Friction Force Calculator
Sliding friction from coefficient and normal force, with tilt angle.
What it does
Friction decides whether a push slides a crate or strains a back. Multiply the surface pair coefficient mu by the pressing normal force and the ceiling appears: mu 0.5 on 200 N holds up to 100.0 N. The tool above prints that ceiling in both force units with the matching tilt angle.
The metric default pairs wood on wood style grip (0.5) with a 200 N press. The product is 100.0 N, which converts to 22.5 lbf, and the grip angle is arctan(0.5) = 26.6 deg. Past that tilt on a ramp, the same block starts its slide.
Two textbook lines anchor the page. OpenStax university physics sets static friction at mu_s times N and kinetic at mu_k times N, with worked crates at 440 N to start and 290 N to keep sliding. Its table spans 0.04 for Teflon on steel to 1.0 for rubber on dry concrete.
Static versus kinetic trips up newcomers. Static friction matches the push up to the ceiling and then lets go, while kinetic friction during motion runs lower and steady. This page prices the ceiling; holding a slope or starting motion asks for the static row, steady sliding for the kinetic one.
How to use
- Pick metric (N) or imperial (lbf).
- Type mu from the table or your test.
- Type the normal pressing force.
- Read friction first: the maximum grip.
- Read the angle to judge ramps and tilts.
Formula
- mu
- Friction coefficient of the surface pair, no units.
- N
- Normal force pressing surfaces together.
- angle
- Steepest tilt held before sliding starts.
Empirical model for dry sliding, good to one or two digits. Oiled films, high speeds, and sticky pads break it, which the source texts state outright.
Worked example
Example: mu 0.5 on 200 N
Metric defaults: mu 0.5, normal 200 N.
- Multiply: 0.5 x 200 = 100.0 N.
- Convert: 100.0 x 0.224809 = 22.5 lbf.
- Angle: arctan(0.5) = 26.6 deg.
- Meaning: pushes under 100 N stick; above it slips.
- Tool shows 100.0 N, 22.5 lbf, 26.6 deg.
Reference table
| Pair | Mu | Friction |
|---|---|---|
| Steel on ice | 0.04 | 4.0 N |
| Wood on wood | 0.5 | 50.0 N |
| Steel dry | 0.6 | 60.0 N |
| Rubber, dry concrete | 1.0 | 100.0 N |
Limits
- Dry sliding model; lubricants need other data.
- Mu values are rough to one or two digits.
- Flat press assumed; wedges redirect forces.
- Ceiling only; resting contact can grip far less.
Common mistakes
- Using weight as normal force on a slope.
- Quoting static mu for steady sliding.
- Treating mu as a force with units.
- Expecting area to change the result.
- Forgetting kinetic runs below the ceiling.
Try it yourself
Quick checks. Answers sit tucked under each question.
Mu 0.3 on 100 N?
0.3 x 100 = 30.0 N.
Mu 0.45 on 980 N?
0.45 x 980 = 441.0 N to start the crate.
Mu 0.7 on 20 lbf?
0.7 x 20 = 14.0 lbf.
Questions
What is mu 0.5 on 200 N?
100.0 N of grip, which is 22.5 lbf.
Static or kinetic here?
The ceiling shown is the static maximum; kinetic runs lower.
What does the angle mean?
Steepest ramp tilt held: arctan(mu), here 26.6 deg.
Can mu pass 1?
Yes for rubbery pairs; 1.0 rubber on dry concrete is tabulated.
Does contact area matter?
Barely in this model; pressure and material set the force.
Why two force units?
Metric problems want N while shop work quotes lbf.