Friction CalculatorFriction force · f = μN
Friction force equals the coefficient of friction times the normal force: f = μN. On a level surface N = mg. Enter a mass and a coefficient to get the friction force, or solve backwards for μ or the normal force. Material presets cover tyres on asphalt, wood, steel and ice, and you also get the stopping distance and angle of repose.
Formula verified against OpenStax — University Physics, Volume 1 · HyperPhysics, Georgia State University
By Manzoor Ahmad · Pharmacist & calculator developerReviewed & updated
Surface & load
Use static μ for “will it start to slide?” and kinetic μ for something already sliding.
Step-by-step working
What is friction?
Friction is the contact force that resists two surfaces sliding, or trying to slide, past each other. Its size is the coefficient of friction μ multiplied by the normal force pressing the surfaces together.
Friction lets you walk, lets tyres grip and lets brakes work. It also wastes energy as heat in engines and machines. Static friction holds things still; kinetic friction slows things that are already sliding.
Quick answers
How do you calculate the force of friction?
Multiply the coefficient of friction by the normal force: f = μN. For a 50 kg box on a level floor with μ = 0.4, f = 0.4 × 50 × 9.81 = 196 N.
How do I find the coefficient of friction?
Measure the force needed to keep an object sliding at constant speed, then divide by its normal force. Or tilt the surface until the object just starts to slide: μₛ = tan θ.
What is the coefficient of friction of a car tyre on the road?
Roughly 0.7–0.9 on dry asphalt, 0.4–0.6 when wet, and as low as 0.1 on ice. That range explains why stopping distances can triple on ice.
How does friction affect braking distance?
With wheels locked or at the grip limit, d = v² ÷ (2μg). Halve μ and the braking distance doubles. The insight box under the results applies this to 100 km/h. For changing speeds, see the acceleration calculator.
Friction formula
Static friction can be anything up to μₛN. Kinetic friction is roughly constant at μₖN once sliding starts.
| Symbol | Meaning | SI unit |
|---|---|---|
| f | Friction force | N |
| μ | Coefficient of friction (μₛ static, μₖ kinetic) | — |
| N | Normal force (perpendicular contact force) | N |
| m | Mass | kg |
| g | Gravitational acceleration | m/s² |
How to calculate friction force
- Find the normal force. On level ground it is the weight, mg. On a slope it is mg cos θ.
- Choose μ: static if nothing is moving yet, kinetic if it is already sliding.
- Multiply: f = μN.
- Point it the right way: friction always opposes the motion, or the attempted motion.
Worked example: dragging a 20 kg crate
A 20 kg crate rests on a floor with μ = 0.5. What friction force must you overcome?
f = μN = 0.5 × 196.1 = 98.07 N (≈ 22 lbf)
The same μ sets the angle of repose, tan⁻¹ 0.5 = 26.6°. Tilt the floor past that and the crate slides on its own.
Coefficient of friction table
Approximate values for clean, dry surfaces unless noted. Real values vary with finish, temperature and contamination.
| Surfaces in contact | Static μₛ | Kinetic μₖ |
|---|---|---|
| Rubber tyre on dry asphalt | 0.9–1.0 | 0.7–0.8 |
| Rubber tyre on wet asphalt | 0.5–0.7 | 0.4–0.5 |
| Steel on steel (dry) | 0.74 | 0.57 |
| Wood on wood | 0.25–0.5 | 0.2 |
| Glass on glass | 0.9–1.0 | 0.4 |
| Teflon on steel | 0.04 | 0.04 |
| Ice on ice | 0.1 | 0.03 |
| Rubber tyre on ice | 0.15 | 0.05–0.1 |
Common mistakes to avoid
- Using the mass instead of the normal force. Multiply by g first; μ × kg is not a force.
- Assuming the normal force always equals mg. Slopes, extra downward pushes and upward pulls all change N.
- Thinking a bigger contact area means more friction. In the simple model, friction doesn’t depend on area.
Manzoor Ahmad
Pharmacist turned Web Developer & Calculator Engineer · 13+ years in web developmentI’m a pharmacist by training who turned into a full-time tech geek, and for 13+ years I’ve designed and coded web tools. My pharmacy degree included physical pharmacy and pharmaceutics — states of matter, heat, flow and reaction kinetics — so the physics behind these tools is familiar ground, not a new hobby.
I’m not a physicist, so I don’t ask you to take my word for it: every formula on this page is traced to an open university textbook or NIST reference data, and the calculator is tested against published worked examples before it goes live. Spot an error? Tell me and it will be fixed and dated on the next update.
Friction Calculator: frequently asked questions
f = μN, where μ is the coefficient of friction and N the normal force. On a level surface with no other vertical forces, N = mg.
Static friction acts before an object moves and can rise up to μₛN. Kinetic friction acts once it slides and is usually smaller, at μₖN.
In the classic Amontons–Coulomb model, no: friction depends on the normal force and the materials, not the contact area. Soft materials such as tyres deviate from this somewhat.
Yes. Racing slicks on hot asphalt, silicone rubber and some clean metals in a vacuum exceed 1. It simply means friction is larger than the normal force.
None. μ is a ratio of two forces, so it is dimensionless.
Yes. Work done against friction turns into heat and isn’t recovered, unlike work done against gravity.
References & sources
- OpenStax — University Physics, Volume 1 — Ch. 6.2, Friction
- HyperPhysics, Georgia State University — friction coefficients
- OpenStax — College Physics 2e — Ch. 5.1, Friction
Disclaimer: This calculator is an educational tool built on idealised textbook models. It is not a substitute for professional engineering or safety calculations.