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Category Physics & Science

Solve for:

Absorbance (A, dimensionless) Optical density. Typical range: 0.1–2.0

Molar Absorptivity (ε, L·mol⁻¹·cm⁻¹) Extinction coefficient at λ_max

Path Length (l, cm) Cuvette width. Standard: 1 cm

Concentration (c, mol/L) Molar concentration (M)

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About

The Beer-Lambert Law (A = ε ⋅ l ⋅ c) defines the linear relationship between absorbance and concentration of an absorbing species in a homogeneous medium. An incorrect molar absorptivity coefficient or an uncalibrated path length will propagate errors through every quantitative measurement in UV-Vis, IR, and atomic absorption spectroscopy. This tool computes any single unknown - A, ε, l, or c - from the remaining three, and simultaneously reports transmittance (T) and percent transmittance (%T).

The law assumes monochromatic radiation, dilute solutions (typically A < 2), no fluorescence or scattering, and chemical homogeneity. Deviations appear at high concentrations due to solute-solute interactions and refractive index shifts. This calculator approximates ideal conditions. Real cuvette path lengths vary by ±0.01 cm from nominal; always verify with a manufacturer certificate.

Formulas

The Beer-Lambert Law relates the attenuation of light to the properties of the material through which the light travels:

A = ε ⋅ l ⋅ c

Where A = absorbance (dimensionless, also called optical density), ε = molar absorptivity (molar extinction coefficient) in L⋅mol⁻¹⋅cm⁻¹, l = optical path length in cm, and c = molar concentration in mol/L (M).

Transmittance is derived from absorbance:

T = 10^−A

%T = T × 100

Rearranging to solve for each variable:

ε = Al ⋅ c

l = Aε ⋅ c

c = Aε ⋅ l

The relationship between absorbance and transmittance can also be expressed as: A = −log₁₀(T). Linearity holds when A < 2 (i.e., %T > 1%).

Reference Data

Compound	Solvent	λ_max nm	ε L⋅mol⁻¹⋅cm⁻¹	Application
NADH	Water	340	6220	Enzyme kinetics
DNA (double-stranded)	TE Buffer	260	6600 per bp	Nucleic acid quantification
BSA (Bovine Serum Albumin)	Water	280	43824	Protein quantification
p-Nitrophenol	0.1 M NaOH	405	18300	Enzyme assay substrate
KMnO₄	Water	525	2455	Redox titration indicator
Bromothymol Blue	Water (pH 7.6)	616	39550	pH indicator
Methylene Blue	Water	664	95000	Biological staining
Chlorophyll a	Diethyl Ether	661	86300	Photosynthesis research
Chlorophyll b	Diethyl Ether	642	56100	Photosynthesis research
β-Carotene	Hexane	453	134000	Antioxidant analysis
Cytochrome c (reduced)	Phosphate Buffer	550	29500	Mitochondrial assays
Fluorescein	0.1 M NaOH	490	76900	Fluorescence standard
Rhodamine 6G	Ethanol	530	116000	Laser dye / tracing
Hemoglobin (oxy)	Water	415	131000	Blood oxygen studies
Tryptophan	Water	280	5500	Protein A280 method
Tyrosine	Water	274	1400	Protein A280 method
Phenylalanine	Water	257	200	Amino acid analysis
Crystal Violet	Water	590	87000	Gram staining
Congo Red	Water	497	45500	Amyloid detection
Caffeine	Water	273	9900	Food/pharma QC

Frequently Asked Questions

At high concentrations (typically above A ≈ 2), solute-solute interactions alter the molar absorptivity ε, which the law assumes constant. Refractive index changes, aggregation, and chemical equilibrium shifts (such as dimerization) cause non-linear absorbance-concentration curves. Dilute samples to bring A into the 0.1 - 1.0 range for reliable measurements.

Absorbance is directly proportional to path length l. Standard cuvettes use 1 cm path length. NanoDrop instruments use path lengths as short as 0.05 cm to handle concentrated samples without dilution. Increasing l to 5 or 10 cm improves sensitivity for trace analytes, but requires proportionally more sample volume.

Transmittance (T) is the fraction of incident light that passes through the sample; it ranges from 0 to 1. Absorbance (A = −log₁₀T) converts this exponential decay into a linear scale proportional to concentration. Spectrophotometers measure T directly via detector current ratios; A is a computed value. Report results in absorbance for quantitative work because concentration linearity simplifies calibration curves.

This tool computes single-component, single-wavelength Beer-Lambert calculations. For multi-component mixtures, absorbances are additive: A_total = ε₁c₁l + ε₂c₂l + … You would need to solve a system of simultaneous equations at multiple wavelengths, which requires matrix algebra beyond this calculator's scope.

Prepare a series of known concentrations (at least 5 points) and measure absorbance at the wavelength of maximum absorption (λ_max). Plot A vs. c. The slope of the linear fit equals ε × l. With a 1 cm cuvette, the slope directly gives ε in L⋅mol⁻¹⋅cm⁻¹. Ensure the R² value exceeds 0.999 for reliable coefficients.

An absorbance of 0 means 100% transmittance - no light is absorbed. Negative absorbance indicates the sample transmits more light than the reference blank, which can result from mismatched cuvettes, fluorescence emission, or an improperly zeroed instrument. Negative A values are physically nonsensical under Beer-Lambert assumptions. Re-blank the instrument and verify cuvette cleanliness.