Beer-Lambert Law Calculator
Solve A = ε · c · l for whichever of the four quantities you leave blank, with transmittance conversion and working-range checks.
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What it does
The Beer-Lambert law relates how much light a solution absorbs to how much absorbing species sits in the beam. It is the reason a spectrophotometer can report a concentration at all, and after the dilution formula it is the most used equation in a wet lab.
How it works
A = ε · c · l. Absorbance is dimensionless and logarithmic: a sample transmitting 10 percent of the light has A = 1, and one transmitting 1 percent has A = 2. The molar absorptivity ε carries the units L·mol⁻¹·cm⁻¹, so concentration in mol/L times path length in cm times ε gives a pure number. Because the four quantities are perfectly symmetric, this page has no mode selector. Whichever field you leave empty is the one that gets solved.
Worked example
A dye with ε = 15000 L·mol⁻¹·cm⁻¹ in a 1 cm cuvette reads A = 0.30. Then c = 0.30 / (15000 × 1) = 2.0e-5 mol/L, which is 20 µM, and the transmittance is 50.1 percent. The same absorbance in a 10 cm cell would mean only 2 µM. Note that A = 0.30 sits comfortably inside the reliable window.
When to use it
Use it to convert a plate reader absorbance into a concentration, to find ε for a dye that arrived without a certificate of analysis, or to decide how far to dilute a sample that read off scale. The dilution helper is the one people reach for most: an absorbance of 1.82 diluted threefold lands at 0.61, back inside the range where the instrument is genuinely linear.
FAQ
- What is the difference between absorbance and transmittance?
- They report the same measurement on a logarithmic versus a linear scale. Transmittance is the fraction of light that gets through, normally expressed as a percentage; absorbance is minus the base-ten logarithm of that fraction. A sample reading 50 percent transmittance has an absorbance of 0.301, one reading 10 percent has an absorbance of 1.0, and one reading 1 percent has an absorbance of 2.0. Calculations use absorbance because it is the quantity proportional to concentration, while transmittance is what the detector physically measures.
- Why should absorbance stay between 0.1 and 1.0?
- Below 0.1 the sample transmits nearly everything, so the detector is comparing two almost equal signals and the relative error of the difference grows quickly. Above 1.0 stray light and detector nonlinearity compress the response, and the reading falls below what the linear law predicts. Both effects come from the instrument rather than from the chemistry. The practical rule is to adjust dilution or path length so readings land near the middle of the window, and to verify linearity with a standard if you genuinely have to work outside it.
- How do I find the molar absorptivity of a dye I just bought?
- Weigh a known mass, dissolve it to a known volume, and read the absorbance. The second block on this page does the arithmetic: enter mass in mg, final volume in mL and molar mass in g/mol and it returns epsilon. Note that mg/mL and g/L are numerically identical, which is a frequent source of thousand-fold errors when the conversion is done by hand. If the material is not pure, enter the purity as well, because a 95 percent dye will otherwise appear to have a lower molar absorptivity than it really does.
- Does the law hold for mixtures and for turbid samples?
- Absorbances of several absorbing species at the same wavelength add up, so a mixture obeys the law provided the species do not interact chemically. Turbidity and scattering do not obey it at all: scattering makes the apparent absorbance rise towards short wavelengths in a way concentration cannot explain, and it does not cancel out against a blank. If a sample is cloudy, filter or centrifuge it before measuring, because at the detector a scattered photon is indistinguishable from an absorbed one.