Static and kinetic dry-friction calculations
The Coulomb dry-friction model relates friction magnitude to normal force through a dimensionless coefficient. Kinetic sliding friction is modeled as fₖ = μₖN; static friction adjusts up to a limiting value fₛ,max = μₛN.
On a simple incline with no other perpendicular force, N = mg cos θ. Real friction depends on surfaces, contamination, speed, temperature, pressure, wear, vibration, and contact history.
How to use the friction calculator
- Choose the unknown: Select friction force, coefficient, or normal force.
- Choose normal-force source: Enter N directly or derive it from mass on a flat surface or simple incline.
- Enter values and units: Use a coefficient matching static or kinetic conditions and select N or lbf output.
- Calculate and verify forces: Confirm that no other perpendicular forces alter the normal force.
Formula and variables
Select a coefficient appropriate to static-limit or kinetic conditions and a normal-force model matching the free-body diagram.
fₖ = μₖN; fₛ ≤ μₛN; N = mg cos θ on a simple incline- f — Friction force
- Force parallel to and opposing relative motion or tendency (N)
- μ — Friction coefficient
- Empirical surface-pair coefficient
- N — Normal force
- Contact force perpendicular to the surface (N)
- θ — Incline angle
- Angle above horizontal (degrees)
Ten-kilogram block on a 20° incline
Estimate kinetic friction for 10 kg, μₖ = 0.30, and θ = 20°.
- Mass
- 10 kg
- Angle
- 20°
- Coefficient
- 0.30
- N = 10 × 9.80665 × cos 20° ≈ 92.15 N
- fₖ = 0.30 × 92.15
Result: Ideal kinetic friction is approximately 27.65 N.
Its direction opposes the actual or impending relative motion along the surface.
Understanding your results
Choose the correct friction condition
Static friction is not automatically equal to μₛN.
- For a stationary object, actual static friction matches the required opposing force up to its maximum.
- For sliding, use an appropriate kinetic coefficient.
- Normal force equals mg or mg cos θ only under the stated simple force conditions.
Assumptions
- The Coulomb dry-friction model is appropriate.
- The surface is rigid and the coefficient is constant.
- Flat and incline modes have no additional force component normal to the surface.
Limitations
- Does not solve full force balance, direction, acceleration, rolling resistance, lubrication, adhesion, drag, or deformation.
- Does not predict a coefficient from material names.
- Not suitable for safety-critical braking, structural, lifting, or machinery design without validated data.
Common mistakes
- Using μN as actual static friction when equilibrium requires less.
- Using weight as normal force on an incline.
- Mixing lbf and newtons.
- Using a textbook coefficient as a guaranteed design value.
Practical use cases
Free-body diagram checks
Calculate one ideal friction quantity after identifying the normal force.
Inclined-plane education
Explore how incline angle reduces the simple normal force and friction limit.
Frequently asked questions
Can a friction coefficient exceed one?
Yes. It is not theoretically limited to one, although many common pairs have lower values.
Is static friction always μsN?
No. Static friction ranges from zero to that limiting magnitude as needed to prevent slipping.
When is N = mg cos θ valid?
For a simple incline when weight is the only force with a component perpendicular to the surface and there is no perpendicular acceleration.
Sources and review
- Inclined Planes — OpenStax Physics. Accessed 2026-07-13.
Reviewed 2026-07-13.