The Beer-Lambert Law Calculator computes absorbance, transmittance, or concentration from A = ε × c × l. The universal spectrophotometric tool for analytical chemistry — from protein and DNA quantification to pharmaceutical quality control and environmental pollutant measurement.
1.5
AU
0.03162278
3.1623
%
0.96837722
1.5
AU/cm
1.5
AU
0.03162278
3.1623
%
0.96837722
1.5
AU/cm
Every UV-visible spectrophotometer in every analytical chemistry laboratory is performing Beer-Lambert Law calculations — typically hidden in firmware but fundamentally the same operation: measuring how much light is absorbed at a specific wavelength and converting that measurement to concentration. The calculator for Beer-Lambert Law applies the fundamental equation in all three directions: compute absorbance from concentration, solve for concentration from measured absorbance, or calculate the molar absorptivity from a known standard.
The Beer-Lambert Law relates absorbance to sample properties:
A = ε × c × l
where A is absorbance (dimensionless; the log₁₀ ratio of incident to transmitted light intensity), ε is the molar absorptivity (L mol⁻¹ cm⁻¹, a substance-specific constant at a given wavelength), c is the concentration (mol/L or M), and l is the optical path length (cm — typically 1 cm for standard cuvettes). Transmittance T = I/I₀ = 10^(−A). Percent transmittance %T = T × 100. A 50% transmittance = A = −log₁₀(0.5) = 0.301; A 1% transmittance = A = 2.000. Reference ε values: myoglobin at 280 nm: 15,200 L mol⁻¹ cm⁻¹; NADH at 340 nm: 6,220 L mol⁻¹ cm⁻¹; para-nitrophenol at 405 nm: 18,400 L mol⁻¹ cm⁻¹ (at pH above 7). Use this online calculator for any absorbance measurement. The advanced Beer-Lambert calculator includes incident intensity and transmission calculations.
The Beer-Lambert Law is linear only within the approximate absorbance range of 0.1–1.0 (90–10% transmittance). Outside this range:
Maximum accuracy is achieved in the 0.3–0.7 absorbance range. If your sample gives A above 1.5, dilute by a known factor, measure the diluted sample, and multiply the calculated concentration by the dilution factor.
Proteins absorb UV light at 280 nm due to aromatic amino acid residues (tryptophan: λmax 280 nm, ε = 5,500; tyrosine: 275 nm, ε = 1,490; phenylalanine: 257 nm, ε = 197). The extinction coefficient of a protein at 280 nm can be calculated from its amino acid composition using ProtParam or similar tools. For a pure protein with known ε₂₈₀, concentration (mg/mL) = A₂₈₀ / (ε₂₈₀ / Mw), where Mw is molecular weight in g/mol. Contamination with nucleic acids (which absorb strongly at 260 nm) inflates A₂₈₀ readings — check the A₂₆₀/A₂₈₀ ratio (should be approximately 0.57 for pure protein; if above 1.0, nucleic acid contamination is significant). The wavelength calculator and spectroscopy calculators provide complementary analytical chemistry tools.
Several factors cause real-world deviations from ideal Beer-Lambert behavior: chemical deviations (equilibria involving the analyte at high concentration, such as acid-base indicators or dimerization); instrumental deviations (non-monochromatic light — polychromatic sources require calibration curves rather than single-ε calculations); and sample deviations (light scattering from particles, fluorescence of the sample contributing to detected light, refractive index changes at high concentration). When calibration curves are nonlinear, use a polynomial or segmented fit rather than forcing Beer-Lambert linearity where it does not apply.
The Beer-Lambert law states:
$$A = \varepsilon l c$$
where A is the absorbance (dimensionless), ε is the molar absorptivity or molar extinction coefficient in L/(mol·cm), l is the optical path length in cm, and c is the molar concentration in mol/L. Absorbance is related to transmittance by:
$$A = -\log_{10}(T) = -\log_{10}\left(\frac{I}{I_0}\right)$$
where T is the fraction of light transmitted and I/I₀ is the ratio of transmitted to incident light intensity. Rearranging:
$$T = 10^{-A} = 10^{-\varepsilon l c}$$
The law assumes: (1) monochromatic radiation, (2) dilute solutions (typically c < 0.01 M), (3) no scattering or fluorescence, (4) no chemical interactions that change the absorbing species, and (5) homogeneous solution. At high concentrations, deviations from linearity occur due to molecular interactions and refractive index changes.
