Beer-Lambert Law Calculator - Absorbance & Concentration
Free Beer-Lambert Law (Beer's Law) calculator: compute absorbance, transmittance, and concentration for spectroscopy, colorimetry, and UV-Vis analysis.
About This Calculator
The Beer-Lambert Law Calculator (also known as Beer's Law Calculator) computes the absorbance (A) and transmittance (%T) of light passing through a solution based on the Beer-Lambert-Bouguer law. It is essential for spectroscopy, colorimetry, and UV-Vis analysis in chemistry, biochemistry, and molecular biology labs. Students, researchers, and lab technicians use this tool to quantify analyte concentrations without manual calculations.
The Beer-Lambert law states that absorbance is directly proportional to the concentration of the absorbing species and the path length of the light beam: A = ε × c × l, where ε is the molar absorptivity (L/mol·cm), c is the concentration (mol/L), and l is the path length (cm). Transmittance is related to absorbance by T = 10−A, expressed as a percentage. The law assumes dilute solutions (typically below 0.01 M), monochromatic light, and no chemical interactions between analyte molecules.
Regional Notes
Global (SI units): Molar absorptivity is expressed in L·mol⁻¹·cm⁻¹, concentration in mol/L, and path length in cm (standard cuvette size). Absorbance is dimensionless. Most spectrophotometers worldwide report absorbance in absorbance units (AU).
United States: Laboratories may use μM (micromolar) concentrations or mg/mL for protein work (e.g., A₂₈₀ for BSA where ε = 43824 M⁻¹·cm⁻¹). Path length is typically 1 cm for standard cuvettes or 0.3–10 mm for micro-volume instruments.
United Kingdom & Europe: Follows the same SI conventions. The Beer-Lambert law is taught at A-level and undergraduate chemistry. The term "optical density" (OD) is sometimes used interchangeably with absorbance, though strictly OD includes scattering losses.
Frequently Asked Questions
What is the Beer-Lambert Law?
The Beer-Lambert Law (Beer's Law) states that absorbance A = epsilon times c times l, where A is absorbance, epsilon is molar absorptivity (L/mol·cm), c is concentration (mol/L), and l is path length (cm). It applies to dilute solutions and monochromatic light.
How do you calculate concentration from absorbance?
To find concentration from absorbance, rearrange Beer's Law to c = A / (epsilon times l). Measure the absorbance of your sample in a spectrophotometer, use the known molar absorptivity (epsilon) for your analyte at that wavelength, and divide by the cuvette path length (typically 1 cm).
What is the difference between absorbance and transmittance?
Absorbance (A) and transmittance (T) are related by A = -log10(T). Transmittance is the fraction of light that passes through a sample (I/I0), while absorbance measures how much light is absorbed. A solution with 1% transmittance has A = 2.0. Most accurate spectrophotometer readings are between A = 0.1 and 1.0.
What is molar absorptivity?
Molar absorptivity (epsilon) measures how strongly a chemical species absorbs light at a given wavelength. It is an intrinsic property of a substance, expressed in units of L/mol·cm. Values range from 0 to over 200,000 L/mol·cm, with high values indicating strong light absorption.
When does the Beer-Lambert Law fail?
The Beer-Lambert Law fails at high concentrations (typically above 0.01 M) due to molecular interactions and changes in refractive index. It also deviates with polychromatic light, stray light, or if the analyte undergoes chemical changes (e.g., dimerization). For reliable results, keep absorbance below 1.5.
How do you prepare a sample for UV-Vis spectroscopy?
Dissolve the sample in an appropriate solvent that does not absorb at the measurement wavelength. Filter to remove particulates, use clean quartz cuvettes for UV measurements (glass absorbs UV), scan a blank (solvent-only) as reference, and measure at the wavelength of maximum absorption (lambda max).
What are common applications of the Beer-Lambert Law?
Common applications include DNA/RNA quantification at 260 nm, protein concentration measurement at 280 nm, enzyme kinetics assays, drug concentration analysis in pharmaceuticals, environmental water testing for pollutants, food coloring concentration, and clinical diagnostics in medical laboratories worldwide.
What is the relationship between absorbance and concentration?
According to Beer's Law, absorbance is directly proportional to concentration (A proportional to c). This linear relationship is the basis for quantitative analysis using calibration curves. A plot of absorbance vs. concentration yields a straight line through the origin, with slope equal to epsilon times path length.