Friction Calculator
Find the force of friction between two surfaces with F = μ × N. Solve for the friction force, the coefficient, or the normal force; add an incline angle, an applied force, and a sliding distance to get the net force, acceleration, the slip angle, and the energy lost to friction.
Formula
Worked example
A 10 kg box on level ground (N = 10 × 9.80665 ≈ 98.07 N) with μ = 0.4: F = 0.4 × 98.07 ≈ 39.23 N of friction. The slip angle is tan⁻¹(0.4) ≈ 21.8°, so the box would start to slide on a ramp steeper than that.
How the friction force is calculated
The force of friction is the product of two quantities: the coefficient of friction μ, a dimensionless number that captures how rough or slippery a pair of surfaces is, and the normal force N, the perpendicular force pressing the two surfaces together. On flat, level ground the normal force simply equals the object weight, N = m·g, where g is the acceleration due to gravity (9.80665 m/s² on Earth). Multiplying these gives the friction force in newtons. Because μ is dimensionless, the units of the answer always match the units of the normal force you supply, whether that is newtons or pound-force.
Solving for the coefficient or the normal force
The same equation F = μ·N can be rearranged three ways. Choose "Solve for coefficient" and enter a measured friction force together with the normal force to get μ = F ÷ N, which is handy when you have run a drag test and want to characterise a surface pair. Choose "Solve for normal force" and enter the friction force and the coefficient to recover N = F ÷ μ. The default "Solve for friction force" mode is the everyday case: pick a coefficient, supply either a normal force or an object mass, and read the resisting force. Whichever way you solve, the calculator also reports the slip angle, tan⁻¹ μ, the steepest slope the object can sit on before it begins to slide.
Inclines, applied force and acceleration
On a ramp tilted at angle θ the surface supports only the component of weight perpendicular to it, so the normal force becomes N = m·g·cos θ and the friction force is F = μ·m·g·cos θ. At the same time gravity pulls the object down the slope with a force m·g·sin θ. Enter an incline angle and the calculator splits weight into these two components for you. Add a push or pull along the surface and it finds the net force, applied force plus the gravity-down-slope term minus friction, then divides by the mass to give the acceleration once the object is sliding. A negative net force means friction wins and the object stays put or slows to a stop.
Static versus kinetic friction and energy lost
Every pair of surfaces has two coefficients. The static coefficient μₛ governs an object that is not yet moving and sets the maximum force before sliding begins; the kinetic coefficient μₖ governs an object already sliding and is almost always smaller, which is why a stuck object lurches forward once it breaks free. Enter whichever matches your situation. Friction also dissipates energy as heat: over a sliding distance d the energy lost is E = F × d in joules. Supply a distance and the calculator reports that loss, useful for estimating braking heat, wear, or how far a sliding object will coast before stopping. Friction is independent of the apparent contact area and, to a good approximation, of sliding speed.
Typical coefficients of friction
| Surface pair | Static μₛ | Kinetic μₖ | Slip angle (μₛ) |
|---|---|---|---|
| Rubber on dry concrete | 1 | 0.8 | 45° |
| Wood on wood | 0.5 | 0.3 | 27° |
| Steel on steel | 0.6 | 0.4 | 31° |
| Aluminum on steel | 0.61 | 0.47 | 31° |
| Teflon on steel | 0.04 | 0.04 | 2° |
| Steel on ice | 0.03 | 0.02 | 2° |
Approximate dry coefficients; real values vary with finish, contamination, and load.
Frequently asked questions
Does friction depend on the contact area?
No. For dry, rigid surfaces the friction force depends only on the coefficient of friction and the normal force, not on how large the contact patch is. A wide tire and a narrow tire of the same weight produce the same friction force; the wider tire just spreads the same load over more area.
Should I use the static or kinetic coefficient?
Use the static coefficient to find the maximum force needed to start an object moving, and the kinetic coefficient to find the resisting force once it is already sliding. The kinetic value is usually a bit lower, so it takes more force to break an object loose than to keep it moving.
How does an incline change the friction force?
On a ramp tilted at angle θ the normal force is N = m·g·cos θ rather than m·g, because only part of the weight presses perpendicular to the surface, so friction becomes F = μ·m·g·cos θ. Gravity also pulls the object down the slope with a force m·g·sin θ. Enter the incline angle and the calculator works out both components, the net force, and the acceleration.
What is the slip angle?
The slip angle is the steepest slope an object can rest on before it starts to slide, and it equals the inverse tangent of the static coefficient: θ = tan⁻¹ μₛ. A coefficient of 0.4 gives a slip angle of about 21.8°. Tilting a surface until an object just slides is a simple way to measure μₛ in practice.
How much energy does friction dissipate?
Friction converts kinetic energy into heat. Over a sliding distance d the energy lost is E = F × d, where F is the friction force in newtons and d is in metres, giving an answer in joules. Enter a sliding distance and the calculator reports this loss, which is what heats up brakes and wears down moving parts.