An absorbance of 1.0 means that 90% of the light is absorbed (10% transmitted). An absorbance of 2.0 means 99% absorbed (1% transmitted). In practice, absorbance values between 0.1 and 1.0 provide the most reliable measurements, as very low absorbances are subject to noise and very high absorbances (>2) suffer from detector limitations and nonlinear behavior. The transmittance output provides the complementary view — what fraction of incident light passes through the sample. Molar absorptivity values vary enormously: weak transitions might have ε ≈ 10, while strongly allowed electronic transitions can reach ε > 100,000 L/(mol·cm).
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Results
A 0.5 mM KMnO₄ solution in a 1 cm cuvette with ε = 2455 L/(mol·cm) at 525 nm gives an absorbance of 1.23. Only about 5.9% of the green light is transmitted, giving the solution its characteristic deep purple color.
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Results
Double-stranded DNA has ε ≈ 6600 L/(mol·cm) per base pair at 260 nm. A solution containing ~76 μM (in nucleotides) gives A₂₆₀ ≈ 0.5, corresponding to approximately 50 μg/mL — a common concentration for molecular biology work.
Molar absorptivity (also called the molar extinction coefficient) is a measure of how strongly a chemical species absorbs light at a particular wavelength. It has units of L/(mol·cm) and is an intrinsic property of the molecule. High ε values (>10,000) indicate strongly absorbing species, typically with extended conjugation or charge-transfer transitions.
Beer's law deviates from linearity at high concentrations (typically >0.01 M) due to molecular interactions, electrostatic effects, and refractive index changes. Other causes of deviation include polychromatic radiation, fluorescence, scattering, chemical equilibria, and stray light in the spectrophotometer.
The optimal range is typically 0.2–0.8 AU, where the relative error in concentration is minimized. At very low absorbances (<0.1), photometric noise dominates. At very high absorbances (>2), stray light and detector limitations cause significant errors. The minimum relative error occurs at A = 0.434.
Standard spectrophotometry cuvettes have a 1 cm path length. For concentrated samples, shorter path lengths (0.1 cm, 0.01 cm) are used. For dilute samples or micro-volume instruments (like NanoDrop), path lengths of 0.05–1 mm are common. Fiber-optic probes can have path lengths of several centimeters.
Measure the absorbance of the unknown solution at the wavelength of maximum absorption (λ_max). If you know ε and l, calculate c = A/(εl). Alternatively, prepare a calibration curve with standards of known concentration, plot A vs. c, and interpolate the unknown from the linear region.
In practice, absorbance and optical density (OD) are often used interchangeably. Strictly, absorbance refers only to absorption of light, while optical density includes all sources of light attenuation (absorption + scattering). For clear solutions, they are equivalent. For turbid samples or cell cultures, OD includes scattering contributions.
Yes. For gases, concentration is replaced by number density (molecules/cm³) or partial pressure, and the molar absorptivity is replaced by the absorption cross-section (σ, in cm²/molecule). The law becomes A = σNl, where N is the number density and l is the path length.
An isosbestic point is a wavelength at which two interconverting species have equal molar absorptivities. At this wavelength, absorbance is independent of the ratio of the two species, depending only on total concentration. Isosbestic points confirm clean interconversion without side reactions.
When multiple absorbing species are present, absorbance is additive: A_total = ε₁lc₁ + ε₂lc₂ + ... By measuring absorbance at multiple wavelengths (one per component minimum), a system of linear equations can be solved simultaneously to determine each component's concentration.
They are logarithmically related: A = -log₁₀(T) or T = 10⁻ᴬ. 0% T = infinite A (all light absorbed), 100% T = 0 A (no absorption). Common conversions: A=0.3 → T=50%, A=1.0 → T=10%, A=2.0 → T=1%, A=3.0 → T=0.1%.
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