Dilution calculator
For a solution that is already mixed and needs to be weaker. Solves the stock volume and the diluent to add.
Educational arithmetic only. Not medical advice and not a dosing protocol.
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Read this with the answer
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.
Most compounds named here are 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. Full disclaimer.
Show the working
C1 × V1 = C2 × V2: the amount of compound does not change when diluent is added, only the volume it is spread through.- Rearranged for the stock volume:
V1 = C2 × V2 / C1. To make 5 mL at 2 mg/mL from a 10 mg/mL stock, take2 × 5 / 10 = 1 mLof stock. - The diluent to add is the remainder:
V2 - V1 = 4 mL. - A target above the stock concentration 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.
What the identity assumes, which is not nothing
C1V1 = C2V2 is exact arithmetic on two assumptions about the physical world. The first is that volumes add: that 1 mL of solution plus 4 mL of diluent makes 5 mL. The second is that the stock really is at the concentration entered. Neither is arithmetic, and neither can be checked by a calculator.
The first is close enough to true for aqueous dilutions at these concentrations that it is not usually where the error comes from. The second is where it usually comes from, especially when the stock concentration was itself derived from mass over diluent without accounting for the displacement of the solid, in which case it was an upper bound rather than a measurement.
Why dilute at all
The usual reason is measurability. 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. Spreading the same amount through more liquid makes the draw longer and the reading error a smaller share of it. That trade-off is worked through on graduations and readability.
The cost is a second preparation step, and a second opportunity for the concentration on the label to stop matching the concentration in the vial.