Beer-Lambert Law Calculator (absorbance ⇄ concentration)

Understanding the Beer–Lambert law calculator — concept and principle

The Beer–Lambert law links how much light a solution absorbs to how much of the absorbing substance it contains. This calculator converts a measured absorbance into concentration and also shows the transmittance, the share of light that passes through. It is the everyday tool of UV-visible spectrophotometry: measuring DNA and protein, following enzyme reactions through NADH, and quantifying dyes and metals.

Absorbance is linear in concentration: A = 0.5 means 31.6% transmitted and 80.4 µM NADH.

How it is calculated

A = ε × l × c, so c = A / (ε × l)

T = 10^(−A), shown as a percentage

A is the absorbance (unitless), ε the molar absorptivity in L/(mol·cm) at the chosen wavelength, l the path length in cm, and c the concentration in mol/L. The calculator multiplies by 10⁶ to show c in µM. The default ε = 6220 L/(mol·cm) is the widely used value for NADH at 340 nm.

The principle

Each thin layer of solution absorbs the same fraction of the light that reaches it, so intensity falls exponentially with depth. Absorbance is defined as the base-10 logarithm of incident over transmitted intensity, A = log₁₀(I₀/I), which turns this exponential decay into a straight line: doubling either path length or concentration doubles A. ε describes how strongly a molecule absorbs at that wavelength and is a property of the substance, solvent and wavelength.

Worked example

Inputs: A = 0.5, ε = 6220 L/(mol·cm), l = 1 cm.
c = 0.5 ÷ (6220 × 1) = 8.0386 × 10⁻⁵ mol/L.
In micromolar: 8.0386 × 10⁻⁵ × 10⁶ = 80.39 µM.
Transmittance: 10^(−0.5) = 0.3162, or 31.62%.

Each point is the calculator re-run with only “Molar absorptivity ε (L/mol·cm)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Molar absorptivity ε (L/mol·cm)	Concentration (µM)
1,555	321.5434084
3,110	160.7717042
4,665	107.1811361
6,220	80.38585209
7,775	64.30868167
9,330	53.59056806
12,440	40.19292605

How to read the result

A = 1 means only 10% of the light passes; A = 2 means 1%. Measurements are most reliable in a middle range, commonly about 0.1 to 1. Above that, little light reaches the detector and stray light causes readings to flatten; below it, the signal is close to noise. Dilute concentrated samples and multiply the result by the dilution factor.

Common mistakes

Forgetting to blank the instrument with the solvent or buffer.
Using ε for the wrong wavelength or in mM⁻¹cm⁻¹ instead of M⁻¹cm⁻¹ (6.22 versus 6220).
Ignoring the dilution factor.
Treating the law as valid at high absorbance or in turbid samples, where scattering adds false absorbance.

Keep in mind: The law assumes monochromatic light, a clear dilute solution and no chemical changes such as association or pH-dependent forms. Check linearity with standards of known concentration.

Frequently asked questions

What is the difference between absorbance and transmittance?

Transmittance is the fraction of light that passes; absorbance is −log₁₀ of that fraction, which is proportional to concentration.

Can I use a 0.5 cm cuvette?

Yes. Enter l = 0.5 and the concentration doubles for the same absorbance.

Why is NADH measured at 340 nm?

NADH absorbs strongly at 340 nm while NAD⁺ hardly does, so the change in absorbance follows the reaction.

Sources: IUPAC Compendium of Chemical Terminology (Gold Book), "Beer–Lambert law" and "absorbance" · D. A. Skoog, F. J. Holler and S. R. Crouch, Principles of Instrumental Analysis, Cengage

Checked 8 Nov 2026. Standard textbook formulas in SI units, computed in your browser. For learning and estimates — real designs must follow your local codes and be checked by a qualified engineer.

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