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Dilution Calculator

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Diluting something does not change how much of it there is — only how much liquid it is spread through. That single fact is the whole of C₁V₁ = C₂V₂, and it means three known values always give the fourth. Enter what you know and this returns not just the missing figure but the instruction you actually need: how much stock to measure out, and how much diluent to add to it.

Fill in three boxes and leave the one you want worked out empty.

Applies to both volumes. Concentrations can be in any unit at all, as long as C₁ and C₂ match each other.

What you are diluting from

mL

How much of it to take

What you want to end up with

mL

How much you want to end up with

Try:

How to use the dilution calculator

  1. 1Choose the unit your volumes are in. Both volumes use it; the concentrations can be in anything at all.
  2. 2Fill in three of the four boxes — the two concentrations and one volume, or one concentration and both volumes.
  3. 3Leave the box you want worked out empty.
  4. 4Press Calculate.
  5. 5Read the stock volume and the diluent volume — those two numbers are the method, and they are not the same as the final volume.

Examples

Making a working solution from a stock

Input
C₁ = 1 M, C₂ = 0.1 M, V₂ = 500 mL
Result
Take 50 mL of stock, add 450 mL of solvent

The two numbers to act on are 50 and 450. The 500 is where you finish, not what you add.

A concentrated buffer

Input
C₁ = 10×, C₂ = 1×, V₂ = 50 mL
Result
5 mL of 10× buffer plus 45 mL of water

Fold notation works exactly like any other concentration unit, because the equation only uses the ratio.

Diluting a cleaning concentrate

Input
C₁ = 70%, C₂ = 20%, V₂ = 1000 mL
Result
285.7 mL of concentrate plus 714.3 mL of water

A dilution factor of 3.5, or one part concentrate to two and a half parts water.

About the dilution calculator

Why the equation works

Concentration times volume gives the quantity of solute present — moles, grams, whatever the concentration is counting. Diluting adds solvent and nothing else, so that quantity is unchanged before and after. Writing the quantity before as C₁V₁ and after as C₂V₂ and setting them equal is the entire derivation, and it is why the relation holds regardless of what is dissolved or what units are used.

It also explains the limits. The equation says nothing about solubility, so it will happily describe a dilution running the wrong way, or a stock concentration that could not exist. It says nothing about heat: diluting concentrated sulphuric acid releases enough energy to boil the water it is added to, which is why acid goes into water and never the reverse. And it assumes the volumes simply add, which is close enough for most purposes but not exactly true — mixing ethanol and water yields slightly less volume than the sum of the two.

For serious analytical work, that last point is why solutions are made up to volume rather than by adding a calculated amount of solvent. Put the stock in the flask, then add solvent until the meniscus reaches the mark. The stock volume this page calculates is exactly right for that method; the diluent volume is a good working approximation for everything else.

Dilution factor, ratio, and the notation problem

The dilution factor is the ratio of the two concentrations, and it is the cleanest way to describe what you did: a 1 M stock taken to 0.1 M is a ten-fold dilution, written 1:10 in most laboratory contexts. The trouble is that 1:10 is genuinely ambiguous across fields. In molecular biology and clinical chemistry it usually means one part stock made up to ten parts total. In some industrial and horticultural contexts it means one part stock added to ten parts diluent, giving eleven parts total and a slightly weaker result.

The difference is about 9% at 1:10 and grows as the dilution gets weaker, which is enough to matter and small enough to go unnoticed. This page states both readings explicitly rather than picking one, so whichever convention your protocol uses, the number you need is on screen.

Fold notation — 10×, 5× and so on — avoids the ambiguity entirely and is why concentrated buffers are sold labelled that way. A 10× stock means exactly what it says: dilute it ten-fold to reach working strength, one part in ten total. When you are writing a protocol for somebody else to follow, it is the notation least likely to be misread.

Frequently asked questions

Do the concentration units have to match anything in particular?
Only each other. The equation uses C₁ and C₂ purely as a ratio, so they cancel entirely — molar, percent, milligrams per millilitre, fold-concentration, parts per million, all work identically as long as both boxes use the same one. The volumes are different: those are divided into and multiplied by real quantities, so they must share a unit, which is what the dropdown enforces.
Is the volume of diluent the same as the final volume?
No, and mixing the two up is the most common way this calculation goes wrong in practice. If you need 500 mL of a diluted solution and the stock volume works out at 50 mL, you add 450 mL of diluent — not 500. Adding the final volume to the stock gives you 550 mL at the wrong concentration. Proper laboratory practice sidesteps this by making up to volume in a volumetric flask rather than adding a measured amount of solvent, since mixing two liquids does not always give exactly the sum of their volumes.
When should I use a serial dilution instead?
When one step would need a volume too small to measure accurately. Diluting a thousand-fold in a single step means pipetting 1 µL into 999 µL, and a small error in that microlitre is a large error in the result. Three successive ten-fold dilutions reach the same place using comfortable volumes each time. The table on this page shows what a ten-fold series does to your stock concentration at each step.
Why does it refuse when the final concentration is higher than the stock?
Because adding solvent can only ever lower a concentration, so no volume of diluent produces that result. In practice the message nearly always means the two concentrations were entered in different units — 5% and 0.05 describe the same thing but only one of them belongs in a box alongside the other. Occasionally it means what you actually need is evaporation or a more concentrated stock, neither of which is a dilution.
Can I use this for medicines or anything I will consume?
No. This page does arithmetic on numbers you type and has no idea what the liquid is, what strength is safe, or what the consequences of an error would be. Dilution in a clinical or pharmaceutical setting is a controlled procedure for good reasons, and a web page is not part of it. The same applies to anything you plan to drink, inhale or apply to skin.

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