Beer-Lambert Law Calculator

The Beer-Lambert Law Calculator solves the equation A = εlc for whichever quantity you need — absorbance, molar absorptivity, path length, or concentration. It is the everyday workhorse of UV-Vis spectrophotometry: enter the three values you know and the calculator returns the fourth, converts your absorbance into percent transmittance, draws the light passing through your cuvette, and plots the calibration line so you can see Beer's law at a glance.

What is the Beer-Lambert Law?

The Beer-Lambert law (also called Beer's law) describes how light is absorbed as it travels through a solution. It states that absorbance is directly proportional to both the concentration of the absorbing substance and the distance the light travels through it. The more concentrated the sample, or the longer the path length, the more light is absorbed and the less is transmitted.

What Each Variable Means

The Four Rearrangements

Because A = εlc has four variables, the same law can be solved four ways. This calculator handles all of them automatically:

Absorbance and Transmittance

Spectrophotometers actually measure transmittance — the fraction of light that makes it through the sample — and convert it to absorbance. The two are related logarithmically:

This logarithmic link is the key insight many students miss: each whole unit of absorbance means ten times less light passes through. A = 0 lets 100% through, A = 1 lets 10% through, and A = 2 lets just 1% through.

Why the Calibration Line Matters

Because absorbance is proportional to concentration, a plot of A against c is a straight line through the origin with slope εl. In the lab you measure several standards of known concentration, draw this calibration line, and then read any unknown's concentration straight off it. Our calculator draws the line for your values and marks your point on it, with the reliable region (A ≤ 1) shaded.

What is a Good Absorbance Reading?

Most bench spectrophotometers are most accurate when absorbance is between about 0.1 and 1.0. Below 0.1 the signal sits near the instrument's noise floor; above roughly 2.0 so little light reaches the detector that stray light dominates and the reading becomes unreliable. If your absorbance is too high, dilute the sample or use a shorter path-length cuvette and measure again.

When Does Beer's Law Break Down?

The Beer-Lambert law assumes a dilute solution, truly monochromatic light, and no interactions between the absorbing molecules. At high concentrations these assumptions fail: molecules interact, the refractive index shifts, and stray light becomes significant. The calibration line then curves away from a straight line — this is called deviation from Beer's law and is the main reason to keep absorbance in the recommended range.

How to Use This Calculator

1. Choose what to solve for: Pick absorbance, molar absorptivity, path length, or concentration. That field disappears and the other three become your inputs.
2. Enter the known values: Type the three quantities you know, selecting units for concentration (M, mM, µM, nM) and path length (cm or mm).
3. Click Calculate: The tool solves the Beer-Lambert law for your unknown.
4. Review the results: See your answer, the percent transmittance, the animated cuvette diagram, the calibration line, and a full step-by-step breakdown.

Worked Example

NADH absorbs strongly at 340 nm with a molar absorptivity of ε = 6220 M⁻¹cm⁻¹. For a 100 µM (1×10⁻⁴ mol/L) solution in a standard 1 cm cuvette, the absorbance is A = 6220 × 1 × 1×10⁻⁴ = 0.622, which corresponds to about 23.9% transmittance — comfortably inside the reliable range.

Frequently Asked Questions

What is the Beer-Lambert law?

The Beer-Lambert law states that the absorbance of light by a solution is directly proportional to the concentration of the absorbing species and the path length the light travels through the sample. It is written A = εlc, where A is absorbance, ε is the molar absorptivity, l is the path length in centimetres, and c is the concentration in moles per litre.

How do I calculate concentration from absorbance?

Rearrange the Beer-Lambert law to c = A / (εl). Divide the measured absorbance by the product of the molar absorptivity and the path length. For example, with A = 0.45, ε = 6220 M⁻¹cm⁻¹, and l = 1 cm, the concentration is 0.45 / 6220 = 7.23×10⁻⁵ mol/L, or about 72.3 µM.

What are the units of molar absorptivity?

Molar absorptivity (also called the molar extinction coefficient) has units of M⁻¹cm⁻¹, equivalent to L mol⁻¹cm⁻¹. These units make absorbance dimensionless when multiplied by concentration in mol/L and path length in cm.

How is absorbance related to transmittance?

Absorbance and transmittance are linked by A = −log₁₀(T), or equivalently T = 10^−A. An absorbance of 1 means 10% of the light passes through (90% absorbed); an absorbance of 2 means only 1% passes through. Each whole unit of absorbance reduces the transmitted light by a factor of ten.

What absorbance range is most accurate?

Most bench spectrophotometers are most accurate for absorbance values between about 0.1 and 1.0. Below 0.1 the signal is close to the instrument noise floor, and above about 2.0 so little light reaches the detector that the reading becomes unreliable. If your absorbance is too high, dilute the sample or use a shorter path length.

When does the Beer-Lambert law break down?

The law assumes a dilute solution, monochromatic light, and no interactions between absorbing molecules. At high concentrations the relationship between absorbance and concentration becomes non-linear because of molecular interactions, refractive-index changes, and stray light, so the calibration line curves away from a straight line.

Additional Resources

• Beer-Lambert Law - Wikipedia
• Molar Absorption Coefficient - Wikipedia