Diluting a stock solution to a working concentration is one of the most common calculations in a lab, kitchen, or darkroom — and it always comes down to the same simple relationship: C1V1 = C2V2. This article covers what the dilution factor actually means, how to rearrange the equation to solve for whichever value you're missing, and where the math breaks down if the numbers don't make physical sense.
Why C1V1 = C2V2 works
When you dilute a solution, you add solvent but you don't add or remove any of the solute itself — the total amount of dissolved substance stays exactly the same. Since amount of solute equals concentration times volume, that conservation law is written as C1V1 = C2V2: the stock's concentration times its volume equals the final concentration times the final volume. Because nothing is created or destroyed, this holds regardless of what unit you use for concentration (molarity, mg/mL, percent, or an arbitrary ×N stock), as long as C1 and C2 use the same unit.
The dilution factor, explained
The dilution factor (DF) is simply C1/C2 — how many times more concentrated the stock is than the target. A DF of 10 means the target is 10× more dilute than the stock, commonly written as a "1:10" dilution. The same ratio equals V2/V1: a 1:10 dilution also means the final volume is 10× the starting stock volume. Knowing the dilution factor alone tells you the ratio, but you need at least one volume to turn that ratio into an actual recipe — hence the separate Final Concentration and Volume Needed tabs, which solve for the volumes directly.
Solving for whichever variable you're missing
C1V1 = C2V2 has four variables, and knowing any three lets you solve for the fourth. If you know your stock concentration and the volumes you're using, rearrange to C2 = C1V1/V2 to find the resulting concentration. If instead you know your stock and want to hit a specific target concentration, rearrange to V2 = C1V1/C2 to find the total volume needed — then subtract the starting volume (V1) to get the diluent to add. This calculator's three tabs are just three different rearrangements of the same equation, chosen for the value you're most likely to be solving for.
When the numbers don't work
A dilution can only ever lower concentration, never raise it — you're adding solvent, not removing it. If your target concentration (C2) comes out higher than your stock concentration (C1), or if a solved final volume comes out smaller than your starting volume, the inputs describe concentrating a solution rather than diluting it, which this calculator flags as an error rather than silently returning a negative diluent volume. Double-check that C1 and C2 are in the same unit — a common source of an apparently "impossible" result is entering one concentration in mg/mL and the other in µg/mL.
Single dilution vs. serial dilution
This calculator handles a single dilution step. When the total dilution factor needed is very large — say, 1,000,000-fold for a bacterial plating series — measuring that in one step is impractical (you'd need either a tiny, imprecise stock volume or an enormous diluent volume). Instead, labs perform a serial dilution: a sequence of smaller, more measurable dilution steps (e.g. five successive 1:10 dilutions to reach 1:100,000) where each step's output becomes the next step's stock. The overall dilution factor is the product of each step's factor.