Friction: friction (F) is the resistive force between two surfaces in contact, defined by F = μN — the coefficient of friction times the normal force. This free calculator solves for the friction force, the coefficient of friction or the normal force, and shows every step of the working.
Friction is the force that resists sliding between two surfaces in contact. To calculate it, multiply the coefficient of friction (μ) by the normal force (N) pressing the surfaces together: F = μ × N. The coefficient μ is a dimensionless number that captures how rough or grippy the surfaces are, while the normal force is measured in newtons (N), so the friction force comes out in newtons too.
There are three steps. First, decide which quantity you want — friction force, coefficient or normal force — and select it in the calculator’s Solve for menu. Second, enter the two values you know; you can use a surface preset such as “rubber on asphalt” to fill in a typical coefficient. Third, read the answer together with the worked steps, which show the formula, your numbers substituted in, and the final value with its units.
It helps to distinguish the two regimes. Static friction acts while an object is still stationary and can rise up to a maximum, F ≤ μs·N, to resist whatever push is applied — until that push wins and the object breaks free. Kinetic friction takes over once the object is sliding and is roughly constant at F = μk·N. Because the static coefficient μs is usually a little larger than the kinetic coefficient μk, it takes more force to get something moving than to keep it moving.
The normal force is what often trips people up. On flat, level ground with nothing else pushing down, the normal force simply equals the object’s weight: N = mg. You can get that weight from the Newton’s second law calculator (F = ma with a = g) or the weight calculator. On a ramp inclined at angle θ, only part of the weight presses into the surface, so N = mg·cos θ and the friction force shrinks accordingly.
A 10 kg crate sits on a level concrete floor where the coefficient of kinetic friction is μ = 0.4. On flat ground the normal force equals the weight: N = mg = 10 × 9.81 = 98.1 N. The friction force opposing a push is then F = μ × N = 0.4 × 98.1 = 39.2 N. So you must push with at least about 39 N to keep the crate sliding steadily. Reading it the other way, if you measured a 39.2 N drag against a 98.1 N normal force, the coefficient would be μ = F / N = 39.2 / 98.1 = 0.4.
Friction is everywhere in engineering and daily life: it lets tyres grip the road and brakes stop a car, lets us walk without slipping, and holds nails and bolts in place. The same force wastes energy as heat in machinery and wears parts down, which is why lubricants and bearings exist to drive the coefficient as low as possible.
The friction force is the coefficient of friction times the normal force: F = μN. Here μ (mu) is the dimensionless coefficient of friction for the two surfaces, and N is the normal force pressing them together. The equation rearranges to μ = F/N and N = F/μ, so you can solve for any one of the three quantities.
Static friction acts on a stationary object and can grow up to a maximum value, F ≤ μs·N, to resist a push until the object starts to move. Kinetic (sliding) friction acts once the object is moving and stays roughly constant at F = μk·N. The static coefficient μs is usually slightly larger than the kinetic coefficient μk, which is why it takes more force to start something sliding than to keep it sliding.
The coefficient of friction (μ) is a dimensionless number that describes how “grippy” a pair of surfaces is. It typically ranges from about 0.04 for very slippery contacts like Teflon up to about 1.0 for rubber on dry asphalt. It depends on the materials and their finish, but not on the contact area or, to a good approximation, the sliding speed.
On a flat, horizontal surface with no other vertical forces, the normal force equals the object’s weight: N = mg, where m is mass and g ≈ 9.81 m/s². For a 10 kg box, N = 10 × 9.81 ≈ 98 N. On a slope the normal force is smaller, N = mg·cos θ, because only part of the weight presses into the surface.
For most dry, solid surfaces, no. The classical model F = μN says friction depends only on the coefficient and the normal force, not on the apparent area of contact. Pressing the same load through a smaller area increases the pressure but not the total friction force. This breaks down for very soft, sticky or deformable materials, where the real microscopic contact area does matter.
Read more: What is friction?