Beer-Lambert Law Calculator: Absorbance, Extinction Coefficient, and Concentration

Core Formula

The Beer-Lambert Law describes the extent to which light is absorbed as it passes through a solution:

A = ε × c × l

• A (Absorbance): dimensionless, read directly from a spectrophotometer; also written as OD (Optical Density).
• ε (Molar Extinction Coefficient, also called molar absorptivity): units M⁻¹cm⁻¹ (= L·mol⁻¹·cm⁻¹); represents the intrinsic capacity of a substance to absorb light at a specific wavelength. Obtain from the literature or a reference handbook; independent of sample concentration.
• c (concentration): units mol/L (M).
• l (path length): units cm; a standard quartz cuvette is 1 cm.

Given any three of the four variables, the fourth can be solved:

Solve for concentration:          c = A / (ε × l)
Solve for extinction coefficient: ε = A / (c × l)
Solve for absorbance:             A = ε × c × l
Solve for path length:            l = A / (ε × c)

Common Reference Extinction Coefficients

The ε of NADH at 340 nm = 6 220 M⁻¹cm⁻¹ is the most widely cited extinction coefficient in biochemistry. All enzyme activity assays that depend on NAD⁺/NADH cofactors (lactate dehydrogenase, malate dehydrogenase, alcohol dehydrogenase, etc.) use this value for conversion — it is a fixed known quantity, used as directly as Avogadro’s number.

Applicable Limits

1. Linear range A = 0.1–0.8: Above 1.0, stray light and detector non-linearity cause readings to be falsely low, systematically underestimating concentration. If the sample is too concentrated, dilute and re-measure, then multiply back by the dilution factor.
2. Monochromatic light: The law assumes monochromatic incident light. Broadband filters introduce positive non-linearity errors at high absorbance.
3. Dilute solutions: At high concentrations (typically > 10 mmol/L), solute–solute interactions alter the electronic environment and ε is no longer constant; the law breaks down.
4. Clear, homogeneous solutions: Turbid or particle-containing samples scatter light (Tyndall effect), inflating the absorbance reading; any “concentration” derived from such a reading is meaningless. Centrifuge to clarify before measuring.

Common Mistakes

• Forgetting to blank the instrument: Always zero against pure buffer before measuring; otherwise the solvent’s own absorbance adds to the reading, inflating the apparent concentration.
• Assuming 1 cm path length on a plate reader: Each well of a standard 96-well plate has a growth area of 0.32 cm² (Gibco Useful Numbers, the same dataset used in the site’s Culture Vessel Converter); 100 µL of sample gives a path length of roughly 0.31 cm — using 1 cm will underestimate concentration by about 3.2-fold. Path length also varies with well geometry and meniscus; most plate readers can measure it directly and apply the correction automatically — use that measured value when available.
• Confusing mass extinction coefficient (L·g⁻¹·cm⁻¹) with molar extinction coefficient: The two differ by a molar mass factor and have different units; mixing them up produces errors of an order of magnitude.

Worked Example

Scenario: LDH enzyme activity assay, 1 cm cuvette, monitoring the decrease in absorbance at 340 nm due to NADH consumption.

t = 0 s:  A = 0.755
t = 60 s: A = 0.133
ΔA = 0.755 − 0.133 = 0.622
(both readings fall within the linear range 0.1–0.8)

ε = 6 220 M⁻¹cm⁻¹, l = 1 cm

Δc = ΔA / (ε × l)
   = 0.622 / (6 220 × 1)
   = 1.000 × 10⁻⁴ mol/L
   = 100.0 µM

NADH consumed in 60 s is exactly 100 µM. This result can be used directly to calculate enzyme activity (µmol/min) and, after dividing by protein content, specific activity (µmol/min/mg).