About the Friction Calculator
This friction calculator finds the friction force between two surfaces using F = μ × N. Enter the coefficient of friction and either the object’s mass (with an optional slope angle) or the normal force directly, and it returns the friction force, the normal force and the component of gravity pulling the object down the slope.
It is useful for physics problems on inclined planes, for estimating how hard you must push a crate or piece of furniture, and for engineers doing quick checks on brakes, conveyor belts or ramps. On a slope it also tells you whether a stationary object will start sliding and reports the angle of repose for the chosen coefficient.
Use the static coefficient (μs) to find the force needed to start motion and the kinetic coefficient (μk) for something already sliding. Coefficients depend strongly on the surfaces and their condition, so the reference table gives typical values only.
With the default inputs, the friction force is 78.453 N. Change any value above to recalculate instantly.
How to use the friction calculator
- 1Choose whether to compute the normal force from mass and angle or enter it directly.
- 2Enter the mass and slope angle (0° for flat ground), or the normal force.
- 3Enter the coefficient of friction — see the table for typical values.
- 4Read the friction force and, on a slope, whether the object will slide.
- 5Use the push-up force to size a winch or estimate effort on a ramp.
Formula and method
Dry friction is roughly proportional to how hard the surfaces are pressed together (the normal force) and independent of contact area. The constant of proportionality is the coefficient of friction μ. On level ground the normal force equals the weight mg; on a slope it drops to mg cos θ while a component mg sin θ pulls the object down the slope.
An object at rest on a slope slides when mg sin θ exceeds μs × mg cos θ, i.e. when tan θ > μs, so the angle of repose is tan⁻¹ μs. Static friction is a maximum value — it only matches the applied force up to that limit. Standard gravity of 9.80665 m/s² is used.
- F_f
- Friction force (N)
- μ
- Coefficient of friction (static μs or kinetic μk)
- N
- Normal force (N)
- θ
- Slope angle from horizontal
Worked examples
20 kg crate on a level floor, μ = 0.4
On level ground N = 20 × 9.80665 = 196.13 N, so friction = 0.4 × 196.13 = 78.45 N. You must push harder than that to start the crate moving.
10 kg box on a 30° ramp, μ = 0.5
N = 10 × 9.80665 × cos 30° = 84.93 N and friction = 0.5 × 84.93 = 42.46 N. Gravity along the slope is 10 × 9.80665 × sin 30° = 49.03 N, which beats friction, so the box slides — 30° is steeper than the 26.6° angle of repose.
Known normal force of 500 N, μ = 0.25
With the normal force given directly, F = 0.25 × 500 = 125 N.
Frequently asked questions
What is the formula for friction force?+
Friction force F = μN, where μ is the coefficient of friction and N is the normal force pressing the surfaces together. On flat ground N equals the weight, mg.
What is the difference between static and kinetic friction?+
Static friction acts on objects at rest and must be overcome to start motion; kinetic friction acts once sliding. Kinetic coefficients are usually lower, which is why it is easier to keep something moving than to start it.
Does contact area affect friction?+
For most dry, rigid surfaces, no — friction depends on the normal force, not on the apparent area. Tyres and soft materials are exceptions, because rubber deforms and grips differently.
How do I find the coefficient of friction?+
Measure the force needed to slide an object and divide by the normal force, or tilt a surface until the object just starts to slide: μs = tan of that angle.
What is a typical coefficient of friction?+
Rubber on dry concrete is around 0.7–1.0, wood on wood about 0.25–0.5, dry steel on steel about 0.6–0.8, and ice or Teflon below 0.1. Values vary with surface finish, moisture and temperature.