The measurement and what it assumes
Absorbance is proportional to concentration, to path length and to the extinction coefficient. Rearranged, concentration is absorbance divided by the product of the other two, and that is the whole calculation.
The assumptions behind it are that the sample is in the instrument's linear range, that the only thing absorbing at that wavelength is your peptide, and that the coefficient you are using belongs to the species actually in the cuvette. Each of those fails in a recognisable way.
Staying in the linear range
Below about 0.1 absorbance the signal approaches the instrument's noise. Above about 1.5 the detector receives so little light that small errors in the transmitted intensity become large errors in the calculated absorbance, and stray light begins to dominate.
A reading outside that window should be brought back inside by diluting or by changing the path length. Correcting it arithmetically does not work, because the departure from linearity is not a fixed factor.
Path length and microvolume instruments
A standard cuvette has a 1 cm path. Microvolume instruments that hold a drop of sample between two surfaces use paths of a millimetre or less, and some of them report a value already normalised to 1 cm while others report the raw reading.
Which of the two your instrument does is worth establishing once, because the difference is a factor of ten or more and produces a plausible-looking wrong answer rather than an obviously wrong one.
The two ways the mass concentration goes wrong
The first is a unit error. Molar concentration multiplied by molecular weight in grams per mole is already grams per litre, which is the same number as milligrams per millilitre. Multiplying by a further thousand, as this calculator once did, overstates the mass concentration by exactly that factor.
The second is using the wrong molecular weight. If the material was weighed out as a salt, the salt's weight is the right one; if the extinction coefficient was calculated from the sequence, the free base weight matches it. Mixing the two introduces an error of ten to twenty percent.
How the Beer-Lambert conversion works
One division for the molar concentration and one multiplication for the mass concentration, with the dilution factor applied once so that both figures describe the same sample.
c (mol/L) = A / (epsilon x path length)
c in stock = c in cuvette x dilution factor
c (mg/mL) = c (mol/L) x molecular weight (g/mol)
worked: A=0.5, eps=1490, l=1 cm, MW=1419.5
c = 0.5 / 1490 = 3.36e-4 M
c = 3.36e-4 x 1419.5 = 0.476 mg/mL- Divide absorbance by the coefficient and the path. Gives the molar concentration in the cuvette. This is the only place the instrument reading enters the calculation.
- Apply the dilution factor. Multiplied once, and applied to the molar and mass figures alike so that both describe the original sample rather than one describing the cuvette and the other the stock.
- Multiply by molecular weight for mass concentration. Moles per litre times grams per mole is grams per litre, which is numerically identical to milligrams per millilitre. No further scaling is applied, and applying one is the thousandfold error this calculator used to make.
- Report both cuvette and stock figures. When a dilution factor is in play, the concentration in the cell and the concentration in the original sample are both shown, so the arithmetic can be followed rather than trusted.
- Refuse an impossible input. A zero extinction coefficient returns no result rather than infinity. A peptide with no chromophore cannot be measured this way, and reporting a number would be worse than reporting nothing.
What this method cannot tell you
- •It assumes only the peptide absorbs at the wavelength used. Nucleic acid, aromatic buffer components and turbidity all inflate the reading.
- •It assumes the reading is inside the instrument's linear range. Outside it, the relationship between absorbance and concentration is not proportional and no arithmetic recovers the true value.
- •It assumes the extinction coefficient matches the species in the cell, including its oxidation state.
- •It says nothing about purity. Impurities that absorb are counted as peptide; impurities that do not are invisible.
Where the numbers come from
UV concentration calculator: frequently asked questions
Absorbance equals the extinction coefficient times the path length times the concentration. Rearranged, concentration is absorbance divided by the other two.
It holds while the sample is dilute enough that molecules absorb independently of each other, which is what defines the linear range.
Divide the absorbance by the extinction coefficient and the path length to get molar concentration, then multiply by the molecular weight for milligrams per millilitre.
An A280 of 0.5 with a coefficient of 1,490 in a 1 cm cell is 3.36 x 10⁻⁴ molar. At a molecular weight of 1,419.5 that is 0.476 mg/mL.
Because moles per litre times grams per mole gives grams per litre, and a gram per litre is the same as a milligram per millilitre.
The units cancel exactly, with no scaling factor. Adding one, as this calculator previously did, made every mass concentration a thousand times too high.
Between 0.1 and 1.0. Below that the signal is near the noise; above about 1.5 the instrument leaves its linear range.
Dilute a sample that reads too high and repeat the measurement, then apply the dilution factor. Do not scale a saturated reading down arithmetically.
The physical path of the cell. A standard cuvette is 1 cm; a microvolume pedestal instrument may be 1 mm or less.
Some microvolume instruments report a figure already normalised to 1 cm. Whether yours does is worth establishing once, because the difference is a factor of ten.
Multiply the measured concentration by it. A tenfold dilution measured at 0.2 mg/mL means the original was 2 mg/mL.
The calculator applies it to the molar and mass figures alike, and shows both the cuvette and the original-sample values so the step is visible.
The same buffer the sample is in, without peptide, in the same cuvette. Anything else leaves a buffer contribution in the reading.
For a sample containing DMSO or another co-solvent, the blank has to contain it at the same concentration, since the co-solvent affects both the baseline and the refractive index.
The common causes, in rough order of frequency:
- •Turbidity from undissolved or aggregated material scattering light
- •Nucleic acid contamination, which absorbs strongly at 260 and substantially at 280
- •An absorbing buffer component that the blank did not account for
- •A reading above the instrument's linear range
Checking absorbance at 320 nm, where nothing in a clean protein sample should absorb, distinguishes scattering from genuine absorbance.
Not at 280 nm. Its extinction coefficient there is zero, and the calculator returns no result rather than dividing by zero.
Measure at 205 or 214 nm, where the peptide bond absorbs, or use a colorimetric assay. Both require more care with the buffer than a 280 nm reading does.
Detecting nucleic acid contamination. A clean protein sample reads about 0.5 to 0.6; pure DNA reads about 1.8.
A high ratio means part of the 280 nm signal comes from something other than peptide, so the calculated concentration is an overestimate.
Very little at ordinary temperatures. Extinction coefficients shift by well under a percent across the range between refrigeration and room temperature.
Condensation on a cold cuvette matters much more than the temperature itself, because it scatters light and inflates the reading.
The one matching the species you are measuring. If the coefficient came from the sequence, use the free base weight from the same sequence.
Using a salt weight against a sequence-derived coefficient mixes two descriptions of the molecule and introduces an error of ten to twenty percent.
Because some presets carried coefficients that did not belong to their peptides. BPC-157 was listed with 1,490 M⁻¹cm⁻¹ despite having no tryptophan, tyrosine or cysteine at all.
Each preset now carries the value computed from its own sequence, and the ones that cannot be measured at 280 nm say so in the entry.
Within a few percent when everything is in order: a clean sample, a reading in the linear range, a correct blank and the right coefficient.
The extinction coefficient is usually the largest source of uncertainty, since a predicted value carries a few percent of its own.
Yes, but the path length depends on the fill volume rather than being fixed by the cell, so it has to be calculated or the instrument has to correct for it.
Most modern readers do this automatically. Keeping the volume identical across wells matters more in a plate than it does in a cuvette.
No. It measures how much light the sample absorbs, and anything absorbing at that wavelength contributes.
Purity is a chromatographic question. The HPLC purity interpreter handles it from peak areas.
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