Beer-Lambert Law Calculator
Find the concentration of a solution from its absorbance, molar extinction coefficient, and path length using Beer-Lambert law, with optional temperature correction. Widely used in spectrophotometry and analytical chemistry labs.
About this calculator
The Beer-Lambert law relates the attenuation of light passing through a solution to the properties of that solution: A = ε × c × l, where A is absorbance (dimensionless AU), ε is the molar extinction coefficient (L·mol⁻¹·cm⁻¹), c is the molar concentration (mol·L⁻¹), and l is the path length (cm). Rearranged to solve for concentration: c = A / (ε × l). This calculator extends the standard law with a solvent correction factor and a temperature-dependent term, giving c = A / (ε × l × S × (1 + 0.002 × (T − 20))), where S is the solvent factor and T is temperature in °C. The temperature term corrects for the slight change in molar absorptivity and solvent refractive index with temperature. The law assumes monochromatic light, dilute solutions (typically A < 1.5), and a homogeneous sample.
How to use
Suppose absorbance A = 0.750 AU, ε = 15,000 L·mol⁻¹·cm⁻¹, path length l = 1 cm, solvent factor S = 1.0, and temperature T = 25 °C. Temperature correction: 1 + 0.002 × (25 − 20) = 1 + 0.01 = 1.01. Denominator: 15,000 × 1 × 1.0 × 1.01 = 15,150. Concentration c = 0.750 / 15,150 ≈ 4.95 × 10⁻⁵ mol/L (≈ 49.5 µM). Enter these values into the calculator to confirm the result instantly.
Frequently asked questions
What is the molar extinction coefficient and how do I find it for my compound?
The molar extinction coefficient (ε), also called molar absorptivity, quantifies how strongly a substance absorbs light at a given wavelength. It is a fixed physical property of the compound measured in L·mol⁻¹·cm⁻¹. You can find it in published literature, spectral databases such as NIST or PubChem, or determine it experimentally by measuring absorbance of a series of known concentrations and applying Beer-Lambert law. Common examples include NADH at 340 nm (ε ≈ 6,220) and DNA at 260 nm (ε ≈ 50 for a 1 mg/mL solution per nucleotide conventions).
Why does Beer-Lambert law break down at high concentrations?
At high concentrations (typically A > 1.5 or concentrations above ~0.01 M), solute molecules are close enough to interact with each other, altering their electronic environment and changing ε. Additionally, stray light in the spectrophotometer and refractive index effects become significant. These deviations cause the absorbance–concentration relationship to curve rather than remain linear. For accurate results, dilute concentrated samples into the linear range before measurement, or construct a multi-point calibration curve.
How does path length affect absorbance measurements in a cuvette?
Path length is the distance light travels through the sample, typically 1 cm for standard cuvettes. Because A = ε × c × l, doubling the path length doubles the absorbance for the same concentration, effectively increasing sensitivity. Micro-cuvettes and fiber-optic probes can have path lengths from 0.01 cm to 10 cm, allowing measurement of very concentrated or very dilute samples respectively. Always enter the actual path length of your cuvette or flow cell into the calculator to get an accurate concentration.