How this instrument works
The Beer-Lambert law relates how much light a solution absorbs to the concentration of whatever's dissolved in it: absorbance equals the molar extinction coefficient times the concentration times the path length the light travels through the sample (A = ε × c × l). Rearranged to solve for what a spectrophotometer measurement is actually trying to find, concentration equals absorbance divided by the product of extinction coefficient and path length — c = A / (ε × l) — which is the calculation this instrument performs directly.
For proteins, the relevant absorbance is almost always read at 280 nanometers, where the aromatic amino acids tryptophan and tyrosine, and to a smaller extent disulfide bonds from cystine, absorb UV light. Because different proteins contain different numbers of these residues, each protein has its own characteristic molar extinction coefficient at 280 nm — there's no single universal value, which is why this field asks you to enter the coefficient for the specific protein you're measuring rather than assuming one.
Path length matters because it's literally how far the light travels through the absorbing solution, and it isn't always the standard 1 centimeter of a full-size cuvette — many modern spectrophotometers use microvolume sample platforms with path lengths under a millimeter to conserve sample. A concentration calculated with the wrong path length will be off by exactly the ratio of the true path length to the assumed one, which makes it one of the more common quiet sources of error in reported protein concentrations.
- Enter your spectrophotometer reading into Absorbance (A) — a unitless number, typically measured at 280 nm for protein.
- Enter your protein's Molar extinction coefficient (M⁻¹cm⁻¹) — look this value up for your specific protein rather than assuming a default.
- Enter Path length (cm) — 1 for a standard cuvette, or your instrument's specific value if using a microvolume platform.
- Read Concentration (M) directly beneath the three inputs.
- Extinction coefficient and path length must both be greater than zero, and absorbance cannot be negative.
Worked example — A = 0.5, ε = 50,000 M⁻¹cm⁻¹, 1 cm path
Enter 0.5 into Absorbance (A), 50000 into Molar extinction coefficient (M⁻¹cm⁻¹), and 1 into Path length (cm). Concentration (M) computes as 0.5 / (50,000 × 1) = 0.5 / 50,000 = 0.00001 M, or 1 × 10⁻⁵ M.
That works out to 10 micromolar — a concentration typical of a moderately dilute purified-protein sample read directly in a standard 1 cm cuvette, with an extinction coefficient in the range common for a mid-sized protein carrying a handful of tryptophan and tyrosine residues.
Questions
Where do I find the molar extinction coefficient for my protein?
Protein databases like ExPASy's ProtParam tool calculate a theoretical molar extinction coefficient at 280 nm directly from a protein's amino acid sequence, based on its tryptophan, tyrosine and cystine content — this is the standard first place to look if your protein's coefficient isn't already published. Well-characterized proteins like bovine serum albumin also have widely cited experimentally measured values (BSA's is about 43,824 M⁻¹cm⁻¹) that are generally more reliable than the sequence-based estimate.
Why is protein absorbance usually measured at 280 nm specifically?
Because that's the wavelength where the aromatic amino acids tryptophan and tyrosine absorb UV light most strongly, and nearly every protein contains at least some of these residues. Nucleic acids, by contrast, absorb most strongly at 260 nm, which is why a 260/280 absorbance ratio is commonly used as a quick check for nucleic acid contamination in a protein sample, or protein contamination in a nucleic acid sample.
What happens if I use the wrong path length in the calculation?
The calculated concentration will be off by exactly the ratio between the path length you entered and the true path length of your measurement — using 1 cm when your instrument actually used a 0.5 mm microvolume path, for instance, would understate the true concentration by a factor of 20. Always use the path length your specific spectrophotometer or cuvette actually used for that reading, not an assumed standard value.
Can I use this formula for something other than protein, like DNA or RNA?
Yes — the Beer-Lambert law itself (A = ε × c × l) applies to any light-absorbing solute, including nucleic acids, as long as you use the correct extinction coefficient and wavelength for what you're measuring. Nucleic acids are conventionally read at 260 nm with their own extinction coefficients, so just substitute the appropriate absorbance reading and coefficient into the same c = A / (ε × l) calculation this instrument performs.
Why does a higher extinction coefficient give a lower calculated concentration for the same absorbance?
Because extinction coefficient measures how strongly a molecule absorbs light per unit of concentration — a protein with a high coefficient absorbs a lot of light even at low concentration, so reaching a given absorbance reading takes less of it in solution. Dividing absorbance by a larger ε therefore correctly yields a smaller concentration for the same measured absorbance value.