SpectralBench
A = εlc — solve for any variable
The Beer-Lambert law (A = εlc) is foundational to quantitative spectroscopy, linking the absorbance of a sample to its concentration, path length, and molar absorptivity. Whether you're determining an unknown concentration from a measured absorbance or planning an experiment around a target optical density, this calculator gives you the answer instantly.
Enter any three of the four variables and SpectralBench solves for the fourth. The built-in graph visualizes how absorbance changes with concentration, making it easy to identify the linear range and spot potential deviations at high optical densities. Pair it with the SNR Calculator to evaluate whether your measurement has sufficient signal quality, or load your spectrum in the Spectral File Viewer to read absorbance values directly from your data.
Select which variable you want to solve for: absorbance, molar absorptivity, path length, or concentration. Enter the three known values into the corresponding fields and SpectralBench calculates the fourth instantly — no page reload, no submit button.
The interactive graph below the calculator plots absorbance as a function of concentration using your current molar absorptivity and path length values. Drag the concentration slider to see how the absorbance reading changes in real time. This visualization makes it easy to identify the linear range where Beer's Law holds and to see where deviations begin at higher concentrations.
The Beer-Lambert law describes the linear relationship between the absorbance of a sample and its concentration in dilute solutions. The equation A = εlc connects four quantities:
The law assumes monochromatic light, dilute solutions, no scattering, and no chemical interactions between analyte molecules. When these conditions hold, a plot of absorbance versus concentration yields a straight line passing through the origin.
Understanding when Beer's Law breaks down is as important as knowing how to apply it. Deviations fall into three categories:
Real deviations occur at high concentrations (typically when absorbance exceeds 1.0) where intermolecular interactions — electrostatic, hydrogen bonding, or aggregation — alter the effective molar absorptivity. The relationship between absorbance and concentration becomes non-linear.
Instrumental deviations arise from polychromatic light sources (no monochromator produces truly monochromatic light), stray light reaching the detector, and detector non-linearity at extreme absorbance values.
Chemical deviations occur when the analyte undergoes fluorescence, scattering, association, dissociation, or chemical equilibria that shift with concentration. In these cases the effective absorbing species changes with dilution.
The interactive graph in SpectralBench's calculator helps you visualize where the linear range ends for your specific parameters, so you can design experiments that stay within the valid regime.
Rearrange the Beer-Lambert law to c = A / (ε × l). Enter your measured absorbance, the molar absorptivity of your analyte at the measurement wavelength, and the cuvette path length. SpectralBench solves for concentration instantly.
Molar absorptivity (ε), also called the molar extinction coefficient, is an intrinsic property of a substance that describes how strongly it absorbs light at a given wavelength. Its units are L mol⁻¹ cm⁻¹. Higher values mean stronger absorption — a small amount of the substance produces a large absorbance reading.
Beer's Law assumes dilute solutions, monochromatic light, no scattering, and no chemical interactions between analyte molecules. It breaks down at high concentrations (typically A > 1) due to intermolecular interactions, with polychromatic light sources, in scattering samples, and when chemical equilibria shift with concentration.
The calculator uses SI-compatible units: absorbance is dimensionless (log₁₀ ratio), molar absorptivity is in L mol⁻¹ cm⁻¹, path length is in cm, and concentration is in mol/L (M). These are the standard units used in analytical chemistry and spectroscopy.