Beer-Lambert Law Calculator
Solve A = ε · l · c for absorbance, concentration, molar absorptivity, or path length.
Transmittance: %T = 10^(−A) × 100 = 1% (at A = 2).
The Beer-Lambert law states A = ε · l · c: absorbance equals molar absorptivity times path length times concentration. For ε = 20000 L·mol⁻¹·cm⁻¹, l = 1 cm, and c = 1×10⁻⁴ mol/L, A = 20000 × 1 × 0.0001 = 2.0, which corresponds to just 1% transmittance.
What the Beer-Lambert law describes
When light passes through a coloured solution, part of it is absorbed. The Beer-Lambert law links the measured absorbance to how strongly the substance absorbs (its molar absorptivity ε), how far the light travels through the sample (the path length l, usually the 1 cm cuvette), and how concentrated the solution is (c). Because absorbance is directly proportional to concentration, a spectrophotometer reading can be turned into a concentration once ε and l are known.
A absorbance (unitless) · ε molar absorptivity (L·mol⁻¹·cm⁻¹) · l path length (cm) · c concentration (mol/L). Transmittance: A = −log₁₀ T
Worked example
A dye with ε = 20000 L·mol⁻¹·cm⁻¹ is measured in a 1 cm cuvette at a concentration of 1×10⁻⁴ mol/L. What is its absorbance, and how much light gets through?
- 1 Pick the unknown. Choose which of A, ε, l, or c you are solving for; the calculator rearranges A = ε · l · c accordingly.
- 2 Enter the three known values. Here ε = 20000 L·mol⁻¹·cm⁻¹, l = 1 cm, and c = 1×10⁻⁴ mol/L, so A = 20000 × 1 × 0.0001.
- 3 Read the absorbance. A = 2.0. Absorbance has no units — it is the log of the light attenuation.
- 4 Convert to transmittance. T = 10^(−A) = 10⁻² = 0.01, so %T = 1%. Only 1% of the incident light passes through the sample.
Absorbance to transmittance
T = 10^(−A); %T = T × 100. Each unit of absorbance cuts transmitted light by a factor of ten.
| Absorbance (A) | Transmittance (T) | %T |
|---|---|---|
| 0 | 1 | 100% |
| 1 | 0.1 | 10% |
| 2 | 0.01 | 1% |
| 3 | 0.001 | 0.1% |
Where the linear law breaks down
It is only linear at low absorbance. Beer-Lambert holds when absorbance is roughly below 1; most instruments are most accurate between about 0.1 and 1.0. Above that, stray light and detector limits make the reading fall below the true proportional value.
High concentrations cause deviations. At high concentration the molecules interact, the refractive index shifts, and analytes may associate or dissociate — so absorbance stops rising in step with concentration. Diluting the sample back into the linear range restores the straight-line relationship.
ε depends on wavelength and conditions. Molar absorptivity is measured at a specific wavelength (usually the absorption maximum) and can change with solvent, pH, and temperature, so quote it alongside those conditions.