Absorbance: A = ε × l × c
Transmittance: T = 10⁻≪ = I/I₀
Concentration: c = A / (ε × l)
Where A = absorbance (dimensionless), ε = molar absorptivity (L/mol/cm), l = path length (cm), c = concentration (mol/L), T = transmittance (0–1).
Beer‑Lambert Law: Formula, Calculator & Complete Guide (2026)
The Beer‑Lambert Law (also called the Beer‑Lambert‑Bouguer Law) is one of the most fundamental relationships in analytical chemistry and spectroscopy. It describes how light is absorbed by a solution as it passes through it — and it forms the mathematical foundation for UV-Vis spectrophotometry, colorimetry, and many clinical laboratory assays. Whether you are a chemistry student, a pharmaceutical analyst, a lab technician, or a researcher, understanding and applying this law is essential for accurate quantitative analysis.
A = Absorbance (also called optical density, OD) — dimensionlessε = Molar absorptivity (molar extinction coefficient) — L mol⁻¹ cm⁻¹l = Path length of light through the sample — cmc = Molar concentration of the absorbing species — mol/LT = Transmittance = I/I₀ = 10⁻≪ (as a decimal, 0 to 1)
A solution of potassium permanganate has ε = 2,420 L/mol/cm at 525 nm.
Path length = 1 cm (standard cuvette). Concentration = 0.0005 mol/L.
A = 2420 × 1 × 0.0005 = 1.21 AU
Transmittance = 10⁻¹·²¹ = 6.2% (above optimal range — consider diluting 2×)
What Is Molar Absorptivity and How Do You Find It?
Molar absorptivity (ε, also called the molar extinction coefficient) is a substance-specific constant that quantifies how strongly a chemical species absorbs electromagnetic radiation at a given wavelength. It has units of L/(mol·cm) and varies with wavelength, temperature, and solvent. High molar absorptivity values (e.g., 10,000–100,000 L/mol/cm) mean a substance absorbs very strongly at that wavelength, allowing detection at very low concentrations. You can find published ε values in spectroscopic databases like the NIST Chemistry WebBook, the Sadtler spectral library, or in peer-reviewed literature specific to your compound.
Understanding Absorbance vs. Transmittance
Absorbance and transmittance are two different ways to express the same measurement. Transmittance (T) is the ratio of transmitted light intensity (I) to incident light intensity (I₀), expressed as a decimal or percentage. Absorbance (A) is the negative base-10 logarithm of transmittance: A = −log₁₀(T). This logarithmic relationship means that each unit increase in absorbance corresponds to a 10-fold decrease in transmittance. A transmittance of 50% equals absorbance of 0.301; 10% transmittance equals absorbance of 1.0; 1% transmittance equals absorbance of 2.0.
| Absorbance (A) | Transmittance (%T) | Light Absorbed (%) | Measurement Quality |
|---|---|---|---|
| 0.05 | 89.1% | 10.9% | ⚠️ Too low — weak signal |
| 0.10 | 79.4% | 20.6% | 🟡 Acceptable minimum |
| 0.20 | 63.1% | 36.9% | Good range |
| 0.50 | 31.6% | 68.4% | Optimal |
| 0.80 | 15.8% | 84.2% | Good range |
| 1.00 | 10.0% | 90.0% | 🟡 Acceptable maximum |
| 1.50 | 3.2% | 96.8% | 🔴 Non-linear deviation likely |
| 2.00 | 1.0% | 99.0% | 🔴 Avoid — stray light errors |
Why Beer‑Lambert Law Fails at High Concentrations
Beer‑Lambert Law assumes that absorbing molecules act independently of each other. At high concentrations, this assumption breaks down. Molecules begin to interact through electrostatic forces, hydrogen bonding, or aggregation, effectively changing their molar absorptivity. Additionally, at high absorbance values (>1.0), stray light in the spectrophotometer — light that reaches the detector without passing through the sample — causes significant errors because the stray light fraction becomes comparable to the transmitted signal. Detector non-linearity at very low light intensities is another contributor. For these reasons, calibration curves often show curvature at high concentrations.
Practical Applications of Beer‑Lambert Law
Beer‑Lambert Law underpins an enormous range of analytical techniques. In clinical chemistry, it is used to measure serum bilirubin, hemoglobin, glucose, creatinine, and hundreds of other analytes in automated clinical analyzers. In pharmaceutical quality control, it verifies drug concentration in formulations. Environmental laboratories use it to measure water contaminants including nitrates, phosphates, and dissolved organic matter. Food scientists use it for color measurement and quality assessment. Research applications include enzyme kinetics (tracking substrate and product concentrations over time), protein quantification (Bradford, BCA, and Lowry assays), and DNA/RNA concentration measurement at 260 nm.
OD600 in Microbiology
In microbiology, optical density at 600 nm (OD600) is the standard measure of bacterial culture density. Unlike most Beer‑Lambert applications, OD600 measures light scattering rather than true absorption — bacteria scatter rather than absorb light. The linear range for OD600 is approximately 0.1 to 0.4; cultures must be diluted before measurement above this range. An OD600 of 1.0 roughly corresponds to 8×10⁸ cells/mL for E. coli, though this varies by strain and growth conditions.
Beer‑Lambert Law for DNA and Protein Quantification
Nucleic acid quantification at 260 nm relies directly on Beer‑Lambert Law. For double-stranded DNA, an absorbance of 1.0 at 260 nm (using a 1 cm path) corresponds to approximately 50 μg/mL. For single-stranded RNA it is 40 μg/mL, and for single-stranded oligonucleotides it varies with sequence. The 260/280 nm ratio indicates purity: pure DNA has a ratio of 1.8; pure RNA has a ratio of 2.0. Modern NanoDrop instruments use a 0.1 mm path length to measure undiluted samples, automatically adjusting the Beer‑Lambert calculation.