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Beer–Lambert Law Calculator

Calculate absorbance, concentration, molar absorptivity (extinction coefficient) or path length with the Beer–Lambert law A = εlc. Also gives percent transmittance.

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    Beer–Lambert Law formula

    A = log10I0I = ε l c
    SymbolQuantitySI unitMeaning
    AAbsorbance—Absorbance (dimensionless)
    εMolar absorptivitym²/molMolar absorptivity / extinction coefficient at the wavelength used
    lPath lengthmOptical path length (cuvette width, usually 1 cm)
    cConcentrationmol/m³Concentration of the absorbing species

    What is Beer–Lambert Law?

    Beer–Lambert Law: The absorbance of light by a solution is proportional to the concentration of the absorbing species and the path length. — Bouguer 1729, Lambert 1760, Beer 1852

    The Beer–Lambert law is the foundation of UV-Vis spectrophotometry. Each thin layer of solution absorbs the same fraction of the light reaching it, so intensity falls exponentially with depth and absorbance (its logarithm) rises linearly with concentration.

    It is used to measure protein and DNA concentrations (A280, A260), to follow enzyme kinetics, for colorimetric assays and in water quality testing. The relationship is most reliable for absorbances between about 0.1 and 1.0.

    How to use this calculator

    1. Choose the quantity you want to find in the Calculate menu. It is highlighted as the result field.
    2. Enter the known values. Scientific notation such as 1.6e-11 is accepted.
    3. Select a unit for each value. Units are converted to SI automatically.
    4. The answer updates as you type. Open Show calculation steps to see the working, or use Copy result to share a link with your inputs.

    Worked example

    NADH absorbs at 340 nm with ε = 6220 L/(mol·cm). What is the absorbance of a 50 µmol/L solution in a 1 cm cuvette?

    1. A = 6220 × 1 × 50 × 10⁻⁶ = 0.311.
    2. Transmittance T = 10−0.311 = 48.9%.

    Frequently asked questions

    Why does Beer's law fail at high concentration?

    At high concentrations molecules interact, refractive index changes, and stray light becomes significant, so absorbance curves below the straight line. Dilute samples so that A is below about 1–1.5.

    What is the difference between absorbance and transmittance?

    Transmittance T = I/I₀ is the fraction of light that passes through. Absorbance is A = −log₁₀ T. A = 1 means 10% transmitted, and A = 2 means 1%.