Beer-Lambert Law Calculator NZ
This calculator applies the Beer-Lambert law to find the absorbance of a solution, and from it the transmittance, the foundation of spectrophotometry and colorimetric analysis. When light passes through a coloured solution, some is absorbed, and the amount depends on three things: how strongly the substance absorbs at that wavelength, captured by the molar absorptivity, how far the light travels through the solution, the path length, and how concentrated the solution is. The Beer-Lambert law states that absorbance is simply the product of these three. Because absorbance is directly proportional to concentration, it is the workhorse of chemical analysis: measure the absorbance of a sample and you can determine its concentration, which is how everything from water-quality testing to clinical blood analysis works. This tool computes it. You enter the molar absorptivity, the path length in centimetres, and the concentration in moles per litre, and the calculator returns the absorbance, the transmittance as a fraction and a percentage, and the path length for reference. The results update as you type. Use it for chemistry and biochemistry study, for spectrophotometry, or to understand the link between absorbance and concentration. Absorbance is the molar absorptivity times the path length times the concentration, a dimensionless number. Transmittance, the fraction of light that gets through, is ten raised to the power of minus the absorbance, so an absorbance of one means ten percent of the light passes through, and an absorbance of two means just one percent. The standard path length in a laboratory cuvette is one centimetre, which makes absorbance directly proportional to the product of molar absorptivity and concentration. Because the relationship is linear, a calibration line of absorbance against known concentrations lets you read off an unknown concentration from its measured absorbance.
Beer-Lambert: absorbance = molar absorptivity x path length x concentration. Transmittance = 10^(-absorbance). Absorbance is proportional to concentration, the basis of analysis.
How it works
The Beer-Lambert law multiplies the molar absorptivity by the path length and the concentration to give the absorbance, a dimensionless number. The transmittance, the fraction of light passing through, is ten raised to the power of minus the absorbance. Multiplying the transmittance by one hundred gives the percentage of light transmitted.
Worked example
For a substance with a molar absorptivity of 5,000, in a 1 centimetre cuvette at a concentration of 0.0001 moles per litre, the absorbance is 5,000 times 1 times 0.0001, which is 0.5. The transmittance is ten to the minus 0.5, about 0.316, so about 31.6 percent of the light passes through the solution.
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