Friction calculator
A 50 kg crate sliding across a level floor with a kinetic coefficient of 0.3 drags against 147.1 N of friction in the friction calculator, since F = 0.3 × 490.3 N.
Kinetic friction
- Kinetic friction N = mg cos θ = 50 kg × 9.80665 m/s² × cos 0° = 490.3 N. F = μkN = 0.3 × 490.3 N = 147.1 N.
- 147.1 N
- The unit algebra Friction and the normal force are both forces, so their ratio is a pure number. The same μ works in newtons or pounds-force.
- μ = F / N, no unit
- Normal force On level ground the normal force is the whole weight, mg.
- 490.3 N
- Slope it slides down at a steady speed arctan μk, where tan θ = μk.
- 16.7°
- Friction in other units
- 147.1 N 0.1471 kN 33.07 lbf
| μ | Friction force | Steady-slide slope |
|---|---|---|
| 0.05 | 24.52 N | 2.862° |
| 0.1 | 49.03 N | 5.711° |
| 0.2 | 98.07 N | 11.31° |
| 0.3 | 147.1 N | 16.7° |
| 0.5 | 245.2 N | 26.57° |
| 0.8 | 392.3 N | 38.66° |
| 1 | 490.3 N | 45° |
- F = μN is a model fitted to measurement: over the ordinary range friction barely depends on the contact area or the sliding speed, and μ for a pair of surfaces is measured, not derived.
- Static friction is not a fixed force. It matches whatever push it resists, up to μsN, and the surfaces slip once the push exceeds that.
- Results are shown to four significant figures. Round to the precision of your least precise measurement.
How the Force Calculator works
The friction formula is F = μN: the friction force equals the coefficient of friction μ times the normal force N, the force pressing the two surfaces together. On level ground N is the object's weight, mg. Both are forces, so μ has no unit.
Worked example: a 50 kg crate on a level floor has N = 50 × 9.80665 = 490.3 N. With a kinetic coefficient of 0.3, sliding friction is F = 0.3 × 490.3 = 147.1 N, or 33.07 lbf. Pushing the crate at a steady speed takes exactly that force; any more and it speeds up.
The kinetic friction formula, Fk = μk × N, gives the drag between surfaces that are already sliding, and it stays close to constant at ordinary speeds. The static friction formula, Fs ≤ μs × N, is a ceiling: static friction matches whatever push it resists until the push reaches μs × N, and then the surfaces slip. For most pairs μs is larger than μk, which is why a heavy box is harder to start than to keep moving.
The coefficient of friction formula is the same equation solved for μ: μ = F / N. A 40 kg box that takes 120 N to keep sliding has N = 392.3 N, so μk = 120 ÷ 392.3 = 0.3059. Coefficients are measured for each pair of surfaces, and they change with moisture, dirt and finish.
On a slope the normal force shrinks to mg cos θ, and gravity pulls along the slope with mg sin θ. On a 20° ramp the same 50 kg crate has N = 460.8 N, kinetic friction of 138.2 N and a downhill pull of 167.7 N, so once it is moving it speeds up.
Force Calculator FAQ
Does friction depend on contact area?
Not in the F = μN model, which fits most dry, hard surfaces well. A brick on its wide face and on its narrow end feels the same friction, because the same weight spread over more area presses less on each part of it. Soft materials such as rubber depart from the model.
What is the steepest slope an object can rest on?
The angle whose tangent equals the static coefficient, because the pull down the slope, mg sin θ, beats the most static friction can give, μs × mg cos θ, once tan θ passes μs. With μs = 0.5 that is arctan 0.5 = 26.57°, so on a 30° ramp, where tan 30° = 0.5774, the object slides.
How do I find the normal force?
On level ground with nothing else pushing, N = mg, which is 9.80665 N for every kilogram. On a slope, N = mg cos θ. A push or pull at an angle adds or removes its vertical part, so in that case work out N separately and enter it directly.
More from the Force Calculator
Sources
- NASA NSSDCA Moon Fact Sheet, bulk parameters table, row "Surface gravity (m/s2)", Moon column (page last updated January 11, 2024) (2026)
- NASA NSSDCA Mars Fact Sheet, bulk parameters table, row "Surface gravity (mean) (m/s2)", Mars column (page last updated May 19, 2025) (2026)