Use the Beer-Lambert law to relate absorbance to concentration, molar absorptivity, and path length. Solve for any variable in A = εbc, essential for spectrophotometry and analytical chemistry.
The Beer-Lambert law (A = εbc) is the foundation of UV-visible spectrophotometry — the technique used in every chemistry lab, biology lab, clinical chemistry analyzer, and analytical instrument to measure concentration by how much light a sample absorbs. The principle is direct: as a beam of light passes through a colored solution, some photons are absorbed by the molecules. The fraction absorbed depends linearly on the molecular concentration, the optical path length, and a molecule-specific constant called the molar absorptivity (also called extinction coefficient).
This calculator lets you solve A = εbc for any of the four variables given the other three. Use it to compute expected absorbance from a known concentration (for setting up an experiment), to back out concentration from a measured absorbance (the most common use), to determine the molar absorptivity of a new compound (characterization), or to verify path length consistency (instrument QC).
The Beer-Lambert law works well for dilute, non-aggregating solutes at a single wavelength. Deviations happen at high concentrations (intermolecular interactions), with stray light in the spectrometer (especially above A = 2), with chemical equilibria that shift composition with concentration, and with very narrow spectral peaks where finite slit width matters. For routine clinical and analytical work in the linear range (A between about 0.1 and 1.5), it's accurate to within a percent or two.
**Scenario:** You purified a protein and measured A₂₈₀ = 1.250 in a 1 cm quartz cuvette. The protein has extinction coefficient ε₂₈₀ = 45,000 M⁻¹·cm⁻¹ and molecular weight 35 kDa. **Calculation:** c = A / (ε × b) = 1.250 / (45,000 × 1) = 2.78 × 10⁻⁵ M = 27.8 μM. Mass concentration: 27.8 μM × 35,000 g/mol = 0.972 mg/mL. **Result:** Protein concentration is ~28 μM or 0.97 mg/mL. For protein crystallization or assays needing 1–10 mg/mL, this might need concentration via ultrafiltration. For storage and long-term use, you might dilute and add stabilizers like glycerol.
**Scenario:** Building a standard curve for a malachite green phosphate assay. ε at 620 nm = 90,000 M⁻¹·cm⁻¹. What absorbance do you expect for 10 μM phosphate in a 96-well plate (path length ~0.3 cm)? **Calculation:** A = ε × b × c = 90,000 × 0.3 × 10⁻⁵ = 0.27. **Result:** Expected A = 0.27 at 10 μM. Good signal — within linear range. Standards at 1, 5, 10, 25 μM would give A of 0.027, 0.135, 0.27, 0.675 — all within the linear range. Cut off at 50 μM where A approaches 1.35 and the linearity might start to degrade.
**Scenario:** You synthesized a new fluorescein analog. Made a 10 μM solution; absorbance at peak wavelength in a 1 cm cuvette = 0.853. **Calculation:** ε = A / (b × c) = 0.853 / (1 × 10 × 10⁻⁶) = 85,300 M⁻¹·cm⁻¹. **Result:** Molar absorptivity is 85,300 M⁻¹·cm⁻¹ — typical for fluorescein-class chromophores (fluorescein itself is ~93,000). The published ε lets others quantify this compound spectrophotometrically without redoing the measurement. Report the value at a specified wavelength and pH (since many absorbers are pH-sensitive).
**Use Beer-Lambert law for any quantitative spectrophotometric measurement:**
- **Protein quantification**: A₂₈₀ Bradford, BCA, Lowry — all rest on Beer-Lambert + a known standard curve. - **DNA/RNA quantification**: A₂₆₀ × conversion factor → μg/mL; A₂₆₀/A₂₈₀ ratio reports purity. - **Enzyme assays**: rate of color change converted to rate of product formation via molar absorptivity. - **Drug content in pharmaceutical formulations**: UV absorption at a known peak. - **Water quality**: nitrate, nitrite, phosphate, ammonia, COD — all measured via colorimetric reactions read on spectrophotometer. - **Food chemistry**: betalain pigments in beets, chlorophyll in oils, anthocyanins in wine. - **Photochemistry**: tracking reactant disappearance or product appearance over time. - **Forensics / clinical**: hemoglobin (cyanmethemoglobin method), bilirubin, drugs of abuse.
**Practical tips:**
- **Match cuvette materials**: quartz for UV (< 350 nm), glass or plastic for visible (350–700 nm). - **Zero with the blank**: always subtract the absorbance of the buffer/solvent alone. - **Mix and degas if necessary**: bubbles look like scattering, change absorbance. - **Use peak wavelength**: for highest sensitivity and least interference from neighbors. - **Check linearity**: the Beer-Lambert law is linear only in a window. Make a calibration curve to verify. - **Watch for stray light**: above A = 2, even a tiny amount of stray light biases measurements.
**Common molecular ε values worth memorizing (biology):**
- **Tryptophan**: 5,500 M⁻¹·cm⁻¹ at 280 nm (dominant chromophore in proteins) - **Tyrosine**: 1,490 at 280 nm (next contributor) - **DNA**: 6,600 M⁻¹·cm⁻¹ per base at 260 nm (≈ 50 μg/mL per A₂₆₀ unit for dsDNA) - **NADH**: 6,220 at 340 nm (workhorse cofactor for enzyme assays) - **NADPH**: 6,220 at 340 nm - **Reduced cytochrome c**: 27,700 at 550 nm
**When Beer-Lambert breaks down:**
- **High concentrations (>~0.01 M)**: aggregation, ground-state complexes change effective ε. - **Polychromatic light or wide bandpass**: averaging over varying ε gives non-linear response. - **Chemical equilibria** (HIn ⇌ In⁻ for indicators): apparent ε depends on pH and concentration. - **Scattering** (turbid solutions, suspensions): scattered light reads as "absorbed." - **Photochemistry during measurement**: photo-conversion changes concentration mid-scan.
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Absorbance
0.5000
% Transmittance
31.62%
Concentration
5.000e-3 M
| Parameter | Value |
|---|---|
| Absorbance (A) | 0.500000 |
| Molar Absorptivity (ε) | 100.00 L/(mol·cm) |
| Path Length (b) | 1.0000 cm |
| Concentration (c) | 5.0000e-3 mol/L |
| Transmittance (T) | 0.316228 |
| % Transmittance | 31.6228% |
| Verification εbc | 0.500000 |
| Formula | A = εbc |