Friction Force Calculator
The force friction is actually applying, what it takes to break an object free, and how far it slides to a stop.
Results
What this tool does
Friction is the force that answers back. Push a box gently and it pushes back exactly as hard, which is why nothing happens; push past its limit and it suddenly gives, and from then on the resistance is lower. This page works out both thresholds from the weight and the two coefficients, tells you which side of the line your applied force falls on, and — if the object is already moving — how far it will slide before friction alone brings it to rest.
Formula
F = μ N · static: F matches the push, up to the limit μₛ N · beyond that: F = μk N
Variables
| Symbol | Meaning | Unit |
|---|---|---|
mass | Mass | kg |
static | Static friction coefficient | — |
kinetic | Kinetic friction coefficient | — |
applied | Force you are applying | N |
speed | Speed | m/s |
normal | Normal force, if you already know it | N |
gravity | Gravitational acceleration | m/s² |
FA | Friction force right now | N |
ST | What the object is doing | — |
FS | Force needed to get it moving | N |
FK | Force needed to keep it moving | N |
NF | Normal force | N |
NE | Force left over | N |
AC | Acceleration | m/s² |
SD | Distance it slides before stopping | m |
Sz | Time to stop on friction alone | s |
AR | Angle at which it starts to slide | ° |
Worked example
- Mass20 kg
- Static friction coefficient0.6
- Kinetic friction coefficient0.4
- Force you are applying0 N
- Speed0 m/s
- Normal force, if you already know it0 N
- Gravitational acceleration9.80665 m/s²
- Friction force right now0.0000 N
- What the object is doingStill — nothing is pushing it
- Force needed to get it moving117.6798 N
- Force needed to keep it moving78.4532 N
- Normal force196.1330 N
- Force left over0.0000 N
- Acceleration0.0000 m/s²
- Distance it slides before stopping0.0000 m
- Time to stop on friction alone0.0000 s
- Angle at which it starts to slide30.964 °
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- The default values are typical reference figures, not measurements of your situation. Replace them with your own data whenever you have it.
Frequently asked questions
Why are there two coefficients?
Because starting something moving is harder than keeping it moving, and the gap is often large. At rest the surfaces settle into each other; once sliding, they skim. The static coefficient sets the highest force friction can push back with before the object breaks free — and up to that point friction exactly matches whatever you apply, which is why nothing moves. Past it, the kinetic coefficient takes over and is usually twenty to thirty per cent lower. That sudden drop is why a heavy box lurches when it finally shifts.
Where do I get the coefficients?
From a table for your pair of materials, and treat whatever you find as a rough guide rather than a constant. The coefficient is not a property of one material but of two surfaces together, and it moves with roughness, cleanliness, moisture, temperature and how long the surfaces have been resting against each other. Published figures for steel on steel span roughly 0.5 to 0.8 depending on the source. This page cannot supply them, because a number that varies by half is not a constant worth publishing as one.