This friction calculator computes the two friction forces of the standard model — maximum static friction and kinetic friction — from the coefficient of friction and the normal force, including the incline effect.
On an incline, gravity’s pull along the slope is mg·sin θ and the normal force is mg·cos θ: the object starts sliding when tan θ exceeds μs — the “slip angle” shown here, measurable with a tilted book and a phone.
The Model, and Its Limits
The schoolbook law is one line: friction force = μ × normal force. Static friction (μs) is a ceiling — it matches your push exactly, up to μsN, then loses. Kinetic friction (μk) is what you fight once sliding, and its near-always smaller value (μk < μs) is why things “break loose.” The model ignores contact area and speed (mostly true for dry, rigid surfaces — which is why tires, adhesives and lubricated joints get their own engineering). Forces themselves combine on our Force Calculator. Part of our Physics Calculators collection.
Typical Coefficients
| Pair | μs | μk | Pair | μs | μk |
|---|---|---|---|---|---|
| Rubber on dry asphalt | ~0.9 | ~0.7 | Wood on wood | ~0.5 | ~0.3 |
| Steel on steel (dry) | ~0.6 | ~0.4 | Steel on ice | ~0.03 | ~0.02 |
| Brake pads on rotor | ~0.4 | — | Ice on ice | ~0.1 | ~0.03 |
| Climbing shoe rubber on rock | ~1.0+ | — | Teflon on steel | ~0.04 | ~0.04 |
Worked Example (Verified)
A 50 kg crate on flat ground (μs 0.5, μk 0.3): normal force = 50 × 9.81 = 490.5 N. It takes up to ≈245 N of push before it budges (static ceiling), and once moving, 147 N keeps it sliding — the 100 N difference is the lurch you feel when furniture finally moves. Tilt the floor: the crate slips on its own at 26.6° (atan 0.5) — how avalanche slopes and roof pitches are first estimated.
Related Tools
- Force Calculator — net force and acceleration
- Torque Calculator — friction’s rotational cousin (clutches, brakes)
- Physics Calculators — the full collection
Frequently Asked Questions
How do you calculate friction force?
Friction = μ × N (normal force). For a mass on flat ground, N = mg: a 50 kg crate with μk 0.3 experiences 0.3 × 490.5 = 147 N of kinetic friction. On an incline, N = mg·cos θ.
What is the difference between static and kinetic friction?
Static friction resists the start of sliding and adjusts up to its ceiling (μsN); kinetic friction opposes motion already happening and sits at μkN. Since μk < μs almost always, starting to move is harder than continuing — with the jerk to prove it.
Does friction depend on contact area?
In the standard model, no — doubling the area halves the pressure, and the two effects cancel. Real life adds wrinkles (soft rubber grips, adhesives, plowing effects), which is why race tires are wide for reasons beyond the simple law.
How do I find the coefficient of friction experimentally?
Tilt the surface until the object just slips: μs = tan θ at that angle (the calculator’s slip angle inverts this). Or drag at constant velocity with a spring scale: μk = pull force ÷ weight.
Why are μ values always approximate?
They depend on both surfaces’ condition — clean vs oily steel differs by a factor of five. Published pairs (like the table here) are starting points; safety-critical work measures the actual pair.
Is this friction calculator free?
Yes — free, instant, no sign-up.