Friction calculator
Choose whether to find the friction force or the coefficient of friction. Give the normal force directly or as a mass resting on a surface, level or tilted. The calculator also shows the slope angle at which an object with that coefficient starts to slide.
Runs in your browser: nothing you enter is sent anywhere.
How to use it
- Choose what to find: the friction force or the coefficient of friction.
- Enter μ, or the measured friction force in newtons.
- Give the normal force: either a mass in kg and the slope angle (0° for a level surface), or a known force in newtons.
- Friction force: F = μ × N. Coefficient: μ = F ÷ N.
- Normal force of a resting mass: N = m × g × cos θ, with g = 9.80665 m/s².
- Pull down a slope: m × g × sin θ. Angle of sliding: θ = arctan μ.
Worked example
A 10 kg crate on a level floor, μ = 0.3: N = 10 × 9.80665 = 98.0665 N, so the friction force is 0.3 × 98.0665 = 29.42 N. With μ = 0.3 as a static coefficient the crate would begin to slide on a slope of 16.7°.
A 5 kg block on a 30° slope, μ = 0.2: N = 5 × 9.80665 × cos 30° = 42.464 N and F = 8.4928 N, while gravity pulls it down the slope with 24.5166 N, so it slides.
Tips and common mistakes
- μ has no unit and does not depend on the contact area, to a first approximation.
- Typical values vary a lot with materials, surface finish, moisture and lubrication, so measure when precision matters.
- Pulling at an angle changes the normal force; in that case work out N yourself and choose “Known force”.
Frequently asked questions
How do you calculate friction force?
Multiply the coefficient of friction by the normal force, F = μ × N. A 10 kg box on a level floor presses with N = 10 × 9.80665 = 98.07 N; with μ = 0.3 the friction is 29.42 N.
What is the difference between static and kinetic friction?
Static friction holds an object at rest and can rise up to μs × N; kinetic friction acts while it slides and equals μk × N. μk is usually smaller, which is why it is harder to start pushing a box than to keep it moving. Enter whichever coefficient you need.
How do I find the coefficient of friction?
Measure the force needed to keep the object sliding at a steady speed (kinetic) or to just start it moving (static) and divide by the normal force, μ = F ÷ N. Or tilt the surface until the object starts to slide: μs = tan θ.
Why does the normal force get smaller on a slope?
Only the part of the weight perpendicular to the surface presses on it, N = m × g × cos θ. The rest, m × g × sin θ, pulls the object down the slope.