Friction Calculator: Ff = μ × N
Solve friction force, coefficient of friction or normal force with Ff = μN. Includes presets for rubber, steel, wood, glass, ice and Teflon, plus a flat and incline helper. Free and private in your browser.
Normal force from a mass
Enter the mass of the block to find the normal force, or type the normal force below.
Fill in all but one field: the empty field is the one you solve for.
About the Friction Calculator
The Friction Calculator solves Ff = μ × N. Fill in any two of Friction force, Coefficient of friction (μ) and Normal force and the third is calculated as you type. A built-in helper works out the normal force for a block on a flat surface or on an incline, and shows the part of its weight that pulls it down the slope.
Friction is the force that resists sliding between two surfaces in contact. It grows in proportion to how hard the surfaces are pressed together, which is the normal force N, and depends on the pair of materials through the dimensionless coefficient μ. The coefficient has no unit, so its unit selector is hidden.
How to use the friction calculator
Steps
- Enter two of the three values and leave the one you want empty. Force is available in N, kN and lbf.
- Choose a material pair from the Surface pair preset menu to fill in μ, then pick Static or Kinetic.
- To find N from a mass, enter the mass in the helper, choose Flat surface or Incline, and press Use as normal force.
All three quantities must be 0 or more. Solving for μ with a normal force of zero, or for N with μ of zero, shows a clear "cannot divide by zero" message instead of a number.
Formula
On a flat surface with no other vertical force, the normal force equals the weight, N = m g. On an incline of angle θ, the surface supports only the component of weight perpendicular to it:
The parallel component is what tries to slide the block downhill. It begins to slide when this component exceeds the maximum static friction, μs m g cos θ, which gives the classic result tan θ = μs. The calculator uses g = 9.80665 m/s².
Static and kinetic friction
Static friction holds an object still and rises up to a maximum of μs N. Once the object slides, kinetic friction takes over with the smaller coefficient μk. That is why it takes more force to start a heavy box moving than to keep it moving. The presets below give typical dry values as static / kinetic:
- Rubber on concrete: 1.0 / 0.8
- Steel on steel: 0.74 / 0.57
- Wood on wood: 0.5 / 0.3
- Glass on glass: 0.94 / 0.4
- Ice on ice: 0.1 / 0.03
- Teflon on Teflon: 0.04 / 0.04
These are typical figures for clean, dry surfaces. Real values change with surface finish, contamination, speed, temperature and load, so treat them as a starting point and measure when it matters.
Worked examples
Example 1: friction force
A crate presses on the floor with 100 N and μ = 0.3. Ff = 0.3 × 100 = 30 N.
Example 2: find the coefficient
It takes 30 N to keep a crate sliding, and its weight is 100 N. μ = 30 ÷ 100 = 0.3.
Example 3: block on an incline
A 10 kg block sits on a 30° slope. N = 10 × 9.80665 × cos 30° ≈ 84.93 N, and the parallel component is 10 × 9.80665 × sin 30° ≈ 49.03 N. With wood on wood static friction of 0.5, the maximum static friction is about 42.5 N, which is less than 49.03 N, so the block slides.
Privacy
Nothing is uploaded; every calculation runs in your browser and never leaves your device.
Related tools
Use the Force Calculator for F = m a, the Weight Calculator for m g on different planets, and the Work Calculator for the work done against friction over a distance.
Frequently asked questions
What is the friction formula?
Friction force equals the coefficient of friction times the normal force: Ff = μ × N. With μ = 0.3 and N = 100 N the friction force is 30 N. The calculator can solve for any of the three values.
How do I find the coefficient of friction?
Divide the friction force by the normal force: μ = Ff ÷ N. If a 30 N pull keeps a 100 N crate sliding at constant speed, μ is 0.3. The coefficient has no unit.
What is the difference between static and kinetic friction?
Static friction stops a resting object from starting to slide and has a maximum of μs × N. Kinetic friction acts on a sliding object with the usually smaller coefficient μk. This is why starting an object moving takes more force than keeping it moving.
How do I get the normal force on a flat surface or incline?
On a flat surface the normal force equals the weight, N = m g. On an incline of angle θ it is N = m g cos θ, and the part of the weight along the slope is m g sin θ. Use the helper and press Use as normal force to copy the value in.
Where do the preset coefficients come from?
They are typical values for clean, dry surfaces as given in common physics references: rubber on concrete 1.0 / 0.8, steel 0.74 / 0.57, wood 0.5 / 0.3, glass 0.94 / 0.4, ice 0.1 / 0.03 and Teflon 0.04 / 0.04 (static / kinetic). Real surfaces vary.
Can the coefficient of friction be greater than 1?
Yes. A coefficient of 1 only means friction equals the normal force. Soft, grippy materials such as racing tyres or silicone rubber can exceed 1, and the calculator accepts any value of 0 or more.
When will a block slide down a slope?
It slides when the component of weight along the slope is greater than the maximum static friction, which happens when tan θ is greater than μs. The helper shows both the normal force and the parallel component to compare.
Does it send my numbers anywhere?
No. The coefficient, normal force and friction force you enter are all calculated locally in your browser, and nothing is uploaded, stored or shared with any server.