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Beer-Lambert Law Calculator

Apply the Beer-Lambert law: absorbance from concentration, concentration from absorbance, or ε from a standard, and convert absorbance to transmittance.

Formula

A=ε ℓ cA = \varepsilon\,\ell\,c
c=Aε ℓc = \dfrac{A}{\varepsilon\,\ell}
%T=10−A×100;A=−log⁡10T\%T = 10^{-A}\times 100;\quad A = -\log_{10}T
AA
absorbance, dimensionless
ε\varepsilon
molar extinction coefficient, in M⁻¹ cm⁻¹
ll
path length, in cm
cc
concentration, in mol/L

How it works

Light passing through an absorbing solution is attenuated exponentially with the path length and the concentration. Expressed as absorbance, the base-10 logarithm of the ratio of incident to transmitted light, it is directly proportional to both: doubling the concentration doubles the absorbance. The constant of proportionality, ε, is characteristic of the substance and the wavelength.

Absorbance measures how much light is absorbed on a logarithmic scale, so A = 1 means 10% of the light gets through and A = 2 means 1%. Readings above about 1 to 1.5 are unreliable because so little light reaches the detector, and stray light makes the response flatten; dilute the sample instead.

Worked example

An NADH solution (ε₃₄₀ = 6,220 M⁻¹ cm⁻¹) reads A = 0.65 in a 1 cm cuvette.

  1. c = A / (ε × l) = 0.65 / (6,220 × 1) = 1.045 × 10⁻⁴ mol/L.
  2. %T = 10^(−0.65) × 100 = 22.4%.

The NADH concentration is 104.5 µM, and 22.4% of the light is transmitted.

These are the values the calculator opens with, so you can check its output against this example.

Assumptions

  • A dilute solution of a single absorbing species, where ε does not depend on concentration.
  • Monochromatic light, and no scattering, fluorescence or chemical change with concentration.
  • The reading is blank-corrected, in the instrument's linear range.

Common mistakes

  • Reading above about A = 1.5 and trusting the result. Dilute and re-read.
  • Using an ε measured at a different wavelength, pH or solvent.
  • Forgetting the dilution factor, or entering the path length of a microplate well as 1 cm.

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Service documentation, failure modes and parts for the instruments this calculation is used with.