Concentration After Volume Change Calculator

The change field accepts a negative number, and that is what makes this page more capable than a plain dilution would be. A positive change is solvent going in: the volume grows, the amount of solute stays where it was, and the concentration falls. A negative change is solvent leaving: the volume shrinks, the same amount of solute is now in less liquid, and the concentration rises. One formula covers both, because the only thing that changes is the sign of the term in the denominator, and the direction of the effect is therefore stated in the input rather than inferred from it.

Worked in the concentrating direction, a 10 mg/mL solution of 5 mL holds 50 mg of solute, and removing 2 mL of solvent leaves 3 mL. Fifty milligrams over three millilitres is 16.67 mg/mL. That is not a dilution and should not be described as one, though it is the same relationship with the sign reversed. The amount of solute is the same 50 mg in both directions; only the denominator moves, which is the whole content of the calculation. The calculator insists only that the resulting volume stays positive, because a negative volume is not a physical situation and cannot be pipetted.

Three different things get described as taking volume out, and only two of them change a concentration. Taking solvent away concentrates the solution, because the solute stays. Taking solution away changes nothing, because the solute leaves with the volume in exactly the proportion the concentration already describes. This page models the first of the three, so entering a negative number for an aliquot withdrawn from a vial produces a plausible concentration that is higher than the truth, with nothing in the output to indicate a problem. That is the point at which the model is being asked something it cannot answer, and it answers anyway.

The distinction matters most when a preparation is aliquoted, because that is when removing solution is the natural mental model and removing solvent is not. If a vial holds 10 mg/mL and 1 mL is drawn off, what remains is still 10 mg/mL in the volume that remains. A calculation that treats the withdrawal as a concentration change is describing an evaporation that did not happen. Where two different strengths genuinely have to be combined, the solution mixing calculator carries both amounts explicitly and is the correct tool for it.

How far the concentration moves is set by how the volume has changed relative to itself, which is why a small addition has a much smaller effect than its size suggests. Adding 1 mL of solvent to 100 mL of a 5 mg/mL solution gives 500 mg in 101 mL, which is 4.95 mg/mL. The drop is about one percent. It is not one millilitre, and it is not exactly one percent either, because the base the percentage is measured against is the new volume rather than the old one.

The ratio rule itself is exact and worth keeping: the finished concentration is the original multiplied by the original volume divided by the new volume. That is the same relationship as the four-term equation with the whole original volume taken as the stock volume, which is why the general dilution calculator reproduces this page exactly when you enter the original concentration and volume as the stock and the new total as the target volume. When the two disagree, look for a volume entered as an amount added rather than as a total.

This page models a single change to a single solution. A series of them is a different calculation, because each step carries its own factor and its own volumes, and the arithmetic compounds rather than staying one ratio. That is what the serial dilution calculator is for, and it produces the table that a chain of additions to the same tube would otherwise require you to build by hand. Working backwards from a target in a known final volume is likewise a different form, and the working solution calculator covers it.

The model also takes the volume change as exactly what you entered, which for evaporation is not true. Drying removes water preferentially, so a solution that concentrates that way changes in ways no single volume entry describes, and a rounded stated concentration feeds every later step in proportion. Temperature works in the opposite direction, since a warm solution holds a larger volume than a cold one at the same composition. Neither effect is large for a single small change, and both are systematic, so across a series they accumulate rather than cancel.