Friction Force Calculator (f = μN)
Calculate kinetic friction force from the coefficient of friction and normal force using f = μN, or solve for either value instead.
Friction formula
Kinetic friction — the force resisting a sliding object — is proportional to the normal force pressing the surfaces together:
- f — friction force, in newtons (N)
- μ (mu) — coefficient of friction — no unit, always 0 or greater
- N — normal force, in newtons (N) — always positive
On a level surface, the normal force equals the object's weight: N = mg.
Enter any two values and leave the third blank; the calculator solves for it and shows the substitution step.
Worked example
A crate rests on a level floor with a normal force of 50 N. The coefficient of friction between the crate and floor is 0.3. What is the friction force?
- Formula: f = μN
- Substitute: f = 0.3 × 50
- Result: f = 15 N
Solving in reverse
The same formula rearranges to find the coefficient of friction or the normal force:
- Coefficient: μ = f/N — enter f and N, leave μ blank. With f = 15 N and N = 50 N, μ = 15 / 50 = 0.3 (no unit).
- Normal force: N = f/μ — enter f and μ, leave N blank. With f = 15 N and μ = 0.3, N = 15 / 0.3 = 50 N.
Common mix-ups
- Forgetting N = mg on a level surface. If you only know an object's mass, first find its weight with the weight calculator (W = mg) — that weight is the normal force N here.
- Using static friction's coefficient. Static friction (before sliding starts) typically has a higher μ than kinetic friction (once moving) — make sure you're using the coefficient for the situation you're modeling.
- Adding a unit to μ. The coefficient of friction is a dimensionless ratio, not a force — only f and N carry units of newtons.
Where this shows up
Friction determines stopping distances for vehicles, how road surfaces are designed for traction, and why some materials feel "grippy" while others feel "slippery." It's closely related to force (F = ma, since friction is itself a force) and to density in material-selection problems where surface properties matter alongside mass.
Frequently asked questions
- What is the formula for friction force?
- Kinetic friction is f = μN, where f is the friction force in newtons (N), μ (mu) is the coefficient of friction (no unit), and N is the normal force in newtons (N).
- What is the coefficient of friction?
- The coefficient of friction, μ, is a unitless number describing how rough two surfaces are against each other — a higher μ means more friction (harder to slide), and μ near 0 means a nearly frictionless surface like ice.
- How do I find the normal force on a level surface?
- On a flat, level surface the normal force equals the object's weight, N = mg, where m is mass and g is gravitational acceleration (about 9.8 m/s²). Use the weight calculator to find N first if you only know mass.
- How do I solve for the coefficient of friction?
- Rearrange the formula to μ = f / N. Enter the friction force and normal force, leave μ blank, and the calculator divides them for you — the result has no unit since μ is a dimensionless ratio.
- Can the coefficient of friction be negative?
- No — physically μ is 0 or positive, with 0 representing a frictionless surface. The normal force N must always be positive too, since it represents a real contact force.
- Does this calculator use static or kinetic friction?
- This calculator uses the kinetic (sliding) friction formula, f = μN, which applies once an object is already moving. Static friction (before motion starts) uses a different, generally higher, coefficient.