Friction Calculator
Find static and kinetic friction on flat ground or a slope, see whether the object slips and what force starts it moving.
🧱 What is Friction?
Friction is the force that resists the relative sliding of two surfaces in contact. It acts along the surface, opposite to the motion or to the tendency to move, and it is the reason a parked car stays put on a hill, a nail holds in wood and your shoes grip the floor. At the scale of everyday objects, the friction force between dry surfaces is described very well by a simple model: it is proportional to the normal force that presses the surfaces together, with a dimensionless constant of proportionality called the coefficient of friction, written mu.
There are two regimes. Static friction acts while the surfaces are not sliding. It is not a fixed number: it automatically grows to match whatever push you apply, up to a maximum of mu_s times the normal force. Once the push is bigger than that maximum, the object breaks away and kinetic friction takes over, with a roughly constant size of mu_k times the normal force. Because mu_k is normally a little smaller than mu_s, the resisting force drops at the moment of slipping, which is why the chart in Flat mode shows a rising line followed by a step down.
This calculator covers the questions people actually ask. How hard must I push a crate to get it moving? Will a box stay on this ramp? How steep can a pile or a loading ramp be before things start to slide? What is the coefficient of friction between these two materials if I measured the pull force or the tilt angle? It also gives the net force and acceleration once an object is sliding, and the angle of repose, where tan(theta) equals mu_s.
Keep the limits of the model in mind. The coefficient is not a pure material property: it depends on the surface pair, finish, cleanliness, moisture, temperature and sometimes speed. The material presets here are typical textbook values for dry, clean surfaces and are labelled as typical for a reason, so use your own measured numbers for design work. For wheels that roll rather than slide, use the rolling resistance calculator, and for a deeper look at ramps see the inclined plane calculator.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Pushing a Wooden Block Hard Enough to Slip
20 kg wooden block on a wooden floor (μs = 0.4, μk = 0.3), pushed with 100 N
Example 2 — A Crate That Stays Put
50 kg steel crate on a dry steel deck (μs = 0.6, μk = 0.3), pushed with 200 N
Example 3 — A Box Resting on a 25 Degree Slope
10 kg box on a 25° slope, μs = 0.5 and μk = 0.4
Example 4 — The Same Idea on a 35 Degree Slope
15 kg wooden block on a 35° wooden ramp (μs = 0.4, μk = 0.3)
Example 5 — Measuring mu From a Pull Test
30 kg object needs 120 N to just start moving and 75 N to keep sliding
Example 6 — Measuring mu From a Tilt Test
A 5 kg block just starts to slide when the board is tilted to 21.8°
❓ Frequently Asked Questions
🔗 Related Calculators
What is the formula for friction force?
The friction force is f = mu N, where mu is the coefficient of friction and N is the normal force. On flat ground N = m g. Static friction can take any value up to mu_s N, while kinetic friction while sliding is a fixed mu_k N.
How do you find the force needed to start an object moving?
The force needed to start motion is the maximum static friction, mu_s N. For a 20 kg wooden block with mu_s = 0.4 on flat wood, N is 196.13 N, so you need more than 78.45 N of horizontal force to make it slip.
What is the difference between static and kinetic friction?
Static friction acts between surfaces that are not sliding and adjusts up to a maximum of mu_s N. Kinetic friction acts while they slide and equals mu_k N. For most pairs mu_k is smaller than mu_s, so friction drops once motion starts.
How do you know if an object will slip?
It slips when the applied force along the surface is greater than mu_s N. On a slope it slips when m g sin(theta) is greater than mu_s m g cos(theta), which simplifies to tan(theta) greater than mu_s.
What is the angle of repose?
The angle of repose is the steepest slope at which an object stays at rest. It satisfies tan(theta) = mu_s, so theta = arctan(mu_s). With mu_s = 0.5 the angle of repose is 26.57 degrees.
Does friction depend on the surface area?
In the simple model used here, friction does not depend on the contact area, only on the normal force and the coefficient. Real surfaces deviate from this, especially soft materials such as rubber and very smooth or very rough contacts.
Does mass affect friction on a slope?
The friction force grows with mass, but so does the pull down the slope, so mass cancels out of the slip condition and of the acceleration a = g (sin(theta) - mu_k cos(theta)). Only the angle and the coefficient decide the outcome.
What is a typical coefficient of friction?
Many dry material pairs have coefficients between 0.3 and 0.6. Textbook values include about 0.4 for wood on wood, 0.6 static for steel on steel, around 1.0 static for rubber on dry concrete, and about 0.05 for oiled steel. Treat these as rough guides.
How do you calculate the coefficient of friction?
Divide the friction force by the normal force. If it takes 120 N to just start a 30 kg object moving on flat ground, N is 294.2 N and mu_s = 120 / 294.2 = 0.408. On a ramp, mu_s equals the tangent of the angle at which the object starts to slide.
Why is the net force zero when the object does not move?
While the push is below the static limit, static friction rises to exactly cancel it, so the forces balance and the object stays at rest. The net force only becomes non-zero after the push exceeds mu_s N and the object breaks away.