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

Core Formula

The Beer-Lambert Law describes the degree 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); reflects the intrinsic ability of a substance to absorb light at a specific wavelength. Must be obtained from the literature or reference handbooks; independent of sample concentration.
• c (concentration): units mol/L (M).
• l (path length): units cm; a standard quartz cuvette has a 1 cm path length.

With any three of the four variables known, 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)

Commonly Referenced 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 the NAD⁺/NADH cofactor — lactate dehydrogenase, malate dehydrogenase, alcohol dehydrogenase, and others — use this value for quantification; it is a known constant, usable directly like Avogadro’s number.

Applicable Range

1. Linear range A = 0.1–0.8: Above A = 1.0, stray light and detector nonlinearity cause readings to be systematically low, leading to underestimation of concentration. If the sample is too concentrated, dilute and remeasure, then multiply by the dilution factor.
2. Monochromatic light: The law assumes incident light of a single wavelength. With broadband filters, positive nonlinearity appears at high absorbance values.
3. Dilute solutions: At high concentrations (generally > 10 mmol/L), intermolecular interactions alter the electronic environment, ε is no longer constant, and the law breaks down.
4. Clear, homogeneous solutions: Turbid or particulate samples exhibit artificially elevated absorbance due to scattering (Tyndall effect), making any derived “concentration” meaningless. Centrifuge to clarify before measuring.

Common Errors

• Forgetting to blank: Zero the instrument against pure buffer before measurement; otherwise solvent absorption is included in the reading and concentrations will be overestimated.
• Plate readers defaulting to 1 cm path length: In a standard 96-well plate, the growth area per well is 0.32 cm² (Gibco Useful Numbers — the same source used by the on-site culture vessel calculator), and 100 µL of liquid gives a path length of approximately 0.31 cm. Using 1 cm will underestimate concentration by roughly 3.2-fold. Actual path length varies with well geometry and meniscus; most plate readers can measure path length directly and correct automatically — use that value when available.
• Confusing mass extinction coefficient (L·g⁻¹·cm⁻¹) with molar extinction coefficient: The two differ by a factor of molar mass and have different units; mixing them produces errors of roughly an order of magnitude.

A Complete Worked Example (subtract ΔA yourself — the calculator handles the rest)

Scenario: LDH enzyme activity assay, 1 cm cuvette, monitoring the decline in 340 nm absorbance as NADH is consumed.

t = 0 s:   A = 0.755
t = 60 s:  A = 0.133
ΔA = 0.755 − 0.133 = 0.622   ← subtract this yourself
(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

100 µM of NADH was consumed in 60 seconds. This result can be used directly to calculate enzyme activity (µmol/min), then divided by protein mass to obtain specific activity (µmol/min/mg).