Beer-Lambert Law Calculator
Determine the concentration of a solution from its measured absorbance, extinction coefficient, and path length using Beer-Lambert law. Essential for spectrophotometry and quantitative analytical chemistry.
About this calculator
The Beer-Lambert law states that A = ε × l × c, where A is absorbance (dimensionless), ε is the molar extinction coefficient (M⁻¹cm⁻¹), l is the path length in cm, and c is the molar concentration (M). Rearranging for concentration gives c = A / (ε × l). This calculator extends the standard formula to account for any prior dilution: c_original = [A / (ε × l)] × dilutionFactor. Absorbance is a logarithmic measure: A = −log₁₀(I/I₀), where I₀ is incident light intensity and I is transmitted intensity. The law holds linearly for absorbance values roughly between 0.1 and 1.0; outside this range, stray light and molecular interactions cause deviations. Path length is typically 1 cm for standard cuvettes.
How to use
A protein solution gives an absorbance of 0.75 at 280 nm. The molar extinction coefficient is 50,000 M⁻¹cm⁻¹, the cuvette path length is 1 cm, and the sample was diluted 5-fold before measurement. Enter: A = 0.75, ε = 50,000 M⁻¹cm⁻¹, l = 1 cm, dilution factor = 5. Concentration = (0.75 / (50,000 × 1)) × 5 = (0.75 / 50,000) × 5 = 1.5 × 10⁻⁵ × 5 = 7.5 × 10⁻⁵ M. The original protein concentration is 75 µM.
Frequently asked questions
What molar extinction coefficient should I use for common biomolecules?
For proteins, the extinction coefficient at 280 nm depends on the number of tryptophan, tyrosine, and cystine residues and can be predicted from the amino acid sequence (e.g., using ProtParam). For DNA, a common approximation is ε₂₆₀ ≈ 50 mL·µg⁻¹·cm⁻¹ for double-stranded DNA. For NADH, ε₃₄₀ = 6,220 M⁻¹cm⁻¹. Always use the extinction coefficient specific to your molecule, wavelength, and solvent conditions for accurate results.
Why does Beer-Lambert law fail at high concentrations?
At high concentrations, solute molecules are close enough to interact with each other, altering their electronic environment and changing the effective extinction coefficient. Additionally, the detector and light source introduce stray-light errors when absorbance exceeds ~1.5, because the transmitted signal becomes very small. Fluorescence from the sample can also interfere. For best accuracy, dilute samples to achieve absorbances between 0.1 and 1.0 before measuring, or use a shorter path length cuvette.
How does path length affect absorbance measurements in spectrophotometry?
According to Beer-Lambert law, absorbance is directly proportional to path length: doubling l doubles A for the same concentration. Standard cuvettes have a 1 cm path length, which is factored into most tabulated extinction coefficients. Micro-volume instruments like the NanoDrop use very short path lengths (0.02–1 mm) to measure concentrated samples without dilution. Always confirm the path length used and enter it correctly into calculations to avoid systematic concentration errors.