Pharmaceutical Analysis

Beer‑Lambert Law Calculator

Solves A = ε · c · l for absorbance, concentration or molar absorptivity, with transmittance and a calibration line.

Absorbance (A)

5.0000

Too high – dilute sample

Values

The field being solved for is filled in for you.

Molar absorptivity ε (M⁻¹cm⁻¹)

Also written L·mol⁻¹·cm⁻¹. Found in the monograph or literature for your λmax.

Concentration c

Molar concentration; 1 mM = 0.001 M.

Path length l

Width of the cuvette — standard cells are 1 cm.

Absorbance A

No unit. Reliable readings are about 0.1–1.0.

Common compounds

Working

A = 5000 × 0.001 M × 1 cm5.0000

Concentration in mol/L1.0000e-3M

Path length in cm1cm

Transmittance T = 10⁻ᴬ × 1000.00%

Calibration curve

Absorbance against concentration (M) for this ε and path length.

A = ε · c · l

T = 10⁻ᴬ × 100%

A = absorbance (no unit), ε = molar absorptivity (L·mol⁻¹·cm⁻¹), c = concentration (mol/L), l = path length (cm). Concentration and path length are converted to M and cm before the formula is applied; a solved concentration is reported back in the unit you selected.

Transmittance is the fraction of light that gets through. An absorbance of 1 lets through 10%, and 2 lets through only 1% — which is why high readings are unreliable.

Sources: IUPAC; USP General Chapter <857>; Harris, Quantitative Chemical Analysis.

Worked example: NADH concentration from its absorbance at 340 nm

A solution of NADH is read at 340 nm in a standard 1 cm quartz cuvette against a buffer blank, giving A = 0.452. The molar absorptivity of NADH at 340 nm is 6220 M⁻¹cm⁻¹. Find the concentration in μM and the transmittance.

Absorbance (A): 0.452
Molar absorptivity (ε): 6220 M⁻¹cm⁻¹
Path length (l): 1 cm
Report concentration in: μM

Rearrange the law
A = ε · c · l → c = A ÷ (ε · l)
Substitute
c = 0.452 ÷ (6220 M⁻¹cm⁻¹ × 1 cm) = 7.2669 × 10⁻⁵ M
Convert to μM
7.2669 × 10⁻⁵ M × 10⁶ μM/M = 72.669 μM (shown as 7.2669e+1)
Transmittance
T = 10⁻ᴬ × 100 = 10⁻⁰·⁴⁵² × 100 = 35.32 %

c ≈ 72.67 μM (7.2669 × 10⁻⁵ M); T = 35.32 %.

About a third of the 340 nm light gets through the cell, and an absorbance of 0.452 sits in the 0.1–1.0 range where readings are most reliable, so the concentration can be trusted as far as ε can. The result is only as good as the ε used: it holds for this wavelength, solvent and pH, and it says nothing about whether the absorbance came from NADH alone. Any other species absorbing at 340 nm is counted as NADH.

Common mistakes

Entering a 10 mm cell as '10' with the unit left on cm. That makes l ten times too long and the concentration ten times too small (7.27 μM instead of 72.67 μM here).

Using a specific absorbance A(1 %, 1 cm) as if it were ε. Convert first: ε = A(1 %, 1 cm) × MW ÷ 10.

Reading the concentration in the wrong unit: the solved value is reported in the unit selected in the concentration field, so 7.2669e+1 with μM selected is 72.67 μM, not 72.67 M.

Not zeroing the instrument on a blank of the same solvent or buffer, so the solvent's own absorbance is counted as sample.

Measuring off λmax, or using an ε quoted at a different wavelength, solvent or pH.

Trusting a reading above about 1.0. Stray light makes the response non-linear there; dilute the sample and multiply back by the dilution factor.

Assumptions and limitations

Linear only over a limited range — roughly A 0.1 to 1.0 on most instruments. At high concentration, molecular interactions and stray light bend the line.

Assumes monochromatic light; a wide spectral bandwidth relative to the absorption band lowers the apparent ε.

Assumes a clear, homogeneous, non-scattering solution in which the analyte does not associate, dissociate or react as concentration changes.

Assumes the analyte is the only absorbing species at that wavelength; mixtures need a separation or a multi-wavelength method.

Uses one literature ε. For a regulated assay, ε (or the slope) comes from a calibration with reference standards on the same instrument.

Calibration Curve CalculatorFit your own standards instead of relying on a literature ε, and check linearity with R².UV-Vis Spectrum PlotterFind λmax from a scan before choosing the wavelength to measure at.mg/mL ↔ Molarity CalculatorTurn a molar result into mg/mL (or the reverse) using the molecular weight.

References

Harris DC, Lucy CA. Quantitative Chemical Analysis. 10th ed. New York: W. H. Freeman (Macmillan Learning); 2019.
International Union of Pure and Applied Chemistry. Compendium of Chemical Terminology (the 'Gold Book'). Source

Common questions

About 0.1 to 1.0. Below 0.1 the reading is close to instrument noise; above 1.0 stray light makes the response non-linear. Dilute or concentrate the sample to land in range.

That is scientific notation: 7.5758 × 10¹ = 75.758 in the unit selected. It keeps very small molar concentrations readable.

Not directly. This calculator uses molar absorptivity. Convert a specific absorbance A(1%, 1 cm) to ε with ε = A(1%, 1 cm) × MW ÷ 10.

No. The value that was being solved for is kept in its field, so you can, for example, compute A and then switch to solving for concentration with that A.

Prepared by the PharmaWallah student team. Verify results with your textbook or instructor. Report an error · Editorial policy