Beer-Lambert Law
Also known as Lambert's law, Beer's law, and the Beer-Lambert-Bouguer law - the fundamental relationship between light absorbance, concentration, and path length in spectroscopy.
A = ε · l · c
What Is the Beer-Lambert Law?
The Beer-Lambert law (sometimes written Beer–Lambert law) describes how the absorption of light by a substance is related to the properties of that substance and the light's path through it. Specifically, absorbance is directly proportional to both the molar concentration of the absorbing species and the distance (path length) the light travels through the sample.
The law is named after August Beer, who in 1852 showed that absorbance is proportional to concentration, and Johann Heinrich Lambert, who in 1760 showed that absorbance is proportional to path length. Pierre Bouguer made a similar observation even earlier (1729), which is why the law is sometimes called the Beer-Lambert-Bouguer law.
The equation is central to UV-Vis spectroscopy, infrared spectroscopy, and virtually every quantitative absorption measurement in chemistry, biochemistry, clinical diagnostics, and environmental science.
Explore the Beer-Lambert Law
Beer-Lambert Law Calculator
Enter any three of A, ε, l, and c to solve for the fourth - instantly and free.
Equation Explained
Understand each variable in A = εlc with definitions, units, and diagrams.
Worked Examples
Four fully solved problems with step-by-step solutions you can verify.
Mathematical Derivation
Derive A = εlc from first principles in three clear steps.
Practice Problems
Eight problems from easy to challenging - test your understanding.
Limitations & Deviations
When and why the Beer-Lambert law breaks down in real experiments.
Molar Absorptivity Table
Reference extinction coefficients for common compounds, with unit conversions.
Absorbance vs. Concentration Graph
Interactive chart showing the ideal linear relationship and real deviations.
Absorbance & Transmittance
Convert between absorbance and %T with an interactive tool and reference table.
Real-World Applications
How A = εlc is used across pharmaceuticals, clinical labs, environmental science, and more.
Frequently Asked Questions
What is the Beer-Lambert Law?
The Beer-Lambert law states that the absorbance of light by a solution is directly proportional to both the concentration of the absorbing species and the path length. The equation is A = εlc, where A is absorbance, ε is molar absorptivity, l is path length, and c is concentration.
What is Lambert's law?
Lambert's law states that absorbance is directly proportional to the path length of light through a material. Combined with Beer's law (absorbance proportional to concentration), it forms the Beer-Lambert law: A = εlc.
What is Beer's law?
Beer's law states that absorbance is directly proportional to the concentration of the absorbing species. Together with Lambert's law (path length dependence), it gives the Beer-Lambert law.
How do I calculate concentration from absorbance?
Rearrange the Beer-Lambert law to c = A / (ε × l). Measure absorbance on a spectrophotometer, look up the molar absorptivity for your compound, and use your cuvette path length (usually 1 cm).
What are the units of molar absorptivity?
Molar absorptivity (ε) has units of L·mol⁻¹·cm⁻¹, also written M⁻¹·cm⁻¹. It is a constant for a given substance at a specific wavelength and temperature.
When does the Beer-Lambert Law not work?
The law breaks down at high concentrations (above ~0.01 M), with polychromatic light, due to stray light, when chemical reactions change concentration, and when refractive index shifts significantly.
Why is absorbance dimensionless?
Absorbance is A = −log₁₀(I/I₀), the logarithm of a ratio of two light intensities. Since both have the same units, they cancel, giving a pure number.
What is the difference between absorbance and transmittance?
Transmittance (T) is the fraction of light that passes through: T = I/I₀. Absorbance is A = −log₁₀(T). The Beer-Lambert law uses absorbance because A is linear with concentration, while T is exponential.
What is the Beer-Lambert Law used for?
It is used in UV-Vis and infrared spectroscopy to determine the concentration of substances in solution. Applications include clinical chemistry, environmental monitoring, pharmaceutical QC, and food science.
What is the Beer-Lambert Law formula?
The formula is A = εlc. It can be rearranged to solve for any variable: c = A/(εl), ε = A/(lc), or l = A/(εc).