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Friction Force Calculator
Find the friction force with F = μ × N. Pick two surfaces (or enter your own coefficients), give the normal force or the mass and slope angle, and see the maximum static friction, the sliding (kinetic) friction and whether the object moves.
Last updated:
Normal force from
kg
°
0° = level floor
N
m/s²
N
Push or pull parallel to the surface, on level ground. Leave empty to skip.
Enter your values to see the result.
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How to use the Friction Force Calculator
- Select the surfaces in contact, or choose Custom and type μs and μk.
- Choose how to get the normal force: from mass (and slope angle) or type it directly.
- Optionally enter an applied force on level ground to see if the object moves.
- Read the friction forces, the slide check and the working.
- Compare other materials in the table and chart.
Friction formulas
| Quantity | Formula | Example (20 kg, wood on wood) |
|---|---|---|
| Normal force (level) | N = m g | 20 × 9.807 = 196.1 N |
| Normal force (incline) | N = m g cos θ | at 20°: 184.3 N |
| Maximum static friction | fs,max = μs N | 0.5 × 196.1 = 98.1 N |
| Kinetic friction | fk = μk N | 0.3 × 196.1 = 58.8 N |
| Angle of repose | θ = arctan μs | arctan 0.5 = 26.6° |
| Sliding deceleration (level) | a = μk g | 0.3 × 9.807 = 2.94 m/s² |
Typical coefficients of friction
| Surfaces | Static μs | Kinetic μk |
|---|---|---|
| Rubber on dry concrete | 1.0 | 0.8 |
| Glass on glass | 0.94 | 0.4 |
| Steel on steel (dry) | 0.74 | 0.57 |
| Aluminium on steel | 0.61 | 0.47 |
| Copper on steel | 0.53 | 0.36 |
| Wood on wood | 0.25–0.5 | 0.2–0.3 |
| Lubricated metal on metal | 0.15 | 0.06 |
| Waxed wood on wet snow | 0.14 | 0.1 |
| Ice on ice | 0.1 | 0.03 |
| PTFE (Teflon) on PTFE | 0.04 | 0.04 |
Values are typical dry-surface figures from physics and engineering references; real surfaces can differ considerably.
Frequently asked questions
What is the formula for friction force?
F = μ × N, where μ is the coefficient of friction and N is the normal force pressing the surfaces together. Static friction can be anything up to μs × N; once sliding, kinetic friction is μk × N.
What is the difference between static and kinetic friction?
Static friction acts on objects at rest and adjusts to match the applied force up to its maximum μs N. Kinetic friction acts while sliding and is roughly constant at μk N. Because μk is usually smaller, it takes more force to start an object moving than to keep it moving.
How do I find the normal force on an incline?
N = m × g × cos θ, where θ is the slope angle. On level ground cos 0° = 1, so N equals the weight m × g. On a 30° slope a 10 kg block has N ≈ 84.9 N.
When does an object slide down a slope?
When the component of gravity along the slope (m g sin θ) exceeds the maximum static friction (μs m g cos θ), which simplifies to tan θ > μs. The steepest angle that holds is the angle of repose, arctan μs.
Does friction depend on contact area?
For dry sliding friction, approximately not: the classical laws (Amontons–Coulomb) say friction depends on the normal force and the materials, not on the apparent contact area. Tyres, soft materials and adhesives are exceptions.
How accurate are the coefficient values?
They are typical textbook values. Real coefficients vary with surface finish, cleanliness, moisture, temperature and speed, so measure them for critical design work.
Are all the tools on FreeToolCabin tested for quality and accuracy?
Yes! Every tool on our site undergoes automated Q/A testing in real browser environments to ensure high precision, correct output, and zero errors. If you happen to spot a bug or have a suggestion, please contact us at [email protected] and our team will review it right away.
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