ChemBench

Beer-Lambert Law Calculator

The foundation of UV-Vis spectrophotometry — how much light a solution absorbs tells you its concentration.

Molar absorptivity (ε)

Concentration (c)

Path length (l)

Absorbance (A)

2.6

Transmittance (%): 0.251

What you entered

Molar absorptivity (ε): 6500Concentration (c): 0.0004Path length (l): 1

1
A = ε × c × l
6500 × 0.0004 × 1= 2.6
2
Transmittance = 10^(−A) × 100
10^(−2.6) × 100= 0.2512%

Result

Absorbance (A): 2.6

With ε = 6500, c = 0.0004 mol/L, and l = 1 cm, the absorbance is 2.6 and transmittance is 0.25%.

Absorbance and transmittance in a 1 cm cuvette

Absorbance is molar absorptivity times concentration times path length. Transmittance is 10 to the power of minus absorbance, so each whole unit of absorbance cuts transmitted light tenfold.

Molar absorptivity	Concentration	Path length	Absorbance	Transmittance
1,000 M-1cm-1	0.0001 M	1 cm	0.1000	79.43%
5,000 M-1cm-1	0.0001 M	1 cm	0.5000	31.62%
1,000 M-1cm-1	0.001 M	1 cm	1.0000	10.00%
20,000 M-1cm-1	0.00005 M	1 cm	1.0000	10.00%
1,000 M-1cm-1	0.002 M	1 cm	2.0000	1.00%
1,000 M-1cm-1	0.003 M	1 cm	3.0000	0.10%

Spectrophotometers are most accurate between about 0.1 and 1.0 absorbance. Above roughly 2.0 almost no light reaches the detector, so dilute the sample rather than trusting the reading.

Every spectrophotometer uses this law

Beer-Lambert's law (A = εcl) says absorbance is proportional to concentration and path length — this linear relationship is why spectrophotometers can measure unknown concentrations by comparing absorbance to a calibration curve of known standards.

When Beer's law breaks down

At high concentrations, molecular interactions (aggregation, refractive index changes) cause deviations from linearity — this is why spectrophotometry is most reliable for dilute solutions, typically below 1–2 absorbance units.

Frequently asked questions

My solution has ε = 6,500 L/(mol·cm), concentration 2.0 × 10⁻⁵ M, and a 1 cm cuvette — what is the absorbance?

A = εcl = 6500 × 2.0×10⁻⁵ × 1 = 0.13. That corresponds to about 74% transmittance (T = 10⁻⁰·¹³).

How is absorbance related to transmittance?

A = -log10(T), where T is the fraction of light transmitted. An absorbance of 1.0 means only 10% of light passes through; A = 2.0 means only 1% gets through.

How does Beer-Lambert relate to the dilution calculator?

Beer-Lambert measures concentration via light absorption. If a sample's absorbance is too high (above ~2), dilute it using M1V1 = M2V2 from the dilution calculator, measure the diluted sample, then multiply back.

Can I use Beer-Lambert for colored solutions visible to the eye?

Yes. The wavelength of maximum absorbance is the complement of the solution's visible color — a blue solution absorbs orange light (~600 nm). Spectrophotometers measure at the wavelength of peak absorbance for best sensitivity.