Working out concentration and volume — the arithmetic

The one equation, three ways

The figures above are arbitrary and chosen because they divide cleanly. They are not a recommendation of any amount — the amount in your own calculation comes from your own protocol, and this page has no view on what it should be.

Unit traps, in order of how often they bite

• ◆Milligrams against micrograms. 1 mg is 1000 mcg. A factor-of-1000 error is the most common mistake in this arithmetic and the easiest to miss because the number still looks plausible.
• ◆Millilitres against 'units' on an insulin syringe. A U-100 syringe is graduated in insulin units where 100 units equals 1 mL, so one unit is 0.01 mL. The graduation is not a volume unit and treating it as one is a hundredfold error.
• ◆Concentration against amount. 'A 5 mg vial' and 'a 5 mg/mL solution' are different statements, and the second depends entirely on how much solvent went in.
• ◆Molar against mass concentration. Comparing your solution against a published figure requires the same unit; papers usually report molarity.

Converting to molarity

Molarity is mass concentration divided by molecular weight. A 2.5 mg/mL solution of a 1419.55 g/mol peptide is 2.5 ÷ 1419.55 grams per litre per gram per mole, which works out at about 1.76 mM.

This conversion is what makes a solution comparable to published work, because the literature reports concentrations in molar terms. Two peptides at the same mass concentration are at very different molar concentrations if their molecular weights differ — and across the compounds in this catalog they differ by more than a factor of twelve.

The correction most calculators miss

The mass on the label is peptide content, not the gross mass of powder in the vial. Counter-ion and residual moisture typically account for 5 to 20 percent of what is physically there, and a calculator that treats labelled mass as pure peptide overstates concentration by that fraction.

Where precision matters, use the peptide-content figure from the Certificate of Analysis rather than the number printed on the vial. Where they are the same number, the COA has told you the correction is already applied.

Worked example

A vial states 10 mg of peptide. The COA reports peptide content at 87 percent of gross mass and confirms the labelled figure is content rather than gross, so 10 mg is the working figure.

Reconstituted in 2 mL, concentration is 10 ÷ 2 = 5 mg/mL. To withdraw an arbitrary 0.5 mg — again, arbitrary, chosen to divide cleanly — the volume is 0.5 ÷ 5 = 0.1 mL, which on a U-100 syringe is the 10-unit graduation.

If the vial had instead been reconstituted in 1 mL, concentration would be 10 mg/mL and the same 0.5 mg would occupy 0.05 mL, or 5 units. The amount did not change; the volume did. That relationship is the entire content of every reconstitution calculator on the internet.

Choosing a reconstitution volume

• ◆More solvent gives a lower concentration and larger, easier-to-measure volumes, at the cost of more solution to store.
• ◆Less solvent gives a higher concentration and smaller volumes, where a graduation error is proportionally larger.
• ◆Very high concentrations risk gelling and aggregation for some sequences — a solubility question, not an arithmetic one.
• ◆The reconstituted shelf life is a few weeks refrigerated, so the volume should relate to what will be consumed inside that window.

What this page deliberately does not do

It does not tell you what amount to calculate toward. These compounds have no approved human use and no established human dosing, so any figure presented here as a target would be invented rather than sourced. The arithmetic is universal; the input is not ours to supply.