Chemistry
Advanced

Beer–Lambert Law

Absorbance of light by a solution.

Formula

A=εlcA = \varepsilon l c

Variables

\varepsilonMolar absorptivity
lPath length
cConcentration

Example

Doubling the concentration of a coloured solution doubles its absorbance.

How it works

The Beer–Lambert law says that the amount of light absorbed by a solution increases with both the number of absorbing particles in the light path and the distance the light travels through the sample. In other words, a more concentrated solution or a longer cuvette gives a larger absorbance because more photons are removed from the beam. The molar absorptivity, ε, is a constant for a given substance at a specific wavelength and measures how strongly that substance absorbs that light.

When to use it

Use this law when determining the concentration of a coloured or UV-absorbing solution from spectrophotometer data, or when predicting how absorbance changes with concentration or path length. It is especially common in analytical chemistry, biochemistry, and environmental testing.

Worked example, step by step

A protein solution has a molar absorptivity of ε = 12,000 L mol^-1 cm^-1 at the measurement wavelength. The sample is placed in a cuvette with path length l = 1.00 cm. The measured absorbance is A = 0.600. Use A = εlc to solve for concentration: c = A / (εl) c = 0.600 / (12,000 × 1.00) c = 0.600 / 12,000 c = 5.0 × 10^-5 mol L^-1 Final answer: the concentration is 5.0 × 10^-5 M.

Common mistakes to avoid

  • Forgetting that ε is wavelength-dependent, so values from a different wavelength may give the wrong concentration
  • Using the wrong path length units; l must be in cm when ε is in L mol^-1 cm^-1
  • Applying the law to very concentrated or strongly scattering samples where the linear relationship breaks down

Did You Know?

The Beer–Lambert law lets a colorimeter find a solution's concentration just from how much light it absorbs.

Share this formula

Reviewed & maintained by the FormulaWon editorial teamLast reviewed September 2026