How Reverse Peptide Calculations Work

A forward calculation starts with what you have and finds what you get. A reverse calculation starts with what you want and works out what you need. The arithmetic is the same; only the direction of the reasoning changes, and that changes which question you can answer.

The three questions, three calculators

The site has three calculators because there are three genuinely different starting points, and conflating them is the common mistake:

The reconstitution calculator starts from a vial mass and a diluent volume, and returns concentration, draw volume and syringe units.
The reverse calculator starts from a target concentration, and returns the diluent volume needed to reach it.
The BAC-water solver starts from a target syringe reading, and returns the diluent volume that makes that reading land on the amount you want.

All three are rearrangements of concentration equals mass over volume. They are not the same question, and using one where another belongs produces a number that is plausible and wrong.

Working backwards from a concentration

Suppose you want 1 mg/mL from a 5 mg vial. The forward direction does not apply, because you are choosing the volume to suit the concentration rather than finding the concentration the volume produces.

Solve concentration for volume instead:

concentration = mass / volume
volume = mass / concentration

5 mg / 1 mg per mL = 5 mL

Running that back through the forward calculator returns exactly 1 mg/mL, and that round trip is the check worth doing. A transposition of mass and volume produces a result that looks reasonable and is wrong, and the round trip catches it immediately because the numbers no longer agree.

Working backwards from a syringe reading

The BAC-water question is different again, and the reason it exists is practical. People reconstitute to round numbers so that reading the barrel needs no arithmetic at all. If a target amount is meant to land on 10 units, the volume that 10 units represents is fixed by the syringe, and everything else follows:

volume of 10 units = 10 / units per mL
concentration     = target amount / that volume
diluent volume    = vial mass / concentration

Worked on a U-100 syringe, where 10 units is 0.1 mL, with a 5 mg vial and a target of 0.1 mg per draw:

volume for 10 units = 10 / 100 = 0.1 mL
concentration      = 0.1 mg / 0.1 mL = 1 mg/mL
diluent volume     = 5 mg / 1 mg per mL = 5 mL

The syringe choice is doing real work in that first line. On a U-40 syringe, 10 units is 0.25 mL, the required concentration becomes 0.4 mg/mL, and the diluent volume becomes 12.5 mL, which may not fit the vial.

When to use which

Use the forward calculator when you have a vial and a volume, because that is what a vial and a volume produce. Use the reverse calculator when a method specifies a concentration. Use the BAC-water solver when you want round syringe readings, and accept the volume it implies.

The relationship between concentration and draw volume holds in all three: one gets you from the other by division, and that division is why adding water always lowers the concentration and always raises the volume needed for the same amount.

What these calculators do not do

They compute volumes. They do not check that the peptide will dissolve at the resulting concentration, which is a real constraint for many peptides and one no arithmetic can settle. They do not model wastage or dead volume, so real yields are lower than the theoretical ones. And they do not recommend a concentration, an amount or a volume; the worked examples above use invented numbers to show the arithmetic.