Dilution calculator
C₁V₁ = C₂V₂ solved for whichever value you leave at zero, with the volume of solvent to add and the dilution factor worked out alongside.
Stock to measure out
25 mL
Solvent to add
75 mL
Final volume
100 mL
Stock concentration
2 mol/L
Final concentration
0.5 mol/L
Dilution factor — one part stock to 3 parts solvent
4
C₁ × V₁ = C₂ × V₂
Every dilution is the same statement: the solute you had is the solute you still have, only spread through more solvent. That is what C₁V₁ = C₂V₂ says, and it is why the equation does not care whether your concentrations are molar, percent or milligrams per millilitre — as long as both sides use the same unit. Leave one of the four boxes at zero and this page fills it in, along with the number people actually need at the bench: how much solvent to add to the stock you measured out.
How it is calculated
C₁ × V₁ = C₂ × V₂
Concentration is amount of substance divided by volume, so a concentration multiplied by a volume is an amount of substance. Adding solvent changes the volume and leaves the amount alone, which makes the product on the left equal to the product on the right. Rearranging for the missing term is the whole calculation; the volume of solvent to add is V₂ − V₁, and it is not the same thing as V₂.
Questions people ask
- Do I add the solvent volume, or top up to the final volume?
- Top up to the final volume, and use the solvent figure as a guide to how much you will need. Mixing two liquids does not always give the sum of their volumes, so measuring 25 mL of stock and adding exactly 75 mL of water can land slightly off 100 mL. For anything analytical, put the stock in a volumetric flask and make up to the mark.
- Does it matter which units I use?
- Only that both concentrations share one unit and both volumes share another. The equation is a ratio, so molar against molar and millilitres against millilitres works exactly as well as percent against percent and litres against litres. The labels on this page say mol/L and mL because that is the common case, not because the arithmetic depends on it.
- Why did I get a negative volume of solvent?
- Because the final concentration you asked for is higher than the stock you started from, and no amount of adding solvent will get you there. The page reports the negative rather than hiding it, since the usual cause is the two concentrations being entered the wrong way round.
- What does a dilution factor of 10 mean?
- That the stock is ten times stronger than the result, so one part stock ends up in ten parts of final solution — one part stock and nine parts solvent. The phrase "1:10 dilution" is used for both readings in different labs, which is exactly why this page gives you the volumes rather than leaving you to interpret the ratio.
- Can I use this for serial dilutions?
- One step at a time, yes. Work out the first step, then treat its final concentration as the stock for the next. The reason serial dilution exists is that a single step to a very low concentration would need a volume of stock too small to measure accurately — if this page tells you to pipette 0.6 µL, that is the signal to split the job in two.
Related tools
Solution concentration calculator
Weigh out a solute, give the volume and the molar mass, and get the molarity, the grams per litre and the mass percent of the solution.
Molar mass calculator
Type a formula — brackets, nesting and hydrates included — for its molar mass in g/mol and how much of that mass each element contributes.
Percentage Calculator
Work out a percentage of a number, the result of adding or removing it, and the percentage change between two values — all at once.
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