 2026. Constants are the CODATA 2018 values; formulas are the standard textbook forms.