Will It Move? Static vs Kinetic Friction

Static friction is not a force with a value; it is a force with a maximum. This compares the push you have along the surface with the μs·N available to resist it and tells you which side of the threshold you are on — and it asks first whether the body is already sliding, because if it is, the static coefficient is the wrong number entirely.

Last updated 11 Nov 2026

Static threshold, or kinetic friction already

Which side of the break-away point you are on

Is the body already sliding?This is the first question and most pages skip it. At rest, the force resisting you is static friction, whose maximum is μ_sN and which cannot be exceeded without motion starting. Once sliding, static friction is gone and kinetic friction takes over at a fixed μ_kN, which is SMALLER. The practical consequence is a body that will not start but will happily keep going, and a push that is too weak to begin the motion yet more than enough to sustain it.

Mass of the bodyIn kilograms, on a horizontal surface. Grams are the usual slip.

Applied forceIn newtons, the magnitude of whatever you are pushing or pulling with. Zero is allowed and is a real case: a body already sliding with no push at all decelerates under friction alone.

Angle of that force to the horizontalIn degrees. POSITIVE means pulling upwards as well as along — a rope over your shoulder — which lifts some weight off the surface, reduces the normal force and so reduces the friction. NEGATIVE means pushing downwards as well as along — a hand on the top of a crate — which presses the body into the surface and makes the friction worse. This sign is the single most useful thing on the page and the reason a crate is easier to pull than to push. Zero means straight along the surface.

Coefficient of static friction, μsDimensionless, from the question. Must be at least as large as the kinetic value, and the page refuses to answer if it is not. Values above 1 are legal and happen with clean rubber on dry road. Published tables for the same pair of materials disagree widely, so this page prints none and takes the number from you.

Coefficient of kinetic friction, μkDimensionless, and smaller than the static value for every ordinary pair of dry surfaces. If a question gives you only one coefficient, it means that number to be used for both, and you can type it twice here. Set both to zero for a “smooth” surface.

Acceleration due to gravity, gTake whichever value the question printed, because the three real ones are not interchangeable in the third figure. Standard gravity is exactly 9.806 65 m/s² — NIST’s 2022 CODATA listing marks it “(exact)”, because it is a conventional value fixed by the 3rd CGPM in 1901 rather than a measurement. The Cambridge 9702 data sheet gives 9.81; NCERT and most CBSE papers use 9.8. Between 9.8 and 9.81 there is 0.10 per cent, which is invisible at two significant figures and visible at four. The 10 is there for mental arithmetic and costs you 2 per cent, so do not hand in an answer computed with it. None of these is the local g, which varies with latitude and altitude by a few tenths of a per cent and which no school question means.

Your push is within the static friction available, so nothing movesExample

A 10 kg box, pulled with 32 N at 20° above the horizontal, μs = 0.35 and μk = 0.25

A maximum, not a value — and the normal force the angle of your push decides

N = mg − P sin φ · f_s ≤ μ_sN · f_k = μ_kN · moves if P cos φ > μ_sN

f_s ≤ μ_sN: static friction, written as an inequality because that is what it is. It takes whatever value is needed to hold the body, up to a ceiling of μ_sN. Below the ceiling it equals your push exactly; at the ceiling, motion starts. There is no such thing as “the” static friction on a body that is not about to move
f_k = μ_kN: kinetic friction, which IS an equals sign. Once sliding, the friction is that value regardless of how hard you push and, to a good approximation, regardless of how fast the body is going
N = mg − P sin φ: the normal force, and the reason the angle of your push matters so much. Pull upwards (φ positive) and you unload the surface, so the friction falls. Push downwards (φ negative) and sin φ is negative, so N is LARGER than the weight and the friction is worse. This is why a crate is easier to drag than to shove
P cos φ: the part of your force that is actually trying to move the body. Tilting the force buys you a smaller normal force and costs you useful component, and there is an optimum angle in between — it is arctan μ_s, the same expression as the angle of repose
μ_s ≥ μ_k: an observation rather than a definition, and this page refuses to answer if you reverse them. The gap between the two is what makes a drawer stick and then slide, and what makes antilock brakes worth fitting

