The absorbance equation (Beer-Lambert law)
The absorbance equation is A = εbc, also written A = εlc or A = abc. Beer's law is the same relationship whichever letters your course uses:
How to calculate absorbance
Multiply the three: A = εbc. For a compound with ε = 6220 M-1cm-1 in a 1 cm cuvette at 50 µM (5×10-5 M): A = 6220 × 1 × 5×10-5 = 0.311.
Absorbance to concentration
Rearrange to c = A / (εb). Reading A = 0.311 with the same ε and cuvette: 0.311 / (6220 × 1) = 5×10-5 M, which is 50 µM.
Finding molar absorptivity
Rearrange to ε = A / (bc). That is how ε is measured in the first place: read the absorbance of a known concentration and divide.
How to find concentration from absorbance
The Beer-Lambert law says absorbance is directly proportional to concentration: A = εbc. Here A is the measured absorbance, ε (epsilon) is the molar absorptivity, a constant for a given substance and wavelength, b is the path length of the cuvette (almost always 1 cm), and c is the molar concentration. To find an unknown concentration, rearrange to c = A / (εb). If your instrument reports %transmittance instead of absorbance, convert first with A = −log₁₀(T), where T is the fraction of light transmitted (%T divided by 100). The law holds best at low absorbance (roughly A < 1); above that, readings deviate from linearity.
Related tools: Dilution calculator · Protein MW & extinction coefficient · all biochem tools.
Worked example 1: finding an unknown concentration
A sample reads A = 0.6 in a standard 1 cm cuvette, and the compound's molar absorptivity at this wavelength is ε = 6000 M⁻¹cm⁻¹ (the tool's default values).
This matches what the calculator shows by default: switch it to "Solve for c" with A = 0.6, ε = 6000, b = 1 and it returns 1.000e-4 M.
Worked example 2: a real assay: NADH at 340 nm
NADH has a molar absorptivity of ε = 6220 M⁻¹cm⁻¹ at 340 nm, a standard readout for enzyme assays that produce or consume NADH. What absorbance would a 50 µM NADH solution give in a 1 cm cuvette?
Set the tool to "Solve for A" with ε = 6220, b = 1, c = 0.00005 to reproduce this. This is the same math behind spectrophotometric enzyme assays like the classic lactate dehydrogenase (LDH) assay, which tracks NADH disappearance at 340 nm over time.
Absorbance ↔ %Transmittance, worked
For A = 0.6: %T = 100 × 10⁻⁰·⁶ = 25.12%. Going backward, A = −log₁₀(25.12/100) = 0.600, confirming the two directions are consistent (the converter above updates both fields live as you type either one).
FAQ
Why does Beer-Lambert break down at high absorbance?
Above roughly A = 1, stray light in the instrument and chemical effects (aggregation, shifted equilibria at high concentration) pull the reading away from strict linearity. Dilute until A is below about 1 before trusting the relationship.
What are the units of molar absorptivity (ε)?
M⁻¹cm⁻¹, per molar, per centimeter. It's specific to the molecule and wavelength (NADH at 340 nm ≈ 6220 M⁻¹cm⁻¹), not a universal constant.
Why is path length usually 1 cm?
Standard cuvettes are manufactured with a 1 cm internal path length so b drops out of A = εbc as simply "×1," letting absorbance compare directly to published ε values with no correction factor.
How do I convert absorbance to %transmittance?
%T = 100 × 10^(−A), and the reverse is A = −log₁₀(T) where T is %T ÷ 100. A = 0 means 100% transmitted (nothing absorbed); higher A means less light gets through.
Practice problems
1. A 0.0002 M solution gives A = 0.85 in a 1 cm cuvette. Find the molar absorptivity ε.
Show answer
2. A spectrophotometer reads 10% transmittance. What's the absorbance?