Science

Beer-Lambert Law Calculator

Calculate absorbance, transmittance, concentration, molar absorptivity, or path length using A = εcl. Leave any one field blank to solve for it.

beer-lambert-calculator
A = ε × c × l  |  A = −log₁₀(T)  |  Leave one field blank to solve for it.
Result
Absorbance (A)
Transmittance (T)
% Transmittance
% Absorbance
Step-by-step

Beer-Lambert law formula

A = ε × c × l A = absorbance (no units) ε = molar absorptivity (L·mol⁻¹·cm⁻¹) c = concentration (mol/L) l = path length (cm) A = −log₁₀(T) where T = I/I₀ (transmittance) T = 10^(−A)

Worked examples

Example 1 — Absorbance from concentration:

ε = 6,500 L·mol⁻¹·cm⁻¹ (caffeine at 272 nm), c = 0.001 mol/L, l = 1 cm A = ε × c × l = 6500 × 0.001 × 1 = 6.5 T = 10^(−6.5) = 3.2 × 10⁻⁷ (0.00003% transmitted)

Example 2 — Concentration from absorbance:

A = 0.42, ε = 5,500 L·mol⁻¹·cm⁻¹, l = 1 cm c = A/(ε × l) = 0.42 / (5500 × 1) = 7.64 × 10⁻⁵ mol/L = 76.4 µM

Real-world applications

Clinical chemistry: Spectrophotometric assays measure glucose, haemoglobin, and bilirubin in blood daily. Beer-Lambert converts absorbance to concentration — the core of automated clinical analysers.

Environmental monitoring: Nitrate (absorbs at 220 nm) and organic matter (254 nm) in water are measured by UV absorbance. Beer-Lambert gives direct concentration readings, enabling real-time water quality monitoring.

Food and beverage: Alcohol content, colour, and turbidity in beer, wine, and juice are measured spectrophotometrically. The Beer-Lambert law quantifies these parameters from absorbance readings without destructive testing.

Molar absorptivity of common compounds

Compoundλ_max (nm)ε (L·mol⁻¹·cm⁻¹)
Benzene254215
Caffeine2729,800
Haemoglobin (oxyHb)415125,000
NADH3406,220
Methylene blue66595,000
KMnO₄5252,300

Common questions

  • The Beer-Lambert law states that the absorbance of a solution is directly proportional to its concentration and the path length of light through it: A = εcl, where A is absorbance (dimensionless), ε is the molar absorptivity (L·mol⁻¹·cm⁻¹), c is concentration (mol/L), and l is path length (cm).
  • Transmittance (T) is the fraction of incident light that passes through the sample: T = I/I₀. It ranges from 0 to 1 (or 0–100%). Absorbance (A) is the negative log of transmittance: A = −log₁₀(T). A = 0 means no absorption; A = 1 means 90% of light is absorbed; A = 2 means 99%.
  • Beer-Lambert law fails at high concentrations (typically above 0.01 M), when solute molecules interact. It also breaks down for stray light, when the light source is not monochromatic, when the sample scatters light significantly, or when the solute undergoes chemical changes at different concentrations.
  • Molar absorptivity (ε), also called the molar extinction coefficient, is a measure of how strongly a chemical species absorbs light at a given wavelength. Units are L·mol⁻¹·cm⁻¹. It is a property of the molecule itself and the wavelength used — not of the concentration or path length.