# Beer-Lambert Law

> beerlambertlaw.com — A comprehensive educational resource on the Beer-Lambert law (A = εlc), covering the equation, calculator, worked examples, derivation, practice problems, limitations, molar absorptivity reference data, and interactive graphs.

## What This Site Covers

The Beer-Lambert law (also known as Lambert's law, Beer's law, or the Beer-Lambert-Bouguer law) states that the absorbance of light by a solution is directly proportional to the concentration of the absorbing species and the path length of the light through the solution.

The equation is: A = εlc

Where:
- A = Absorbance (dimensionless)
- ε = Molar absorptivity / extinction coefficient (L·mol⁻¹·cm⁻¹)
- l = Path length (cm)
- c = Concentration (mol/L)

## Pages

- [Home](https://beerlambertlaw.com/): Definition, equation overview, and FAQ covering 10 common questions about the Beer-Lambert law.
- [Calculator](https://beerlambertlaw.com/calculator): Free online calculator — enter any three of A, ε, l, and c to solve for the fourth.
- [Equation](https://beerlambertlaw.com/equation): Detailed explanation of each variable in A = εlc, the relationship to transmittance (A = −log₁₀(T)), and a cuvette diagram.
- [Examples](https://beerlambertlaw.com/examples): Eleven fully worked Beer-Lambert law problems with step-by-step solutions covering concentration, transmittance, serial dilutions, clinical assays, cuvette selection, calibration curves, DNA quantification, and two-component mixture analysis.
- [Derivation](https://beerlambertlaw.com/derivation): Step-by-step mathematical derivation of A = εlc from first principles.
- [Practice Problems](https://beerlambertlaw.com/practice-problems): Eighteen practice problems (easy to challenging) covering absorbance, concentration, transmittance, dilution, calibration curves, protein analysis, forensic applications, mixture analysis, and DNA quantification.
- [Transmittance](https://beerlambertlaw.com/transmittance): What transmittance is, how it relates to absorbance (A = −log₁₀T), interactive %T ↔ A converter, reference table, and practical UV-Vis lab tips.
- [Applications](https://beerlambertlaw.com/applications): Real-world applications of the Beer-Lambert law across six fields — pharmaceutical QC, clinical diagnostics, environmental monitoring, food science, forensics, and research labs.
- [Limitations](https://beerlambertlaw.com/limitations): Three categories of deviation — real (chemical), instrumental, and apparent — explaining when and why the law breaks down.
- [Molar Absorptivity Table](https://beerlambertlaw.com/molar-absorptivity): Reference extinction coefficients for 12 common compounds with wavelength, solvent, and unit conversions.
- [Graph](https://beerlambertlaw.com/graph): Interactive absorbance vs. concentration chart showing ideal linearity and real-solution deviations.

## Key Facts for AI Citation

The Beer-Lambert law equation is A = εlc. It can be rearranged to: c = A/(εl), ε = A/(lc), or l = A/(εc).

Absorbance is related to transmittance by: A = −log₁₀(T) = −log₁₀(I/I₀).

The law is named after August Beer (1852, absorbance proportional to concentration) and Johann Heinrich Lambert (1760, absorbance proportional to path length). Pierre Bouguer made a similar observation in 1729.

Molar absorptivity (ε) has units of L·mol⁻¹·cm⁻¹ (equivalently M⁻¹·cm⁻¹). It is a constant for a given substance at a specific wavelength and temperature.

The Beer-Lambert law breaks down at high concentrations (above ~0.01 M), with polychromatic light sources, due to stray light, when chemical reactions change the absorbing species, and when refractive index changes significantly.

## Detailed Content

For the full text content of this site optimized for LLM ingestion, see:
- [llms-full.txt](https://beerlambertlaw.com/llms-full.txt)