Friction Force

The engineering

Coulomb friction's strangest feature is what's missing: contact area appears nowhere. A brick on its end grips exactly as well as on its face, because real contact happens at microscopic asperities whose total area scales with load, not footprint. What does matter is µ — and published values are the number that bites, swinging ±50% with humidity, oxide films, and one fingerprint of oil.

Static µ exceeds kinetic, which is why things let go all at once: the instant sliding starts, resistance drops and the motion runs away — the physics of stick-slip squeal, earthquake faults, and why you steer out of a skid rather than brake harder. Design clamps and friction joints on the low percentile of µ, never the handbook average.

Where this math comes from

Leonardo da Vinci's notebooks, circa 1493, already contain the two laws — friction proportional to load, independent of contact area — complete with sketches of the test rigs; the results stayed unpublished for centuries. Guillaume Amontons rediscovered both laws in 1699, to the point that the French Academy initially doubted him, and they carry his name today.

Charles-Augustin de Coulomb's prize memoir on friction, published 1785, added the third law — kinetic friction roughly independent of sliding speed — and the static/kinetic distinction, from experiments on ship-launching ways and machine slides. 'Coulomb friction' remains the working model in every statics text, tribology's later molecular story notwithstanding.

1. 1493Leonardo da Vinci (circa)Friction laws found experimentally — and left in notebooks.
2. 1699Guillaume AmontonsFriction laws published: load-proportional, area-independent.
3. 1785Charles-Augustin de CoulombStatic vs kinetic friction; the engineering model completed.

See the full timeline of the math behind every calculator →

Runs entirely in your browser — nothing you enter leaves this page. Your recent runs are stored only on your device.