Molar Absorptivity Calculator

This tool to calculate the molar extinction coefficient is based on Beer-Lambert law: A = ε × c × l. Enter three of the following four quantities (Absorbance, Concentration, Path length, Molar extinction coefficient) and leave the fourth blank to obtain the answer in the units selected.

During the calculation, absorbance is converted into transmittance and percent transmittance, and it will be indicated whether the measured values are within a reliable range. In addition, a calibration curve can be made for the sample according to Beer-Lambert law.

What the molar extinction coefficient says:

The molar extinction coefficient is usually denoted by ε and gives the light absorption of a substance at a particular wavelength. Substances that show strong absorption (such as dyes) can have an ε value close to 50,000 L/mol/cm, making them appear colored even in very dilute solutions.

Substances with low absorption have an ε value close to 10 but are nearly transparent at the same wavelength. ε is a property of the molecule itself and does not change when concentration or cuvette size is changed. For this reason, reference tables list ε values for proteins, dyes, and reagents.

Because absorption peaks at particular wavelengths, ε is usually quoted with λmax, the wavelength of maximum absorption. The value of ε must always correspond to the wavelength used. Even for the same compound, values can vary considerably if different wavelengths are used.

Lambert-Beer's Law: The Formula

This law expresses absorbance as the product of three factors: how strongly a compound absorbs light, its concentration and the path length through which the light passes in the medium.

In this case A is the absorption (dimensionless number), ε is the molar extinction coefficient (with the unit L/mol/cm), c is the molar concentration (with the unit mol/Liter) and l is the layer thickness (with the unit cm). As the units of ε, c and l cancel out completely, the absorption itself has no unit.

When the formula is rearranged, it results in this relationship for calculating the molar extinction coefficient:

Calculation of individual quantities:

As it is an equation with four variables, the formula can be rearranged to solve for any of them. The following are the four forms used by calculators:

Example calculation:

Suppose you prepare a blue dye with a concentration of 20 micromoles (equivalent to negative fifth power of 2.0 times 10) and put it in a standard cuvette with length of 1 cm. You then measure the absorbance at its maximum wavelength. The spectrophotometer reads A = 0.25. What is the molar extinction coefficient?

If you enter the value of 0.25 for absorbance, 20 micromoles for concentration and 1 cm for path length and leave molar extinction coefficient blank, then the calculator will return a value of 12,500 L/mol/cm. If you double the concentration to 40 micromoles in the same cuvette, then the measured absorbance is approximately 0.50.

Units and conversions:

As different units are often used in spectroscopy, the calculation tool accepts the most commonly used units for each quantity and converts them if necessary. The conversion factors used are as follows:

If the path length is given in millimeters or meters, it will be converted to centimeters before using the formula. If the concentration is given in micromoles, nanomoles, or millimoles, it will be converted into moles per liter. This allows you to perform calculations regardless of what units are used in the problem.

Absorbance, Transmittance, %Transmittance

A spectrophotometer actually measures the transmission, which is the amount of light that passes through a sample. The absorbance is the negative logarithm of this fraction to base 10.

Thus, 0 absorbance means all the light passes through (T = 1, or 100 percent). An absorbance of 1 means one-tenth of the light passes through (10 percent). An absorbance of 2 means one-hundredth of the light passes through (1 percent). The calculator shows both transmission and percentage transmission next to each result, so these two measures can be easily converted from one another.

Stay within a reliable range

Lambert-Beer's law shows the highest linearity when the absorbance is generally between 0.1 and 1.0. Below 0.1, the signal is too small and strongly affected by noise. Above about 1.0 to 2.0, measurements deviate from the linear relationship due to stray light and detector limits.

If the absorption is outside this range you should not take that value as reliable without further adjustment of your sample. A sample with too high an absorbance should be diluted and a sample with too low an absorbance should be concentrated before re-measuring. The calculator will indicate in which range the measured values are, so it's easy to see at a glance.

The slope of a calibration curve and the Beer-Lambert law.

Since the absorption is proportional to concentration, when plotting A against c at a constant path length, a straight line through the origin results. The slope of this line corresponds to the product of epsilon and the path length.

In the laboratory this calibration curve is generated with a series of standard solutions of known concentration and the concentration of unknown samples can be read directly from the curve. By displaying the calibration curve you can check that the line is based on the stated epsilon value and path length, as well as its slope. If a measured slope is present then epsilon can be determined by dividing this slope by the pathlength.

Typical values for molar extinction coefficients.

The range of values for ε is very wide and close to 1 in weak transitions but can also reach hundreds of thousands in strongly colored dyes. To get an idea of the magnitude, some reference values are given below.

Fields of application.

The Lambert–Beer law is the basis of UV-vis spectroscopy. Biochemists determine protein concentration at 280 nm from the known absorption coefficient of tryptophan and tyrosine residues, and observe the absorption of NADH at 340 nm to follow enzymatic reactions.

Environmental chemists use the same method to quantitatively analyze trace metals and pollutants, while in pharmaceutical labs it is used to determine drug concentrations and check for impurities. Once a substance's absorption coefficient is known, converting the measured absorbance value into a concentration is minimally involved: simply divide the absorbance by the absorption coefficient and path length.

Tips for accurate measurements:

Some practices can increase the reliability of your measurements. Use the same solvent in which the sample is dissolved to blank the instrument. Otherwise, each measurement will contain the absorbance of the solvent itself. Wipe the optical surface of the cuvette before every measurement. Fingerprints are a common cause of erroneous results.

Keep the absorbance between 0.1 and 1.0. Always record both wavelength and absorbance together. Adjust temperature and pH to ensure that conditions match those of the comparison. For dyes or proteins sensitive to pH, spectra can change dramatically depending on conditions.

When the Law of Lambert-Beer does not apply:

This law holds as long as the solution is transparent and dilute and contains only one type of absorbing species. At higher concentrations, molecules begin to interact with each other distorting the linear relationship and the law no longer applies. It also does not apply for turbid samples or those that scatter light since in these cases the light is lost due to scattering rather than being absorbed.

It cannot be readily applied to mixtures of several absorbing substances. In this case the total absorbance at a given wavelength is the sum of the contributions from each component, which requires analysis with multiple wavelengths and multiple components rather than a single ε value. However, if a transparent dilute solution contains only one type of compound, then the Lambert–Beer law is accurate and reliable.