How this instrument works
Diluting a solution — adding solvent to lower its concentration — doesn't change how much solute is present, only how spread out it is. That single fact is captured in the dilution equation, C1V1 = C2V2, where C1 and V1 are the concentration and volume of the starting (stock) solution, and C2 and V2 are the concentration and volume of the diluted solution you're aiming to make. Because the amount of solute (concentration times volume) stays constant through dilution, the product on both sides of the equation must match.
This calculator solves that equation specifically for V1 — the volume of stock solution you need to measure out — given the stock concentration and your target concentration and final volume: V1 = C2 x V2 / C1. Once you've measured out that volume of stock, adding solvent up to the target final volume, V2, completes the dilution at exactly the concentration you specified.
The same equation can be rearranged to solve for any of the other three quantities instead — if you already know how much stock volume you're using and want to know what final volume to dilute it to for a target concentration, or what concentration a given stock-and-solvent combination will produce, the same C1V1=C2V2 relationship handles all of those, just solved for a different unknown.
- Enter your stock solution's concentration into Stock concentration, C1.
- Enter the concentration you want the final, diluted solution to be into Desired final concentration, C2.
- Enter the total final volume you want to end up with into Desired final volume, V2.
- Read Stock volume needed, V1 below the inputs — measure out exactly this much stock solution, then add solvent until the total reaches V2.
Worked example — diluting a 1 M stock to 20 mM
Enter 1 into Stock concentration, C1, 0.02 into Desired final concentration, C2 (20 mM expressed as 0.02 M), and 0.5 into Desired final volume, V2 (0.5 L). Stock volume needed, V1 reads 0.01: V1 = (0.02 x 0.5) / 1 = 0.01 L, or 10 mL.
In the lab, that means measuring out exactly 10 mL of the 1 M stock solution into a container, then adding solvent (typically water or whatever the stock was originally dissolved in) until the total volume reaches 0.5 L — at which point the solution is at exactly 0.02 M (20 mM), the target concentration, because the total moles of solute in that 10 mL of stock haven't changed, only the volume they're now spread across.
Questions
Why does C1V1 have to equal C2V2?
Because the product of concentration and volume equals the total amount of solute present, and diluting a solution with pure solvent doesn't add or remove any solute — only spreads the same amount across a larger volume. Since the amount of solute before dilution (C1V1) and after dilution (C2V2) must be identical, those two products are always equal, which is exactly the dilution equation.
What units should I use for concentration and volume?
Any consistent units work, as long as C1 and C2 use the same concentration unit as each other, and V2 (and the resulting V1) use the same volume unit as each other — molarity and liters are the most common pairing in a chemistry lab, but percent concentration and milliliters work identically. Mixing units (for instance, entering C1 in M but C2 in mM without converting) will produce an answer that's off by whatever conversion factor was skipped.
Does V2 mean the volume of solvent I add, or the final total volume?
The final total volume — V1 (stock) plus whatever solvent gets added to reach it, not the solvent volume added on its own. Practically, this means measuring V1 of stock into a container, then adding solvent until the total volume reads V2, rather than adding a separately calculated solvent volume and hoping the total comes out right.
Can this equation be used to solve for something other than V1?
Yes — C1V1=C2V2 is symmetric in what it can solve for, given the other three quantities: solve for C2 (what concentration will this dilution produce) as C1V1/V2, for V2 (how far can I dilute to hit a target concentration) as C1V1/C2, or for C1 (what stock concentration do I need) as C2V2/V1. This calculator is fixed to solving for V1 specifically, since 'how much stock do I need to measure out' is the most common practical question.
What if my desired final concentration is higher than my stock concentration?
Then this equation and calculation don't apply — diluting a solution can only lower its concentration, never raise it, since you're adding solvent, not more solute. A target concentration higher than the stock concentration means you'd need a more concentrated stock solution to start from, or you'd need to add more solute directly rather than dilute.