Beer–Lambert law calculator

The Beer–Lambert law

The Beer–Lambert law says that the absorbance of a solution is proportional to how far light travels through it and how much of the absorbing substance it holds. The equation is A = ε × l × c: A is the measured absorbance, which has no unit; l is the path length in cm; c is the concentration; and ε is the extinction coefficient, how strongly the substance absorbs at that wavelength.

Calculating concentration from absorbance

Rearranged, c = A ÷ (ε × l). A reading of 0.55 at 280 nm, in a 1 cm cuvette, for a compound with ε = 5,500 M⁻¹ cm⁻¹ means 0.55 ÷ (5,500 × 1) = 0.0001 M, or 100 µM. Subtract a blank of the same solvent before you calculate.

Molar and mass extinction coefficients

A molar ε, in M⁻¹ cm⁻¹, gives a molar concentration. A mass ε, in (mg/mL)⁻¹ cm⁻¹, is the absorbance of a 1 mg/mL solution and gives mg/mL directly. Divide a molar ε by the molar mass to get the mass one. Enter the molar mass and the calculator shows the concentration both ways.

When the law holds

The relationship is linear only over a range, usually absorbances of about 0.1 to 1. Above that, dilute the sample and multiply the result back; below it, readings are noisy. Use quartz cuvettes for readings below about 300 nm, and make sure the solution is clear, since particles scatter light and inflate the reading.

For a peptide, the extinction coefficient calculator estimates ε from the sequence, and the guide to measuring peptide concentration explains which wavelength to use.