Beer-Lambert Law Calculators

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The Beer-Lambert law (Beer's law) describes the linear relationship between the absorbance of a solution and the concentration of the absorbing species and the path length through which light travels. The law states: A = ε × c × l, where A is absorbance (dimensionless), ε is the molar extinction coefficient (L/mol/cm), c is the concentration (mol/L), and l is the path length (cm, typically 1 cm). This fundamental relationship in analytical spectrophotometry enables direct calculation of concentration from measured absorbance, provided the measurement is within the linear range (OD 0.1–0.8).

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Beer-Lambert Formula

A = ε × c × l

A = absorbance = log₁₀(I₀/I) = −log₁₀(%T/100). ε = molar extinction coefficient (L/mol/cm) — a property of the substance at a specific wavelength. c = molar concentration (mol/L). l = path length (cm). Rearranged for concentration: c = A / (ε × l).

Molar Extinction Coefficients

  • DNA at 260 nm: ε (per base pair) = 6600 L/mol/cm; or use the practical conversion: 1 OD₂₆₀ = 50 μg/mL for dsDNA
  • RNA at 260 nm: 1 OD₂₆₀ = 40 μg/mL
  • BSA protein at 280 nm: ε ≈ 43,800 L/mol/cm; or A₂₈₀ = 1.0 ≈ 0.67 mg/mL for BSA
  • NADH at 340 nm: ε = 6220 L/mol/cm (key for coupled enzyme assays)
  • Hemoglobin at 415 nm (Soret band): ε ≈ 125,000 L/mol/cm

Linearity Range

Beer-Lambert law is linear only up to A ≈ 0.8–1.0. Above this, detector saturation and stray light cause non-linear response (measured A underestimates true c). Always dilute samples to keep A in the 0.1–0.8 range. At A < 0.1, signal-to-noise becomes poor. NanoDrop instruments auto-adjust path length to extend the linear range.

Deviations from Beer-Lambert Law

Chemical deviations: concentration-dependent association/dissociation of the absorbing species. Instrumental deviations: stray light (especially above A = 2); polychromatic light (monochromator bandwidth too wide); fluorescence from sample. These cause the calibration curve to deviate from linearity at high concentrations.

Glossary

Beer-Lambert Law
A = εcl; absorbance is proportional to molar concentration × path length × molar extinction coefficient; linear in the range A = 0.1–0.8; used to calculate concentration from absorbance.
Molar Extinction Coefficient (ε)
The absorbance of 1 mol/L of a substance in a 1 cm path length at a specific wavelength; units L/mol/cm; a fixed physical constant for each molecule-wavelength combination.
Absorbance (A)
A = log₁₀(I₀/I) = εcl; dimensionless measure of light attenuation; related to transmittance by A = −log₁₀(%T/100); linear with concentration per Beer-Lambert law below A ≈ 0.8.

Frequently Asked Questions

Beer-Lambert law: A = εcl, where A = absorbance, ε = molar extinction coefficient (L/mol/cm), c = concentration (mol/L), l = path length (cm). It states that absorbance is directly proportional to concentration and path length — the relationship is linear. To find concentration from absorbance: c = A/(ε × l). Example: a solution measured at A₃₄₀ = 0.45 using a 1 cm cuvette, ε_NADH = 6220 L/mol/cm: c = 0.45/(6220 × 1) = 7.24 × 10⁻⁵ M = 72.4 μM NADH.

The molar extinction coefficient (ε, also written ε_M) defines how strongly a substance absorbs light at a given wavelength: ε (L/mol/cm) = A/(c × l). It is a fixed physical constant for a given molecule at a given wavelength. Sources: published literature; ExPASy ProtParam tool calculates ε for proteins from sequence; manufacturer specifications for biochemical reagents; NIST chemistry database for small molecules. Key values in biochemistry: NADH at 340 nm = 6220; ATP at 260 nm ≈ 15,400; heme at 550 nm (reduced myoglobin) ≈ 14,000; β-carotene at 455 nm ≈ 139,000 L/mol/cm.

Beer-Lambert linearity holds only when absorbance is in the 0.1–0.8 range. Below 0.1: signal is small relative to detector noise (poor signal-to-noise ratio); small absolute errors translate to large relative concentration errors. Above 0.8: detector approaches saturation; stray light (a small fraction of the beam that bypasses the sample) becomes relatively significant compared to transmitted light, causing underestimation of true absorbance; this makes the measured concentration lower than actual. At A = 2 (only 1% transmission), stray light effects are severe and Beer-Lambert fails completely. Always dilute samples to keep A in the optimal range.

For pure proteins, A₂₈₀ is used: ε depends on the number of Trp, Tyr, and Cys residues (which absorb at 280 nm). Calculate ε from sequence using ExPASy ProtParam. Then: c (mg/mL) = A₂₈₀ / (ε/MW), where MW is in g/mol. For BSA: ε = 43,824 L/mol/cm; MW = 66,430 g/mol; specific ε = 43824/66430 = 0.660 mL/(mg·cm); so c = A₂₈₀/0.660 mg/mL. Important: A₂₈₀ doesn't distinguish intact from denatured protein; contaminating nucleic acids (absorbing at 260 nm) can inflate A₂₈₀. For mixed or impure samples, use colorimetric assays (BCA, Bradford) or fluorometric methods (NanoOrange) instead.