The Beer-Lambert law is the backbone of UV-Vis quantitation. Given an absorbance reading, an extinction coefficient, and a path length, this calculator returns the concentration of your protein or compound, corrects for dilution, and optionally converts a molar result to mg/mL.
How it works
The law states A = eps x c x l. Solving for concentration gives c = A / (eps x l). With a molar coefficient (inverse molar per centimetre) the answer comes
out in moles per litre; with a mass coefficient (the absorbance of a 1 mg/mL
solution over 1 cm) it comes out directly in mg/mL.
If you diluted before reading, the displayed value is multiplied by your dilution factor to give the original concentration. Supplying a molecular weight converts a molar result to mg/mL, since one molar of a species equals its molecular weight in grams per litre.
Worked example
A purified protein with a molar extinction coefficient of 43,824 read in a 1 cm
cuvette at A280 of 0.85 has a concentration of 0.85 / (43824 x 1) = 1.94e-5 M,
or 19.4 µM. If its molecular weight is 14,300 g/mol that is about 0.28 mg/mL.
Practical tips
Keep absorbance readings in the accurate range, roughly 0.1 to 1.0, by diluting samples that read too high. Always confirm the path length of microvolume instruments, which is often 0.1 cm rather than 1 cm. For proteins, derive the molar coefficient from the sequence using tryptophan, tyrosine, and cystine content rather than guessing.
Common sources of error in spectrophotometric quantitation
Path length errors are the most frequent mistake when moving between instrument types. Standard benchtop cuvettes use a 1 cm path; NanoDrop and similar microvolume instruments use paths as short as 0.1 mm. If you enter the wrong path length, the calculated concentration is off by the same factor. Always check the instrument documentation and confirm which path was in use before interpreting a result.
Linearity range. The Beer-Lambert law is only linear within a certain absorbance window. Below about A = 0.1 the signal-to-noise ratio becomes poor; above about A = 1.5–2.0 many instruments start to deviate from linearity because the detector saturates. Dilute samples that read high before trusting the result, and remeasure samples that read very low in a longer-path cuvette if possible.
Buffer and contaminant absorption. At A280, common laboratory contaminants absorb significantly. Nucleic acid contamination from cell lysis increases A260/A280, inflating your protein estimate. Some buffers absorb at or near 280 nm. If your extinction coefficient was derived for pure protein in a simple buffer, contamination from the preparation will cause a systematic overestimate of concentration. The A260/A280 ratio is a quick check: a pure protein preparation typically gives a ratio of 0.55 to 0.65; a ratio above 0.8 suggests nucleic acid contamination.
Using the wrong extinction coefficient. Published extinction coefficients for proteins vary by source, and values derived from sequence (using the Pace method — counting Trp, Tyr, and disulfide bonds) are more reliable than older literature values for many proteins. For recombinant proteins, always use the sequence-derived value from ProtParam or an equivalent tool rather than a generic “IgG” or “albumin” coefficient unless you are measuring exactly that protein.
Dilution factor: when and how to apply it
If you diluted the sample 1:10 before reading (for example, 10 µL sample + 90 µL buffer), enter a dilution factor of 10. The calculator multiplies the result by 10 to recover the original concentration. This is the concentration of the stock solution, which is what you need for setting up experiments, preparing working dilutions, or reporting yield. Forgetting to account for dilution is a frequent cause of reported concentrations being an order of magnitude too low.