Friction Force Calculator

friction force = μ × normal force friction angle = arctan μ

μ

Coefficient of friction for the pair of surfaces, a pure number. Around 0.05 for ice, 0.6 to 0.9 for rubber on dry concrete, 1.4 for a hot racing tyre. It must not be negative, but it can be above 1 — there is no rule against it

N

Normal force in newtons, the force pressing the surfaces together — the weight of the object on level ground, less on a slope, more if something is pressing down. The field also takes kilonewtons, pounds-force and kilogram-force, and zero is a legal value here because nothing pressed together means no friction

F

The friction force, in newtons, kilonewtons and pounds-force — the three rows are the same number in three scales. It is the force needed to keep the object sliding at a steady speed, and the largest force the surface can supply if something else is trying to move it

θ

The friction angle, arctan μ, in degrees. It depends only on the coefficient, not on the load — which is why it still has a value when the normal force is zero, and why it is the one row of the output panel that does not move when you change the weight

Use this page when you know what the surfaces are and need to know the force: whether a winch is big enough to drag a pallet, how hard a clamp has to grip before the part slips, what the braking limit of a vehicle is on a given road, how much force a conveyor belt can carry uphill before the load slides back, or how hard a push a person can actually deliver on a wet floor. It is the direction of the equation that turns material data into something a machine has to be designed around, which is why it comes up far more often in practice than the measuring direction. Two habits make the answer more useful. First, design against the static coefficient, not the kinetic one: starting something moving takes ten to twenty percent more force than keeping it moving, so a winch sized exactly to the number this page gives will fail to break the load away. Second, check what the normal force really is before typing it — on a slope it is mg × cos θ rather than the weight, and on a ramp the friction force falls while gravity's pull along the slope rises, which is why things slide on inclines that seem gentle.

1. A 100 lb crate on a concrete floor, pushed sideways

   1. The crate weighs 100 lbf, which is 444.82 N — that is the normal force on level ground (the field takes SI and converts)
   2. Friction force: 0.6 × 444.82 = 266.9 N
   3. In the other scales: 0.267 kN, or 60 lbf
   4. Friction angle: arctan 0.6 = 30.96°

   Sixty pounds of push to keep a hundred-pound crate sliding, which is a useful thing to have a feel for: it is more than most people expect, and it is why a crate that a person can lift is often one they cannot shove. Read the last row against the first: the angle did not need any of the force numbers to be worked out, because it is a property of the surfaces alone. That independence is worth remembering when you are choosing a coefficient — 0.6 is 31° whether the crate weighs 10 lbf or 1000, and it is only the force that scales.

2. The same floor with twice the default load

   1. Only the normal force changes: 1000 N instead of the default 500 N, a factor of two
   2. Friction force: 0.6 × 1000 = 600 N
   3. In the other scales: 0.600 kN, or 134.9 lbf
   4. Friction angle: arctan 0.6 = 30.96° — unchanged, because μ did not change

   This pair of examples is the entire structure of the page: the force is linear in the normal force, and the angle does not care. It is also the reason friction is described as independent of weight in the sense that matters for vehicles — a heavier car needs proportionally more force to stop, and has proportionally more available, so its braking distance is roughly unchanged. That tidy cancellation is why the friction angle on this page is the number that transfers between situations, and the newtons are the number that has to be recomputed whenever the load changes.

3. A hot racing tyre on dry asphalt

   1. Coefficient 1.4, cornering load on the tyre 8000 N
   2. Friction force: 1.4 × 8000 = 11200 N
   3. In the other scales: 11.200 kN, or 2517.9 lbf — about 1.14 short tons of sideways grip
   4. Friction angle: arctan 1.4 = 54.46°

   A coefficient above 1 is a legal input here and gives an answer that is larger than the load, which is exactly what a racing tyre does: it can pull sideways harder than the weight pressing it down. Nothing has been violated — the everyday impression that μ stays below 1 comes from ordinary surfaces, not from the definition, and this is the case where the difference shows up. The friction angle of 54.46° is the steepest slope the tyre would hold on before sliding, which is a slope no road is ever built at, and that is the point: the grip is not there for hills, it is there for corners.

