What this calculator does
This tool solves the dilution equation \(C_1 V_1 = C_2 V_2\) for \(V_1\) — the volume of your concentrated stock solution you need to take in order to prepare a more dilute solution at a known final concentration and volume. It is widely used in chemistry, biology, and pharmacy labs whenever you dilute a stock reagent, buffer, or drug.
How to use it
Enter the three known values: the stock (starting) concentration \(C_1\), the desired final concentration \(C_2\), and the desired final volume \(V_2\). The calculator returns \(V_1\), the volume of stock to measure out, plus the amount of diluent (solvent such as water or buffer) to add to reach the final volume. Keep both concentrations in the same units (e.g. M and M) and both volumes in the same units (e.g. mL and mL); the answer for \(V_1\) comes out in the same volume unit as \(V_2\).
The formula explained
The dilution principle states that the amount of solute is conserved: concentration times volume before equals concentration times volume after, so $$C_1 \times V_1 = C_2 \times V_2.$$ Rearranging for the unknown gives $$V_1 = \frac{\text{Final Conc. (C2)} \times \text{Final Volume (V2)}}{\text{Stock Conc. (C1)}}.$$ Because you are diluting, \(C_1\) is larger than \(C_2\), so \(V_1\) will always be smaller than \(V_2\) — the difference is the diluent you add.
Worked example
You have a 10 M stock and need 100 mL of a 1 M working solution. $$V_1 = \frac{1 \times 100}{10} = 10 \text{ mL}.$$ So measure 10 mL of stock and add 90 mL of diluent to reach 100 mL.
FAQ
Do the units need to match? Yes. \(C_1\) and \(C_2\) must share one unit; \(V_2\)'s unit determines the unit of \(V_1\).
Can I use percentages or X-fold? Yes — any consistent concentration unit (M, mM, %, mg/mL, X) works as long as \(C_1\) and \(C_2\) use the same one.
What is the diluent value? It is \(V_2 - V_1\), the volume of solvent to add to your measured stock to reach the final volume.
