Thinning a solution

For a preparation that is already liquid and too strong. Solves how much of it to take and how much liquid to add to it.

Educational arithmetic only. Not medical advice and not a dosing protocol.

Fill the fields in and the answer appears here.

What the bench will not tell you

This is educational arithmetic on figures entered by the reader. It is not medical advice, not a dosing protocol, and not a recommendation that anything be prepared, obtained or administered.

Nothing here states what quantity is appropriate for anyone, and there is no function in it that produces an amount to administer. A question about anyone’s health belongs with a licensed clinician who can examine the person asking.

Compounds of the kind this arithmetic is used on are largely research chemicals that are not approved by the FDA for human use. An exact calculation is not an accurate measurement: what is actually in a syringe depends on the preparation and the device, neither of which this page can see.

No qualified clinical reviewer is recorded against this site, and no credential is claimed anywhere on it. the limits of this bench.

The arithmetic, step by step

C1 × V1 = C2 × V2: adding liquid does not change how much compound is present, only the volume it is spread through.
Rearranged for the stock to take: V1 = C2 × V2 / C1. Five millilitres at 2 mg/mL out of a 10 mg/mL stock needs 2 × 5 / 10 = 1 mL of stock.
The diluent is the rest: V2 - V1 = 4 mL.
A target above the stock strength is refused rather than returned as a negative diluent volume. Adding liquid cannot make a solution stronger, and a negative volume is the kind of output that passes a type check and means nothing physically.

The two assumptions inside the identity

C1V1 = C2V2 is exact arithmetic resting on two claims about the physical world. The first is that volumes add: that 1 mL of solution plus 4 mL of liquid makes 5 mL. The second is that the stock really is at the strength entered. Neither is arithmetic and neither can be checked here.

The first is close enough to true for watery dilutions at these strengths that it is rarely the source of an error. The second usually is, and especially when the stock strength was itself derived from a mass over a diluent volume without accounting for displacement, in which case it was a ceiling rather than a measurement.

What thinning buys and what it costs

What it buys is readability. A small amount of a strong solution is a short draw, and a short draw on a barrel marked every unit carries a large relative reading error. Spread the same amount through more liquid and the draw gets longer while the error stays the same size, so it shrinks as a share of the measurement.

What it costs is a second preparation step, and with it a second chance for the strength on the label to stop matching the strength in the container.

Next to this on the bench

Diluent for a strength
For a solid that has not been mixed yet.
Volume for an amount
Once the new strength is settled.
Rounding to the nearest mark
The readability trade-off, with numbers on it.