The formula says friction is proportional to the normal force and independent of everything else, and nothing else is quite true. It ignores the contact area, which is a good approximation for rigid materials; it ignores the sliding speed, which matters for rubber and for brakes, where the coefficient falls as the surfaces heat up; and it ignores how long the surfaces have been in contact, which matters for polymers that creep into each other. This page works out the kinetic coefficient you give it, so for the interesting question — will it start moving at all — you need the static value, which is ten to twenty percent higher, and there is no field on the page for it. The normal force is an input, so if the object is on a slope you have to supply mg cos θ, and if it is being pressed down or lifted by something else that has to be included; a page that takes N as given cannot warn you when N is wrong. It assumes a single flat contact: a crate on four castors, a belt wrapped round a drum and a rope over a capstan all have several contacts or a varying normal force, and all of them are outside this model. It says nothing about rolling resistance, which is a different coefficient two orders of magnitude smaller and which is what actually governs anything on wheels. And it is a steady-state result: the force at the instant something breaks away is higher than this, and the force while it is being accelerated is this plus the mass times the acceleration.

What is the friction force formula?

F = μ × N, the coefficient of friction times the normal force pressing the surfaces together. A crate on a concrete floor with μ of 0.6 and a weight of 500 N needs 0.6 × 500 = 300 N of push to keep it sliding. The force is linear in both terms, so doubling the load or doubling the coefficient doubles the force, and halving either halves it.

Why does the friction angle not change when I change the load?

Because it is arctan μ, and μ is a property of the surfaces rather than of the load. Doubling the normal force doubles the friction force as well, so the ratio between them — which is what sets the angle — is unchanged. That is also why the angle still has a value when the normal force is zero: with nothing pressed together there is no friction force, but the surfaces still have a coefficient, and the angle describing it is still 30.96° for μ = 0.6.

Do I need the static or the kinetic coefficient here?

It depends on the question. If you are asking how much force is needed to keep something moving at a steady speed, the kinetic value is the right one, and that is what this page computes from whatever you type. If you are asking whether a winch or a person can get it moving at all, you need the static value, typically ten to twenty percent higher — so size the pull against the static coefficient, and expect the load to lurch once it breaks away and the force drops.

Can the friction force be larger than the weight of the object?

Yes, whenever the coefficient is above 1. A hot racing tyre at μ = 1.4 generates 11200 N of sideways force from 8000 N of load, which is more than the load itself. There is nothing unusual about it — the coefficient is a ratio between two forces, and nothing requires the ratio to be below one. It only looks surprising because most everyday surfaces happen to sit below it, which is where the familiar rule of thumb comes from.

Is the normal force just the weight?

Only on level ground with nothing else touching the object. On a slope it is mg × cos θ, so a 20-degree incline already reduces it by about six percent, and the object also has a component of gravity pulling it down the slope — which is why things slide on ramps at angles well below the friction angle. If something presses down on the object, or it is being pulled upwards, that changes N too, and this page takes your value for N as given.

How much force does it take to push a box on a floor?

Multiply the coefficient by the weight. A 50 kg crate (490 N) on concrete at μ = 0.6 needs 294 N to keep moving, and about 10 to 20 percent more than that to start — roughly 340 N, which is more than most people can push while standing on the same slippery floor. The short answer for a person: you can usually push about 200 to 300 N in a comfortable stance, so a crate much above 40 kg on concrete is a two-person job or a trolley job. Pushing anything heavy along a smooth floor is a good deal easier than lifting it, which is what the coefficient is measuring.

• Friction (College Physics 2e, §5.1) — F = μN, the measured coefficient table, and why static friction is larger than kinetic — OpenStax
• Friction — the normal force as the multiplier in F = μN, and the reason the coefficient depends on the pair of surfaces rather than on one material — Wikipedia
• NIST Guide to the SI — the newton and the exact pound-force and kilogram-force factors used in the input field and the output rows — National Institute of Standards and Technology