The Beer-Lambert law states that absorbance equals the extinction coefficient times concentration times path length, A = e x c x l, so a peptide’s concentration at 280 nm is c = A / (e x l). This post covers rearranging that equation for whichever quantity is missing, and how the extinction coefficient itself is calculated from a sequence.
What is the Beer-Lambert law formula for peptide concentration?
The Beer-Lambert law relates absorbance to concentration, path length, and a compound-specific extinction coefficient:
A = e x c x lwhere A is absorbance (a dimensionless reading from a spectrophotometer), e (epsilon) is the molar extinction coefficient in units of inverse molar times inverse centimeters, c is molar concentration, and l is the path length in centimeters, usually 1 cm for a standard cuvette.
The Beer-Lambert absorbance calculator computes A directly from e, c and l when all three are known, which is useful for predicting what a reading should look like before running a sample.
Solving for concentration
More often, absorbance is the measured quantity and concentration is the unknown. Rearranging:
c = A / (e x l)The Beer-Lambert concentration calculator performs this division once you supply the extinction coefficient and path length, converting a spectrophotometer reading into a molar concentration.
Solving for path length
Less commonly, path length is the unknown, for example when working backward from a known concentration and a known extinction coefficient to check what path length a given reading implies:
l = A / (e x c)The Beer-Lambert path length calculator covers this third rearrangement. All three calculators implement the same underlying identity; which one to use depends only on which of the three quantities you do not already know.
Where the extinction coefficient comes from
None of the three equations above work without an extinction coefficient, and a peptide’s extinction coefficient at 280 nm is not looked up from a single fixed table for every peptide; it depends on the peptide’s own sequence. Absorbance at 280 nm in a peptide comes almost entirely from three side chains: tryptophan, tyrosine, and cystine (a pair of cysteines joined by a disulfide bond). Their individual molar extinction coefficients at 280 nm are:
Trp: 5500 M^-1 cm^-1
Tyr: 1490 M^-1 cm^-1
cystine: 125 M^-1 cm^-1These values, and the additive method of combining them, come from Gill and von Hippel (1989) and Pace et al. (1995), the same method ExPASy’s ProtParam tool uses. The sequence’s extinction coefficient is the sum of each contributing residue’s coefficient times its count:
e = (Trp count x 5500) + (Tyr count x 1490) + (cystine pairs x 125)Cystine bonds cannot be inferred from a sequence alone (whether a given pair of cysteines is actually disulfide bonded depends on the folded structure, not the linear sequence), so the extinction coefficient calculator takes the number of cystine bonds as a separate input rather than assuming one. This method is an additive approximation that ignores tertiary structure and is exact only for a fully denatured, reduced peptide, not a correction some sequences need and others do not.
Putting the pieces together
A typical workflow is: derive the extinction coefficient from the sequence, take an absorbance reading at 280 nm, then solve for concentration. That concentration comes out in molar units; if the next step is diluting the sample or converting to a mass concentration, the unit conversion guide covers moving between molar and mass-based concentration units without losing track of the molecular weight the conversion depends on.
Limits worth remembering
A 280 nm reading only captures absorbance from tryptophan, tyrosine and cystine. A peptide with none of those (many short research peptides do not contain them) will read at or near zero absorbance at 280 nm regardless of how much peptide is actually present, because there is nothing in that sequence to absorb at that wavelength. Beer-Lambert measurements at 280 nm are only meaningful for sequences that actually contain the residues the method depends on.
In short, Beer-Lambert absorbance for a peptide is A = e x c x l, so concentration is c = A / (e x l), using an extinction coefficient built from that sequence’s tryptophan, tyrosine and cystine content.
Primary scientific literature and citations
- Gill, S. C., & von Hippel, P. H. (1989). Calculation of protein extinction coefficients from amino acid sequence data. Analytical Biochemistry, 182(2), 319-326. PubMed PMID: 2610349. DOI: 10.1016/0003-2697(89)90602-7. This paper established the standard additive molar extinction coefficients at 280 nm for tryptophan (5,500 M^-1 cm^-1), tyrosine (1,490 M^-1 cm^-1), and cystine disulfide bonds (125 M^-1 cm^-1).
- Pace, C. N., Vajdos, F., Fee, L., Grimsley, G., & Gray, T. (1995). How to measure and predict the molar absorption coefficient of a protein. Protein Science, 4(11), 2411-2423. PubMed PMID: 8563639. DOI: 10.1002/pro.5560041120. Validated prediction accuracy across 80 proteins in denaturing conditions (6 M guanidine hydrochloride).
- Edelhoch, H. (1967). Spectroscopic determination of tryptophan and tyrosine in proteins. Biochemistry, 6(7), 1948-1954. PubMed PMID: 6049437. The foundational spectrophotometric characterization of aromatic amino acid absorption profiles.
- IUPAC Compendium of Chemical Terminology (Gold Book). Beer-Lambert law entry. Pure and Applied Chemistry, 1996, 68, 2223. Formal definitions of optical absorbance, molar attenuation coefficient, and cuvette path length.