Worked example

A 10 kg box, pulled with 32 N at 20° above the horizontal, μs = 0.35 and μk = 0.25
THE NORMAL FORCE, WHICH THE ANGLE CHANGES. The weight is 10 × 9.8 = 98 N, but the rope is lifting as well as pulling: 32 sin 20° = 10.9446 N upwards. So N = 98 − 10.9446 = 87.0554 N. Using 98 here would overstate every friction figure below by 13 per cent.
THE USEFUL COMPONENT. Along the surface you have 32 cos 20° = 30.0702 N. The other 1.93 N of your 32 has gone into the geometry.
THE STATIC CEILING. μ_sN = 0.35 × 87.0554 = 30.4694 N. Compare: you are pushing with 30.0702 and the surface can resist up to 30.4694. It does not move, by a margin of 0.40 N — about one and a third per cent. The friction actually acting is 30.0702 N, equal to your push, and not the 30.4694 ceiling.
WHAT A NUDGE WOULD DO. Once it is sliding, the resisting force falls to μ_kN = 0.25 × 87.0554 = 21.7638 N. Your 30.0702 N then exceeds it by 8.3064 N, which on 10 kg is an acceleration of 0.83 m/s². So this box cannot start and can easily keep going. Switch the first field to “already sliding” and the page says so.
AND THE SIGN OF THE ANGLE. Push DOWNWARDS at 20° instead — type −20 — and N rises to 108.9446 N, the static ceiling rises to 38.1306 N, and the same 30.0702 N along the surface is now nowhere near enough. Same force, same box, opposite sign on one angle, and a comfortable margin instead of a near miss.

An inequality, a threshold, and the question of whether it is moving already

The first thing to get right is that static friction has no value until you ask it to resist something. It is defined by an inequality: f_s ≤ μ_sN. Push a crate with 10 N and friction pushes back with 10 N. Push with 20 and it pushes back with 20. Keep going and at some point — μ_sN — it runs out and the crate goes. So the friction on a stationary body is almost never μ_sN; it is whatever your push is. Writing μ_sN into a free-body diagram of something that is not moving is the error this page exists to prevent, and it shows up as a body that accelerates backwards in a question where nothing happens.

The second thing is that kinetic friction is smaller, and it is an equation rather than an inequality. Once the body is sliding, the resisting force is μ_kN exactly — and μ_k is less than μ_s for every ordinary dry pair of surfaces. That gap has consequences you can feel. A drawer sticks, then slides too easily. A box you cannot start is simple to keep going once someone nudges it. A braked wheel that locks stops gripping as well as one that is still turning, which is the entire argument for antilock braking. This page asks whether the body is already sliding before it does anything else, because the answer decides which coefficient is the relevant one, and nothing else on the page can be right if that is wrong.

The angle of the applied force is the third thing, and it is worth more marks than it gets. The normal force is not the weight whenever your force has a vertical component: N = mg − P sin φ. Pull upwards and you unload the surface, cutting the friction; push downwards and you press the body in, making it worse. That is the real reason a heavy crate is easier to drag by a rope than to shove with a shoulder, and it is why the worked example above flips from “nearly moving” to “firmly stuck” when the sign of one angle changes. There is even an optimum pulling angle, at arctan μ_s, where the gain in reduced friction exactly stops outweighing the loss of useful horizontal component.

Where the coefficients come from, and why this page prints none. A coefficient of friction belongs to a PAIR of surfaces in a particular state, not to a material: steel on steel is a different number dry, oiled, polished or rusted, and published tables for nominally the same pair disagree by more than any marking scheme’s tolerance. So every μ here comes from you, and the honest laboratory route is to measure it — tilt a plank until the block slips and μ_s = tan θ, or drag the block at a constant speed and μ_k = P/N. Nothing forbids a coefficient above 1: the inequality μ ≤ 1 is not a law, and clean rubber on dry asphalt beats it.

Which boards examine this. The CBSE Class XI Laws of Motion unit lists “static and kinetic friction, laws of friction, rolling friction, lubrication” as content, so coefficients, thresholds and the angle of repose are all examinable. Cambridge 9702 takes the opposite line and states that “no treatment of the coefficients of friction and viscosity is required”, asking only for a qualitative understanding of frictional forces. If you are on 9702 and a question hands you a μ, it came from another syllabus.

Frequently asked questions

Why does the page ask whether the body is already moving?

Because it decides which coefficient applies, and the two give different answers. At rest you are testing your push against a MAXIMUM, μ_sN, and nothing happens until you exceed it. Already sliding, you are competing with a fixed force, μ_kN, which is smaller. The worked example on this page is a box that cannot be started by a 32 N pull and would accelerate at 0.83 m/s² if it were already going. Same numbers, opposite conclusions.

