Friction
Calculate friction force with Ff = μN from coefficient and normal force, static or kinetic. Free online calculator with formulas and step-by-step solutions.
Key formula
Ff = muN
How do you calculate friction force?
Use Ff = μN. Multiply the coefficient of friction by the normal force. For kinetic friction while sliding, Ff = μk N. Maximum static friction before sliding is Ff,max = μs N. Friction points opposite the tendency to slide.
About this tool
Friction opposes sliding along a surface and scales with how hard the surfaces are pressed together. This page keeps Ff = μN visible so you can find friction force, coefficient μ, or normal force without mixing static and kinetic cases.
How to use this calculator
- Choose the variable you want to solve for and confirm which values are already known.
- Enter inputs in consistent units before calculating so the formula is applied correctly.
- Check whether the result is physically reasonable by comparing it with the size of the inputs.
- Use the step-by-step breakdown to see how the equation was rearranged and evaluated.
Worked examples
Example 1: box on a floor, μk = 0.40
m = 10 kg on horizontal floor, g = 9.8. N = mg = 98 N. Ff = μk N = 0.40 × 98 = 39.2 N opposite motion.
Example 2: find μ from measured friction
Ff = 25 N, N = 100 N. μ = Ff/N = 25/100 = 0.25.
Example 3: block on a 30° ramp
m = 5.0 kg, θ = 30°, μk = 0.20, g = 9.8. N = mg cosθ = 49 × cos(30°) ≈ 42.4 N. Ff = 0.20 × 42.4 ≈ 8.5 N up the ramp (opposing slide down).
Frequently asked questions
What is the friction formula?
Ff = μN, where μ is the coefficient of friction and N is the normal force perpendicular to the surface. Rearrange to μ = Ff/N or N = Ff/μ.
What is the difference between static and kinetic friction?
Static friction (μs) acts before sliding and can vary up to μs N. Kinetic friction (μk) acts during sliding and is usually Ff = μk N. Typically μs ≥ μk.
Why is normal force in the formula, not weight?
Friction depends on how hard the surfaces press together — that is N. On a ramp N = mg cosθ, not mg. On a horizontal floor with no extra forces, N = mg.
How does friction relate to inclined planes?
On a ramp sliding down with kinetic friction, a = g(sinθ − μk cosθ). The block stays at rest if μs ≥ tanθ. Use the inclined plane calculator for full ramp problems.
Does friction always equal μmg?
Only on a horizontal surface with N = mg and the appropriate μ for the situation (static max or kinetic). On inclines, curved paths, or with extra vertical forces, use the actual N in Ff = μN.