Beer–Lambert law calculator

Choose the unknown, then enter the other quantities. Absorbance can be typed directly or as percent transmittance.

A = log₁₀(I₀ ÷ I) = −log₁₀ T = ε l c

ε is the molar (decadic) absorption coefficient in M⁻¹ cm⁻¹ (L mol⁻¹ cm⁻¹), l the path length in cm and c the concentration in mol/L. With a mass coefficient (the absorbance of a 1 mg/mL solution, in mL mg⁻¹ cm⁻¹) the concentration is in mg/mL. A molar mass converts between the two.

Limits

• The law holds for dilute, clear solutions at one wavelength. Most instruments become non-linear above an absorbance of about 1 to 1.5 (under 3–10 % of the light gets through): dilute and measure again.
• Subtract a blank of the solvent and cuvette, and use the ε measured under the same conditions (wavelength, pH, solvent, temperature).
• Scattering samples (cells, precipitates) and fluorescent samples break the law.

Worked example

NADH at 340 nm has ε = 6220 M⁻¹ cm⁻¹. An absorbance of 0.311 in a 1.00 cm cuvette gives c = 0.311 ÷ (6220 × 1.00) = 5.00 × 10⁻⁵ M = 50.0 µM; that absorbance transmits 48.9 % of the light.

References

• IUPAC Gold Book: absorbance, molar (decadic) absorption coefficient and Beer–Lambert law
• IUPAC, Quantities, Units and Symbols in Physical Chemistry (Green Book), 3rd edition (2007)