Example 1
μ = 0.4, m = 10 kg, flat → T ≈ 39.24 N.
Friction calculator
Type μ and mass m. The calculator computes T = μ N. On the flat N = mg, so 0.4 and 10 kg give about 39 N. Angle α is optional.
μ from T and N: friction coefficient. Sliding: incline with friction.
Result
Friction coefficient μ, Mass m and Angle α (degrees, optional). The result shows up here.
How it works
Classroom friction is T = μ N. On a table the normal is the weight: N = m g. At μ = 0.4 and m = 10 kg you get N = 98.1 N and T ≈ 39.24 N, about 39 N on the page. At μ = 0.2 and 5 kg, T ≈ 9.81 N. At μ = 0.05 and 80 kg you are back near 39 N, a smaller coefficient on a larger mass. At μ = 0.35 and 25 kg about 86 N. At μ = 0.25 and 200 kg about 491 N.
On an incline N = m g cos α, so the same block rubs less than on the flat. At 0.4, 10 kg and 30°, cos 30° ≈ 0.866, N drops to about 85 N and T ≈ 34 N. At 0.3, 12 kg and 15°, T ≈ 34 N. At 0.4, 8 kg and 45°, T ≈ 22 N. Blank α leaves the board flat. g is 9.81 m/s², no field.
The first field is μ with no unit. The second is mass in kilograms. The third, optional, is the angle in degrees. Result T is in newtons. A comma and a period are the same μ: 0,4 and 0.4. Typed 0 in μ gives T = 0: a no-friction model. μ and m both need a number before 39 N can appear.
One μ field. The problem says whether that is μ_s or μ_k. The calculator does not split static from kinetic. The coefficient from a measured T and N is next door: 39.24 N on 98.1 N gives 0.4 again.
Slide acceleration a = g(sin α - μ cos α) lives on incline with friction. That page also gives time and vₖ when you add length L. Here the result stays the friction force. F = m a is another calculator: you can take T and divide by m if the problem asks for a on the flat.
Type 0.4 and 10, leave α blank, click Calculate, and match about 39 N. Then add 30 and watch T drop. The header symbol does not pin the block to the table.
How to use
- In the first field enter μ, for example 0.4. That is a number with no unit.
- In the second field enter mass m in kilograms, for example 10.
- Leave α blank for the flat, or type 30 if the block sits on an incline.
- Click Calculate. 0.4 and 10 kg on the flat give T ≈ 39.24 N, about 39 N on the page.
- For a slide with μ, open incline with friction. μ from T and N is on the friction-coefficient page.
Formula
T = μ·N
N = mg (flat) or mg cosα (incline)
g = 9.81 m/s².
T, μ, and N on a table or incline
Classroom friction here is T = μ N. At μ = 0.4 and 10 kg on the flat, N = 98.1 N and T ≈ 39.24 N. Optional α cuts N through cos α.
- T
- Friction force in newtons. At 30° the same 0.4 and 10 kg pair gives T ≈ 34 N, less than on the flat.
- μ
- Coefficient with no unit. One field: the problem says whether that is μ_s or μ_k. Typed 0 gives T = 0.
- N
- Normal force. On the flat N = m g. On an incline N = m g cos α. At 10 kg and 30°, N drops to about 85 N.
- α
- Incline angle in degrees, optional. Blank α leaves the board flat.
- m
- Mass in kilograms. At μ = 0.05 and 80 kg you are back near T ≈ 39 N, another path to the same order.
Real-life examples
Example 2
μ = 0.2, m = 5 kg, α = 30°.
Example 3
μ ≈ 0.7, m = 1400 kg.
Example 4
μ = 0.05, m = 80 kg.
Example 5
μ = 0.35, m = 25 kg.
Example 6
μ = 0.3, m = 12 kg, α = 15°.
Example 7
μ = 0.25, m = 200 kg.
Example 8
μ = 0.4, m = 8 kg, α = 45°.
Example 9
μ = 0.6, m = 50 kg.
Ways to use this calculator
- You compute T for a 10 kg crate at μ = 0.4 on a table.
- You compare T on the flat and at α = 30°.
Frequently asked questions
How much T at μ = 0.4 and 10 kg on the flat?
N = 10 × 9.81 = 98.1 N. T = 0.4 × 98.1 ≈ 39.24 N, about 39 N on the page.
How much T at the same 0.4 and 10 kg, but α = 30°?
N = 98.1 × cos 30° ≈ 85 N. T ≈ 34 N, less than on the flat, because cos α cuts the normal.
Which units do I type?
μ with no unit, m in kg, α in degrees. Result T in newtons. g is 9.81 m/s².
What does blank α do?
Blank α is the flat, N = m g. A typed angle is an incline, N = m g cos α.
How much at μ = 0.05 and 80 kg?
T = 0.05 × 80 × 9.81 ≈ 39 N. The same order as 0.4 and 10 kg, another way.
How is this different from the coefficient page?
Here μ and m give T. There T and N give μ. 39.24 N and 98.1 N give 0.4 again.
Is this a slide down an incline?
Here T alone. Slide time and vₖ live on incline with friction, a = g(sin α - μ cos α).
μ_s or μ_k?
One μ field. Classroom model with no split unless the problem gives one μ.
Does a comma in 0.4 work?
Yes. 0,4 and 0.4 are the same μ. A comma and a period mean the same value.
Where is a = T/m?
On the F = m·a page. Here the result is T. On the flat a = T/m if friction is the only horizontal force.
Knowledge sources
The formula is the school one. Units follow SI; NIST SP 330 and BIPM define the measures, not your result.
Page updated in 2026.