Calculate absorbance, transmittance, molar absorptivity, concentration, and path length using the Beer-Lambert law for spectrophotometry.
The Beer-Lambert law (also called Beer's law) is the foundational equation in spectrophotometry that relates the absorption of light to the properties of the material through which the light is traveling. It states that absorbance is directly proportional to the concentration of the absorbing species and the path length of the sample cell. This linear relationship is expressed as A = εlc, where A is absorbance, ε is the molar absorptivity (extinction coefficient), l is the path length, and c is the concentration.
Understanding and applying the Beer-Lambert law is essential in analytical chemistry, biochemistry, environmental science, and clinical diagnostics. Whether you're measuring protein concentration with a UV-Vis spectrophotometer, quantifying pollutants in water samples, or determining drug concentrations in pharmaceutical formulations, this calculator simplifies the math and helps you solve for any unknown variable.
This calculator supports solving for absorbance, transmittance, concentration, molar absorptivity, or path length — simply enter the known values and select what you want to find. It also provides the percent transmittance (%T) conversion, optical density interpretation, and a reference table of common molar absorptivities for frequently analyzed compounds.
This calculator eliminates manual computation errors when working with spectrophotometric data. It handles unit conversions, solves for any unknown in the Beer-Lambert equation, and provides reference data for common compounds — saving time in both teaching labs and research settings. This beer-lambert law calculator helps you compare outcomes quickly and reduce avoidable mistakes when making day-to-day care decisions. Use the estimate as a planning baseline and confirm final decisions with a qualified professional when risk is high.
Beer-Lambert Law: A = ε × l × c, where A = absorbance (dimensionless), ε = molar absorptivity (L mol⁻¹ cm⁻¹), l = path length (cm), c = concentration (mol/L). Transmittance: T = 10^(−A), %T = T × 100.
Result: Absorbance = 3.11, Transmittance = 0.0776%
NADH at 340 nm has ε = 6220 L/(mol·cm). With a 1 cm cuvette and 0.5 mM concentration: A = 6220 × 1 × 0.0005 = 3.11. Transmittance = 10^(−3.11) = 0.000776, or 0.0776%.
The Beer-Lambert law forms the theoretical basis for nearly all quantitative spectrophotometric analyses. In UV-Vis spectroscopy, a beam of light at a specific wavelength passes through a sample in a cuvette. The amount of light absorbed depends on three factors: the identity of the absorbing molecule (molar absorptivity ε), how much of it is present (concentration c), and the distance the light travels through the sample (path length l). When these three factors are multiplied together, you get the absorbance value, which is what the spectrophotometer reports.
Beer's law is used extensively in clinical chemistry (measuring hemoglobin, bilirubin, glucose), environmental monitoring (nitrate, phosphate in water), pharmaceutical quality control (drug assay), and biochemistry (protein quantification via Bradford or BCA assays). However, it assumes ideal conditions — monochromatic light, dilute solutions, no scattering, and no chemical interactions between solute molecules. At high concentrations, intermolecular interactions cause deviations from linearity, which is why calibration curves are essential for real-world analyses.
In practice, analysts prepare a series of standard solutions at known concentrations, measure their absorbance, and plot a calibration curve (absorbance vs. concentration). If Beer's law holds, this plot is linear with a slope equal to ε × l. Unknown sample concentrations are then determined by interpolation. This approach accounts for instrumental and matrix-specific deviations that the theoretical equation cannot predict.
It states that absorbance is directly proportional to concentration and path length: A = εlc. It applies when light passes through a solution and some wavelengths are absorbed by the solute.
Deviations occur at high concentrations (>0.01 M), with scattering solutions, fluorescent samples, polychromatic light sources, or when chemical equilibria shift with concentration changes.
Molar absorptivity (extinction coefficient) is an intrinsic property of a substance describing how strongly it absorbs light at a given wavelength. Units are L/(mol·cm).
Use T = 10^(−A). For example, A = 1.0 gives T = 0.1 or 10% transmittance, meaning 90% of light is absorbed.
Standard cuvettes have a 1 cm path length. Microcuvettes may be 0.1 cm, and flow cells can vary from 0.01 to 10 cm.
Optical density (OD) is often used synonymously with absorbance. An OD of 1 means 90% of light is absorbed; OD 2 means 99% is absorbed.
Beer's law applies at each wavelength independently. For mixtures, use simultaneous equations at multiple wavelengths with each component's ε values.