Half the bench work in an intro lab is dilution. You are handed a 5 M stock and asked for 50 mL at 1 M, or told to make a 1:10 and then immediately asked what the final concentration is. The maths is one line long, and it is also the thing people get wrong under time pressure because they confuse the volume you start with, the volume you finish with, and the volume of water you actually pour.
This calculator takes the guessing out of it. Pick which of the four values you want, fill in the other three, press Calculate, and it hands back the missing one to four decimal places. Solve for C1, V1, C2, or V2 — same equation, four rearrangements.
It does one step and it does it correctly. It does not chain serial dilutions, it does not convert percent to molarity, and it does not know that your graduated cylinder reads to within half a millilitre. That is what the sections below are for.
Solve dilution problems using C1V1 = C2V2. Enter any three values and select which variable to solve for.
The equation and its four faces
C1V1 = C2V2
Concentration of stock times volume of stock equals concentration of final solution times volume of final solution. It holds because the amount of solute does not change when you add solvent: the same stuff is just sitting in more liquid.
Rearranged for each variable:
- C1 = C2V2 ÷ V1
- V1 = C2V2 ÷ C1
- C2 = C1V1 ÷ V2
- V2 = C1V1 ÷ C2
Two rules keep this honest. C1 and C2 have to be in the same unit, molarity with molarity or percent with percent. V1 and V2 have to be in the same unit too, mL with mL or litres with litres. The equation does not care which pair you pick, only that each pair matches.
A worked example
You need 50 mL of 1.0 M and your stock bottle says 5.0 M. The unknown is how much stock to pipette, so solve for V1.
V1 = C2V2 ÷ C1 = (1.0 × 50) ÷ 5.0 = 10.0000 mL. Pipette 10 mL of the 5 M stock into a flask, then take it up to the 50 mL mark with solvent. That second half is where most people slip: you add 40 mL of water, not 50, because the stock is already contributing 10 mL of the final volume.
Run the same problem the other way and it checks out. Take that 10 mL of 5.0 M and dilute it to a total of 50 mL, and C2 = C1V1 ÷ V2 = (5.0 × 10) ÷ 50 = 1.0000 M. Same dilution, fivefold, approached from either direction.
Third case, the one that catches people on a quiz: you have 10 mL of something and you know it should become 50 mL at 1.0 M, but you have forgotten what was in the bottle. Solve for C1 = (1.0 × 50) ÷ 10 = 5.0000. The stock was 5 M.
Where dilution maths goes wrong
The classic error is treating V2 as the volume of water. It is the total final volume. If the tool returns V1 = 10 mL for a 50 mL final, you add 40 mL of solvent and stop at the mark. Add 50 mL of water to 10 mL of stock and you have 60 mL at 0.83 M, and the experiment downstream quietly fails for a reason nobody can find.
Units are the second trap. Typing C1 in millimolar and C2 in molar will produce a number, and the number will be wrong by a factor of a thousand. Same for mixing mL and litres across V1 and V2. Convert before you type.
Serial dilutions are a different job. Ten-fold dilution repeated three times is 1:1000 overall, and working that out means multiplying dilution factors, not applying this equation once. This tool handles a single step, so for a chain of them, run each step separately or use the serial dilution calculator.
And watch the decimals. The tool prints four of them because that is how the arithmetic comes out, not because your glassware is that good. A 10 mL pipette is rated to a tenth of a millilitre at best, so treat 10.0000 as 10.0.
Other tools
- Disinfectant dilution — stock and water volumes for a target percentage
- Equipment wipe log — record what you cleaned and when
- Glove change reminder — keep the schedule straight on a long session
Frequently asked questions
What is the equation actually saying?
That the amount of solute stays constant. Whatever mass of chemical was in V1 of C1 has to be the same mass sitting in V2 of C2, because you only added solvent. Divide mass by a bigger volume and the concentration drops in proportion.
Is V2 the amount of water I add?
No. V2 is the total final volume, solvent plus stock. Subtract V1 to get the water: 50 mL final minus 10 mL stock means 40 mL to add. This single confusion is behind most wrong dilutions.
Does it matter which unit I use?
Not for the equation, as long as pairs match. Molarity with molarity and mL with mL is the usual setup, but percent with percent and litres with litres works just as well. Never mix the two members of a pair.
Why does it give four decimal places?
Because the division produces them. It is arithmetic precision, not measurement precision. Round to whatever your glassware justifies before you write it in your lab notebook.
Can I use this for buffer or media prep?
Yes, if it is a straightforward one-step dilution from a concentrated stock. Anything with multiple components, pH adjustment, or a serial step needs more than C1V1 = C2V2, and this calculator will not catch that for you.