# Beer-Lambert Law Calculator

Created by Davide Borchia
Last updated: Jul 11, 2022

Light is the swiss army knife of analytical chemistry: with our Beer-Lambert's law calculator, you will learn how to use the dimming of a light beam to measure the concentration of a sample.

• What is absorbance?
• How does the Beer's law equation connect the absorbance to the concentration;
• How to calculate the concentration from the absorbance: the other way round; and
• How do laboratory techniques employ the Beer-Lambert's law equation to perform analysis on solutions?

## What is absorbance

Absorbance is a property of a solution (or a material): it measures the fraction of light that can pass through the material in terms of intensity. The absorbance of a material is given by the equation:

$A=\log{\left(\frac{I_0}{I}\right)}$

Where:

• $A$ is the absorbance:
• $I_0$ is the initial intensity of the light; and
• $I$ is the intensity of the light after passing through the material.

The argument of the logarithm is related to another important physical quantity: the transmittance, $T$:

$T=\frac{I}{I_0}$

The formula for the absorbance is then:

$A=\log{\left(\frac{1}{T}\right)}$

As you can easily see from the expressions, both the absorbance and the transmittance are dimensionless quantities. Neither the transmittance nor the absorbance has units.

The intensity, however is measured as a power density, in $\text{W}/\text{m}^2$.

## How to calculate absorbance: the Beer-Lambert law

In this section, you will learn how to calculate absorbance. The equation of Beer-Lamber's law is fairly simple:

$A = \varepsilon \cdot l \cdot c$

Where:

• $\varepsilon$ is the absorptivity of the species responsible for the attenuation;
• $l$ is the length of the optical path; and
• $c$ is the concentration of the attenuating species (expressed, for example, as molarity or molality).

The calculations for Beer-Lambert's law are straightforward: the formula for absorbance tells us that this quantity is directly proportional to the other ones in the equation. Beer-Lambert's law states that an increase in one, or more, of the three quantities on the right-hand of the equation corresponds to an increase in absorbance, which translates into a smaller fraction of the incident light passing through the solution.

## How to calculate the concentration from the absorbance

More often than not, we don't use Beer-Lambert's law to calculate the absorbance of a sample. We can rearrange Lambert-Beer's law equation to isolate the concentration:

$c = \frac{A}{\varepsilon \cdot l}$

The equation above is widely employed in spectroscopic techniques in analytic chemistry. Measuring the absorbance is a relatively easy task: with the right instrument, we can perform analysis at varying frequencies and intensity and using tables of the absorptivity of the chemical species, we can measure the concentration in an unknown sample.

Mind that it may be necessary to create calibration curves with samples with known concentration, for example, using consecutive dilutions. Find how to calculate the concentrations with the solution dilution calculator.

## How to use our Beer-Lambert's law calculator

Our Beer-Lambert's law calculator is a handy tool with all the functionalities you need, whether you are doing some homework or performing some experiments.

First, choose the units of the path length, the concentration, and the absorptivity. The measurement unit of absorbance is out of this list since this quantity is dimensionless.

Then insert the known quantities: remember that our calculator also works in reverse: you can use it both to calculate the absorbance from the concentration or vice versa.

🙋 As a small "extra", we added a field for the calculations of the transmittance. Worry not: it's not a crucial element of the calculations of the Beer-Lambert's law equation; however, it's a useful quantity.

Davide Borchia
Molar absorption coefficient
/
M
•cm
Concentration
mol
/L
Path length
cm
Absorbance
Transmittance
%
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