Beer-Lambert Law Calculator
Solve A = εlc for absorbance, molar absorptivity, path length or concentration.
What is Beer-Lambert Law?
The Beer-Lambert law links how much light a solution absorbs to how concentrated it is: A = εlc. It is the principle behind every spectrophotometer reading, and the reason a calibration curve is a straight line. ε is a property of the substance and the wavelength, not of your experiment — its units are L·mol⁻¹·cm⁻¹, which is why it is easy to miss.
How it works
Absorbance is dimensionless, path length is almost always 1 cm for a standard cuvette, concentration is in mol/L and ε comes from a reference table for the dye at the wavelength you are using. Leave the value you want blank and the tool rearranges the equation for it, reporting transmittance — the percentage of light that gets through, which is what the instrument measures directly — as a cross-check.
- Enter what you know. Every field recalculates as you type — there is no submit button. Leave the quantity you want blank and the page solves for it.
- Read the answer and the working. The result appears above the fold; underneath it is the formula with your numbers substituted, so the arithmetic can be checked rather than trusted.
- Check the units and the size. Units are shown on every value and selectable per field, so a result in kJ, kPa or km/h is converted rather than assumed. Sanity-check the magnitude against a known landmark such as 1 g/cm³ for water.
Examples
A textbook problem with a known answer
Every tool here is checked against standard example problems — the molar mass of C6H12O6 is 180.16 g/mol, and free fall from 20 m takes about 2.02 s at g = 9.8 m/s².
A result you want to reason backwards from
Leave the quantity you already know blank instead: given the final answer, most tools recover the starting value — the mass needed for a target concentration, or the height a fall must have had.
Common mistakes
Forgetting that a formula is only as good as its subscripts
H2O and H2O2 are different compounds. The formula field shows its parse — element by element — so a mis-typed subscript is visible before it reaches the arithmetic.
Mixing units in the middle of a calculation
The most common source of a wrong answer is a value in grams next to a formula expecting kilograms, or Celsius next to a gas constant expecting kelvin. This category converts on the way in and labels what it used.
Frequently asked questions
What is ε and where do I get it?
The molar absorptivity (or extinction coefficient) is how strongly a substance absorbs light at a given wavelength. It comes from published reference tables for the specific dye and wavelength — it is not something you measure by hand, though a calibration curve determines it experimentally.
What is the difference between absorbance and transmittance?
Transmittance is the fraction of light that passes through the sample; absorbance is its negative base-10 logarithm. A sample that lets half the light through has 50% transmittance and an absorbance of 0.301.
Why is the path length usually 1 cm?
Because that is the standard cuvette. It matters because absorbance scales with path length — the same solution in a 1 cm and a 10 cm cell gives ten times the absorbance, which is the whole point of the l term.