Beer-Lambert Law Calculator

The Beer-Lambert Law (also called Beer's Law) describes how light is absorbed as it passes through a solution. It states that absorbance (A) equals the product of the molar extinction coefficient (ε), the path length (l), and the concentration (c): A = ε × l × c. The law is fundamental in spectrophotometry and analytical chemistry.

Absorbance is dimensionless — it has no units. It is defined as the negative logarithm (base 10) of transmittance: A = −log₁₀(T). Because it is a ratio of intensities, the units cancel out. Typical absorbance values in laboratory work range from 0.1 to 2.0 for reliable measurements.

Rearrange the Beer-Lambert equation to isolate ε: ε = A / (l × c). You need the measured absorbance, the known path length (usually 1 cm), and the known concentration in mol/L. The result is expressed in units of M⁻¹ cm⁻¹.

Rearrange the formula to c = A / (ε × l). Measure the absorbance of your sample spectrophotometrically, then divide by the product of the known extinction coefficient and path length. This is one of the most common uses of Beer's Law in laboratory settings — for example, determining protein or DNA concentration.

Transmittance (T) and absorbance (A) are related by: T = 10^(−A), and expressed as a percentage: %T = 10^(−A) × 100. For example, an absorbance of 1.0 corresponds to 10% transmittance, meaning 90% of the incident light was absorbed by the sample.

Beer's Law assumes a linear relationship between absorbance and concentration, which holds true only at relatively low concentrations (typically below 0.01 M). At high concentrations, interactions between solute molecules, stray light effects, and non-monochromatic radiation can cause deviations. The law also assumes the solution is homogeneous and the solute does not fluoresce or scatter light significantly.

Most standard laboratory cuvettes have a path length of 1 cm, which simplifies the equation to A = ε × c. However, micro-cuvettes, flow cells, and fiber-optic probes can have different path lengths. Always confirm your cuvette's path length before performing calculations, especially for non-standard setups.

Beer's Law is widely used in UV-Vis spectrophotometry to determine the concentration of solutions such as DNA, RNA, proteins, and small molecules. It is also applied in environmental monitoring (measuring pollutant concentrations in water), pharmaceutical quality control, food and beverage analysis, and clinical diagnostics such as hemoglobin measurement in blood.