Reverse peptide calculator

A reconstitution is described by three quantities: a mass, a volume and a concentration, of which only two are independent, because the concentration is their quotient. The forward direction takes the mass and the volume and reports the concentration. This direction takes the mass and the concentration and reports the volume. Neither is more correct than the other. What differs is which two you happen to be holding, and because the mass in a vial is fixed by its label while a concentration is usually dictated by whatever document you are working from, the reverse direction is frequently the one whose inputs are ready to go.

The consequence is that no free variable is left once two values are supplied, so the calculation cannot be underdetermined in the way a question with three unknowns would be. What it can be is unphysical. The volume that falls out may be too large for the container, or too small for the peptide to dissolve in, or the concentration typed in may not be the one that was meant. Those are not arithmetic failures. They are the arithmetic working correctly on inputs describing a preparation nobody should make, which is the distinction this page tries to keep visible. The BAC-water solver is the same algebra again, with the syringe rather than a stated concentration supplying the third number.

A concentration on its own does not determine a preparation. It says how densely the peptide sits in the liquid, not how much liquid there is and not how much peptide there is, so the mass has to arrive from somewhere. In practice it comes from the vial label, and that is an assumption worth naming out loud rather than absorbing silently. The calculator treats the printed figure as the mass of active peptide: not as a gross vial weight, not as a purity-adjusted mass, and not as a salt weight. Every one of those readings is a different number and two of them are common.

The second loose end is the volume itself. The result is a volume of diluent, and treating that as the finished volume is right only while the dissolved solid contributes no measurable volume, which is a good approximation for a lyophilised peptide and a poor one for anything already in solution. It is also a volume and not a mass, which sounds obvious and is the source of a recurring class of error: a number in millilitres typed into a field expecting milligrams is accepted rather than rejected. The guide to mass concentration against molarity covers the difference between describing a preparation by mass per volume and by moles per volume, which is the distinction that keeps getting lost at exactly this step.

Every division has an inverse, and here the inverse is another calculator rather than another line of arithmetic, which makes the round trip unusually cheap to perform. Take the volume this page returns, feed it into the forward calculation as the volume of diluent, and the concentration that comes out should equal the concentration that was asked for. If it does not, one of the two inputs was transcribed wrongly. The failure this catches most often is a mass and volume swapped in the source document, which is exactly the kind of error that survives a re-read, because both numbers are individually plausible.

It also helps to know how an error travels, because that tells you what a wrong answer looks like. The volume is inversely proportional to the concentration, so any relative error in the concentration reappears as the same relative error with the opposite sign in the volume. A concentration entered a factor of ten low produces a volume a factor of ten high. A concentration entered a factor of ten high produces a volume so small it may barely wet the powder. Neither result carries a warning. The stock solution calculator and the working solution calculator make the same decomposition explicit in two steps, which is easier to check by eye than a single quotient.

The arithmetic assumes the vial contains exactly the stated amount of peptide, fully dissolved, with nothing retained anywhere along the way. Each clause is an assumption rather than a fact. Retention happens on a filter, on the vial wall and stopper, and in the dead space of whatever is used to draw the solution out, and every one of those losses lowers the amount actually available without changing a single number on this page. The recovery percentage calculator is the tool for the case where a recovery figure is known rather than guessed, and for most readers it will not be.

The arithmetic also assumes that volumes are additive, which is very nearly true for dilute aqueous solutions and untrue for concentrated ones. Both assumptions point the same way: the concentration this page computes is an upper bound on what the vial actually delivers, and the gap widens as the volume shrinks. That is a property of the physical system rather than of the equation, and no additional calculation on this page will close it. The guide to how reverse calculations work arrives at the same conclusion from the other direction, by setting out what the method can and cannot settle before anything is entered.