Is friction on a stationary body always μs × N?

No, and this is the mistake that costs the most marks. On a stationary body the friction equals whatever force is trying to move it, up to a ceiling of μ_sN. A 2 N push on a crate with a 40 N ceiling meets 2 N of friction, not 40. Only at the instant of breaking away does static friction actually reach μ_sN.

Does it matter whether I push or pull?

Very much. The normal force is mg − P sin φ, so pulling at an angle above the horizontal lifts weight off the surface and cuts the friction, while pushing downwards at an angle increases the normal force and makes the friction worse. Type a negative angle on this page to see it. The best pulling angle is arctan μ_s, which is about 19° for μ_s = 0.35.

Can a coefficient of friction be greater than 1?

Yes. The coefficient is a ratio of two forces and nothing caps it at unity; values above 1 simply mean the friction available exceeds the normal force, which clean rubber on dry road and some soft metals manage. The matching statement in geometry is that the angle of repose passes 45°. What a coefficient cannot be is negative.

Does the contact area change the friction?

Not in the model every school syllabus uses: f = μN contains no area at all, which is why a brick slides the same way on its face as on its edge. The usual explanation is that a larger apparent area carries a smaller pressure and the real contact area, where the surfaces actually touch, comes out much the same. Real tyres and polished flats depart from this, but no school question does.

Why did the page refuse my coefficients?

Because the static value you typed was below the kinetic one, and for ordinary dry surfaces that does not happen: the force needed to start sliding is at least the force needed to maintain it. Check for a transposition in the question. If the question gives you a single coefficient and no label, it means that one number for both, so type it into both fields.

Related calculators

References

PHYSICS (042) Curriculum, Class XI–XII, Central Board of Secondary Education, session 2025–26 (read 11 November 2026). Unit III, Laws of Motion, reads in part: “Intuitive concept of force, Inertia, Newton’s first law of motion; momentum and Newton’s second law of motion; impulse”, “Equilibrium of concurrent forces, Static and kinetic friction, laws of friction, rolling friction, lubrication” and “Dynamics of uniform circular motion: Centripetal force, examples of circular motion (vehicle on a level circular road, vehicle on a banked road)”. Unit V, Motion of System of Particles and Rigid Body, reads in part: “Moment of a force, torque, angular momentum, law of conservation of angular momentum and its applications” and “Moment of inertia, radius of gyration, values of moments of inertia for simple geometrical objects (no derivation)”. Quoted to establish what is in scope, not to claim any endorsement by the board.
Cambridge International AS & A Level Physics 9702, syllabus for examination in 2025, 2026 and 2027, Cambridge Assessment International Education (read 11 November 2026). Two exclusions on this syllabus are worth more than most inclusions, because they explain why a question from one board looks unanswerable to a student taught on another. Topic 3.2 asks only for “a qualitative understanding of frictional forces and viscous/drag forces including air resistance” and states that “no treatment of the coefficients of friction and viscosity is required”. Topic 3.3 states that “knowledge of the concept of coefficient of restitution is not required”, while still requiring that for an elastic collision “the relative speed of approach is equal to the relative speed of separation”. Its data sheet gives the acceleration of free fall as 9.81 m s⁻².
Fundamental Physical Constants — Complete Listing, NIST Reference on Constants, Units and Uncertainty, 2022 CODATA adjustment (read 11 November 2026). The line this batch depends on is “standard acceleration of gravity 9.806 65 (exact) m s⁻²”. The word exact is the point: g_n is a conventional value, not a measured one, so it carries no uncertainty and it is not the g where you are standing. The same listing gives the Newtonian constant of gravitation as 6.674 30 × 10⁻¹¹ m³ kg⁻¹ s⁻² with an uncertainty of 0.000 15 × 10⁻¹¹, which is 22 parts per million — the worst-known of the constants a school paper quotes, and a useful reminder that “constant” and “exact” are different claims.
The International System of Units (SI), 9th edition, 2019, Bureau International des Poids et Mesures (read 11 November 2026). Table 4 gives the newton as kg m s⁻², which is the only definition of force this site uses: a newton is not a unit of mass and a kilogram is not a unit of force. Appendix 1 lists the 3rd CGPM of 1901, whose declaration both separated mass from weight and fixed the conventional value of g_n — the two things a force question most often conflates. Cited, not reproduced.