Friction Calculator
μ·N with the myths priced out: the maximum grip a surface pair offers, the tilt that starts the slide, and the stopping distance it buys — which never once asks how heavy you are.
Friction Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- Flat-surface, dry-contact Coulomb model
- Single μ — static and kinetic not separated
In short: A 70 kg person on a μ = 0.3 surface: normal force N = 686.465500 N (their weight), so maximum friction f = μN = 205.939650 N. Tilt the floor and they slide past the angle of repose, arctan(0.3) = 16.699244°. Braking on this grip decelerates at μg = 2.941995 m/s² — exactly 0.3 g, regardless of mass — so 14 m/s stops in v²/2μg = 33.310730 m, and a 700 kg cabinet stops in the SAME distance. That mass-cancellation is the page's quiet lesson, and the area myth dies beside it: friction reads the load, never the footprint.
Formula
f = μ·N, N = m·g (flat) · slide angle = arctan μ · braking a = μ·g · d = v²/(2μg)
Amontons' two laws hide in one line: friction is proportional to the LOAD, not the contact area, and the coefficient is a property of the PAIR of surfaces, not of either alone. Static μ exceeds kinetic μ — the stick-slip origin of squeaks and earthquake behaviour. Commonly cited static ranges: rubber–concrete 0.7–0.9 dry, steel–steel 0.5–0.8 dry and 0.05–0.15 lubricated, wood–wood 0.25–0.5, teflon–steel near 0.04.
Worked Example
- Enter the load and the coefficient for YOUR pair of surfaces — test it, or borrow a cited range and name it as borrowed.
- Read the maximum friction; below this, static grip holds.
- Read the slide angle for ramps and stacks, the stopping card for brakes.
- Change only the mass and watch the stopping distance refuse to move.
Defaults: 205.939650 N of grip at μ = 0.3; slides past 16.699244°; stops 14 m/s in 33.310730 m. At μ = 0.8 the slide angle is 30.963757° and the same speed stops in 12.491524 m.
Strengths & Limits Of This Model
Where this engine is strong
- Mass-cancellation and area-myth both priced live
- Slide angle and stopping distance from one μ
Where it stops
- No velocity dependence or lubrication films
- No inclined-plane force breakdown
Practical Use Cases
Driving
tyre grip and stopping distance honestly
Rigging
ramp angles before the load slides
Teaching
the area myth, retired with numbers
Methodology & Editorial Standards
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Friction Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
Why doesn't a wider tyre stop you faster?
Because friction is proportional to the LOAD, not the area — Amontons' law, and this page's loudest lesson. More rubber spreads the same load over more area; the product stays. Width buys heat capacity and wear life, which are real, but the μN bill never reads the footprint.
Static versus kinetic — why two coefficients?
Surfaces bonded at rest grip better than the same surfaces sliding: μₛ exceeds μₖ, which is why the first push is hardest and why squealing doors chatter — stick, slip, stick. This page prices the static ceiling; sliding typically runs a quarter to a third under it (commonly cited, pair-dependent).
What is the angle of repose?
The tilt at which gravity's downhill pull exactly reaches the maximum static friction: tanθ = μ, so θ = arctan μ — 16.699244° at μ = 0.3, 30.963757° at 0.8. Past it, slides start on their own; below it, ramps hold their loads for free.
Why does mass cancel from the stopping distance?
Doubling mass doubles both the friction available (μN) and the momentum to kill, and the two doublings divide out: a = μg for everything on the same surfaces. The 70 kg person and the 700 kg cabinet stop in the same 33.310730 m from 14 m/s — the page computes both if you ask.
Is μ = 0 possible?
Only as an honest ideal: the page prints zero grip, zero slide angle and refuses the stopping card, because v²/(2·0) is unbounded — nothing ever stops. Teflon-on-steel at about 0.04 is as close as the catalogue comes, and even that is not nothing.
Where do the cited μ ranges come from?
Tribology tables, measured pair by pair — rubber–concrete 0.7–0.9 dry, steel–steel 0.5–0.8 dry, wood–wood 0.25–0.5. They are RANGES because finish, film and contamination move the number; the chip you type should be your pair's test, not a table's average.
Does friction always oppose motion?
It opposes RELATIVE sliding of the surfaces — which is why it can DRIVE you: a car accelerates because the tyre pushes backward on the road and friction pushes the tyre forward. The direction follows the tendency to slip, not the travel, and that subtlety is why every-wheel drive climbs where two-wheel drive spins.
How does this page link to the curve page?
As budget to demand: a flat curve asks μ ≥ v²/(r·g), and this page owns the supply side. The centripetal page computes the demand from your speed and radius; whichever number is smaller wins the argument quietly.