Friction Calculator

Calculate the friction force between any object and a surface

Based on the simple formula F = μN, this calculator finds friction force, friction coefficient, or normal force.

Last updated: December 21, 2025

CreatorFrank Zhao

Friction coefficient (μ)

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Normal force (N)

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Friction force (F = μN)

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Overview

In many everyday “dry contact” situations, the maximum friction force scales with how hard two surfaces are pressed together. The pressing force is the normal force $N$ (perpendicular to the surface).

Intuition: more load on the surface usually means more friction.

If you double $N$ while keeping the same materials/condition, this simple model predicts roughly double friction.

Variable meanings

$F$ : friction force (units of force)
$N$ : normal force (units of force)
$\mu$ : coefficient of friction (dimensionless, typically 0 to 1)

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Quick Start

You can solve for any one of the three values: friction force, coefficient, or normal force. Type two of them and the calculator will solve the third.

Step 1

Enter $\mu$

Example: $\mu = 0.25$

Step 2

Enter $N$ and pick units

Use N/kN/MN/GN/TN or lbf.

Step 3

Read the result

The calculator reports friction $F$ in your chosen unit.

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Formula

The model used is the classic Coulomb friction relationship:

Friction force equation

F = \mu N

You can also rearrange it to solve for the other quantities:

Solve for coefficient

\mu = \frac{F}{N}

Solve for normal force

N = \frac{F}{\mu}

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Quick sanity check

If $\mu = 0.2$ and $N = 500\,\text{N}$ , you should expect $F \approx 100\,\text{N}$ . If your result is wildly different, units are the first thing to double-check.

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Real-World Examples

Forward Calculation

Most Common

Given: $\mu = 0.13$ , $N = 250\,\text{N}$

Solution

F = \mu N = 0.13 \times 250\,\text{N} = 32.5\,\text{N}

The coefficient of 0.13 with a 250 N normal force produces a friction force of 32.5 N.

Reverse Calculation

Measurement Based

Measured: $F = 80\,\text{N}$ , $N = 400\,\text{N}$

Solution

\mu = \frac{F}{N} = \frac{80}{400} = 0.2

By dividing measured friction by normal force, we estimate the surface has a coefficient of 0.2 (moderate grip).

Energy & Power

Advanced

Scenario: Object slides distance $d$ with constant friction $F$

Energy Dissipated

W = F \cdot d = (\mu N) \cdot d

This represents the mechanical energy converted to heat as the object slides against friction.

💡 Tip: Convert to power by dividing work by time using our Work and Power Calculator.

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Tips

Pick the right coefficient

Static friction uses $\mu_s$ (before motion) while kinetic friction uses $\mu_k$ (during sliding). Often $\mu_k < \mu_s$ .

Normal force is not always weight

On a flat surface with no other vertical forces, $N \approx mg$ . On an incline, a common component is $N = mg\cos(\theta)$ .

Don’t force negative values

In many problems, direction is handled by your sign convention (friction points opposite motion). The calculator treats $F$ , $N$ , and $\mu$ as magnitudes.

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Frequently Asked Questions

What is the difference between static and kinetic friction?

Static friction ( $\mu_s$ ) acts when an object is stationary, preventing it from starting to move. Kinetic friction ( $\mu_k$ ) acts when the object is already sliding. Usually, $\mu_s > \mu_k$ , which is why it's harder to start moving a heavy box than to keep it moving.

Can the coefficient of friction be greater than 1?

Yes. While many common materials have $\mu < 1$ , some combinations (like rubber on dry asphalt or certain metals in a vacuum) can have coefficients significantly greater than 1.

What are the units for the friction coefficient?

The coefficient $\mu$ is dimensionless. It is a ratio of two forces ( $F/N$ ), so the units cancel out.

Does surface area affect friction?

In the simple Coulomb model ( $F = \mu N$ ), friction is independent of the contact area. While this is a good approximation for many hard solids, it doesn't hold true for deformable materials like tires or adhesives.

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Limitations & Sources

Model limitations

$F = \mu N$ is a useful first-order model, but real friction can depend on surface condition, lubrication, speed, temperature, wear, and load history. For safety-critical design, use appropriate standards and testing.

Recommended References

Basic Theory & Laws

Popova, E., & Popov, V. L. (2015). "The research works of Coulomb and Amontons and generalized laws of friction." Friction, 3(2), 183-190. https://doi.org/10.1007/s40544-015-0074-6
Beer, F. P., & Johnston, E. R. Jr. (1996). Vector Mechanics for Engineers (6th ed.). McGraw-Hill. ISBN 978-0-07-297688-5.
Meriam, J. L., & Kraige, L. G. (2002). Engineering Mechanics (5th ed.). John Wiley & Sons. ISBN 978-0-471-60293-4.

Friction Data

Barrett, R. T. (1990). "Fastener Design Manual (NASA-RP-1228)." NASA Technical Reports Server, 16. https://hdl.handle.net/2060/19900009424
"Friction Factors – Coefficients of Friction." Engineering Reference Tables. [Comprehensive data for various material pairings]

Modern Research & Applications

Hanaor, D., Gan, Y., & Einav, I. (2016). "Static friction at fractal interfaces." Tribology International, 93, 229-238. https://doi.org/10.1016/j.triboint.2015.09.016
Popov, V. L., Voll, L., Kusche, S., Li, Q., & Rozhkova, S. V. (2018). "Generalized master curve procedure for elastomer friction..." Tribology International, 120, 376-380. https://doi.org/10.1016/j.triboint.2017.12.047

Historical Context

Dowson, D. (1997). History of Tribology (2nd ed.). Professional Engineering Publishing. ISBN 978-1-86058-070-3.
Hutchings, I. M. (2016). "Leonardo da Vinci's studies of friction." Wear, 360-361, 51-66. https://doi.org/10.1016/j.wear.2016.04.019

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