Beer-Lambert Law Calculator

The Beer-Lambert Law Explained

The Beer-Lambert law (often just called Beer's law) relates how much light a sample absorbs to how concentrated it is — the basis for using spectrophotometers to measure concentration.

$$A = \varepsilon c l$$

Percent transmittance relates to absorbance by:

$$\%T = 10^{-A} \times 100\%$$

Worked Example: A Dilute Colored Solution

Using the calculator's defaults — a molar absorptivity of 15,000 L/(mol·cm), a concentration of 2 × 10⁻⁵ mol/L, and a standard 1 cm cuvette — absorbance works out to $A = 15{,}000 \times 2\times10^{-5} \times 1 = 0.3$. That corresponds to a percent transmittance of $10^{-0.3} \times 100 \approx 50.1\%$ — about half the light passing through, a typical, easily-measurable absorbance value in the middle of a spectrophotometer's reliable range.

Why Spectrophotometry Is So Widely Used

Because absorbance is directly proportional to concentration, a spectrophotometer measurement combined with a calibration curve (a plot of known concentrations vs. their measured absorbance) lets chemists find an unknown sample's concentration almost instantly, without needing to run a full titration or gravimetric analysis. This makes UV-Vis spectrophotometry one of the fastest, most common quantitative techniques in analytical chemistry and biochemistry labs, used for everything from protein concentration assays to water quality testing.

A Brief History of the Beer-Lambert Law

Pierre Bouguer first noted the relationship between light absorption and path length in 1729, and Johann Heinrich Lambert formalized it mathematically in 1760. August Beer extended the relationship to include concentration in 1852, completing the law in the form used today. The combined law became especially practical once reliable spectrophotometers were developed in the 20th century, turning what had been a theoretical relationship into a routine, everyday laboratory measurement.

Common Beer-Lambert Law Mistakes

Assuming the law holds at any concentration is a common error — real samples deviate from strict linearity at high concentration due to molecular interactions, so measurements are usually kept within a verified linear range. Confusing absorbance with percent transmittance (they're related but not the same, and one is logarithmic while the other is linear in the amount of light passing through) is another frequent mix-up. Forgetting to account for path length when comparing measurements from different cuvettes is a third common oversight, since absorbance scales directly with how far light travels through the sample.

Spectrophotometry Terms You Should Know

Absorbance (A) — a unitless logarithmic measure of how much light a sample absorbs.

Molar Absorptivity (ε) — how strongly a substance absorbs light at a given wavelength, per unit concentration and path length.

Percent Transmittance (%T) — the percentage of light that passes through a sample without being absorbed.

Calibration Curve — a plot of known concentrations vs. measured absorbance, used to find unknown concentrations.

This calculator assumes ideal linear Beer-Lambert behavior; real samples may deviate at high concentration or with certain chemical interactions.