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 law formula
Worked examples
Example 1 — Absorbance from concentration:
Example 2 — Concentration from absorbance:
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
| Compound | λ_max (nm) | ε (L·mol⁻¹·cm⁻¹) |
|---|---|---|
| Benzene | 254 | 215 |
| Caffeine | 272 | 9,800 |
| Haemoglobin (oxyHb) | 415 | 125,000 |
| NADH | 340 | 6,220 |
| Methylene blue | 665 | 95,000 |
| KMnO₄ | 525 | 2,300 |
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.