Friction is the force that resists sliding between two surfaces. This calculator uses the classic model f = μN to find the friction force, the coefficient of friction or the normal force, and it can work out the normal force for you from a mass resting on level ground or on a slope. On a slope it also compares the friction with the pull of gravity, so you can see whether a crate holds still or slides.
How to use the friction calculator
- Under Solve for, choose Friction force, Coefficient μ or Normal force.
- Set the Type of friction: Static (max) for the force needed to start an object moving, Kinetic (sliding) once it is moving. Enter the matching coefficient, μs or μk.
- Under Normal force from, either enter it directly, or choose a mass on level ground (N = mg) or a mass on an incline (N = mg cos θ) and enter the Mass of the object and the Incline angle.
- Read the friction force in N, lbf, kgf or kN. With a mass, the tape also shows the normal force used; on an incline it adds the pull down the slope and either a “does it slide?” verdict (static) or the net force and acceleration down the slope (kinetic).
μ, the friction force and the incline angle cannot be negative, the normal force and mass must be positive, and the angle must be below 90°.
Friction formulas
The normal force is the push of the surface perpendicular to itself. The calculator uses standard gravity, 9.80665 m/s²:
Incline at angle θ: N = mg cos θ · pull down the slope = mg sin θ
For static friction, f = μs·N is a ceiling, not a fixed value: a box nobody is pushing has zero friction on it. Kinetic friction always points against the direction of sliding.
Worked example
Level surface: μ = 0.4 and N = 500 N give f = 0.4 × 500 = 200 N (44.96 lbf or 20.39 kgf).
Incline: a 50 kg crate rests on a 20° ramp with μs = 0.4.
N = 50 × 9.80665 × cos 20° = 460.76 N, so the maximum static friction is 0.4 × 460.76 = 184.31 N.
Gravity pulls it down the ramp with 50 × 9.80665 × sin 20° = 167.70 N. Since 167.70 < 184.31, static friction holds the crate.
Tilt the ramp to 25° and the pull rises to 207.22 N while the friction limit drops to 177.76 N, so the crate starts to slide. If the sliding coefficient is μk = 0.3, kinetic friction is 133.32 N, leaving a net 73.91 N down the slope and an acceleration of 1.478 m/s².
The angle of repose
Setting mg sin θ equal to μs mg cos θ, the mass cancels and tan θ = μs. The steepest angle at which an object stays put is therefore θ = arctan μs, the angle of repose: 21.8° for μs = 0.4. Tilting a board until a block just starts to slip and measuring the angle is a simple way to measure μs.
Typical coefficients of friction
Approximate textbook values for clean, dry surfaces unless noted. Real values vary a lot with surface finish, moisture, temperature and contamination, so measure when the number matters.
| Surfaces | μs (static) | μk (kinetic) |
|---|---|---|
| Rubber on dry concrete | ≈ 1.0 | ≈ 0.8 |
| Steel on steel, dry | ≈ 0.7 | ≈ 0.6 |
| Wood on wood | ≈ 0.25–0.5 | ≈ 0.2 |
| Metal on metal, lubricated | ≈ 0.15 | ≈ 0.06 |
| Ice on ice | ≈ 0.1 | ≈ 0.03 |
| PTFE (Teflon) on PTFE | ≈ 0.04 | ≈ 0.04 |
Why contact area does not matter
The rules behind f = μN go back to Guillaume Amontons (1699) and Charles-Augustin de Coulomb (1785): friction is proportional to the load, independent of the apparent contact area, and kinetic friction barely depends on sliding speed. Surfaces touch only at microscopic high points. Press harder and those points flatten into more real contact; spread the load over a larger face and each point carries less, so the real contact area — and the friction — stays about the same. The model is an approximation that works well for dry, hard materials; lubricated, sticky and very soft surfaces need more detailed treatment.
Friction is usually one of several forces on an object. Combine it with the others in the force calculator, or find the energy it dissipates over a distance with the work calculator.
Frequently asked questions
What is the formula for friction force?
f = μN, where μ is the coefficient of friction and N is the normal force pressing the surfaces together. With μ = 0.4 and N = 500 N the friction force is 200 N, about 45 lbf.
What is the difference between static and kinetic friction?
Static friction acts while surfaces are not sliding and grows to match the push, up to a maximum of μs·N. Kinetic friction acts once sliding starts and stays roughly constant at μk·N. For most materials μk is smaller than μs, which is why an object is harder to start than to keep moving.
Does friction depend on contact area?
For ordinary dry surfaces, no. Amontons' laws say friction depends on the normal force, not the apparent contact area, so a brick slides just as easily on its narrow side as on its broad face. Soft materials such as tire rubber are the main exception.
How do I know if an object will slide down a slope?
It slides when the slope angle exceeds the angle of repose, arctan μs. With μs = 0.4 that angle is about 21.8°, whatever the mass. Choose an incline as the normal-force source with static friction and the calculator gives a yes-or-no answer.
Can the coefficient of friction be greater than 1?
Yes. μ is a ratio, not a percentage, and soft rubber on dry concrete or racing tires on a warm track can exceed 1. The calculator accepts any non-negative value but flags results above about 1.5 for a second look.