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Dilution Calculator

C₁V₁ = C₂V₂: the amount of solute does not change when you dilute, only the volume it is spread through.

Result

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How this was worked out

    The formula

    C₁ · V₁ = C₂ · V₂

    SymbolQuantityUnit
    C₁Initial concentrationM
    V₁Initial volumeml
    C₂Final concentrationM
    V₂Final volumeml

    What it means

    Diluting adds solvent without adding solute, so the number of moles stays fixed. Concentration times volume gives that fixed amount, which is why the products on both sides must be equal.

    How to work it out by hand

    1. Multiply the starting concentration by the starting volume
    2. Divide by the concentration you want
    3. The result is the final total volume, not the volume to add

    What is worth knowing

    The commonest slip is treating the answer as the volume of solvent to add: it is the final total. To get from 100 mL of 2 M to 0.5 M you need 400 mL in total, so you add 300 mL. The units only need to be consistent, not SI — millilitres on both sides work fine. And for concentrated acids the order matters for safety: always add acid to water, never the reverse, because the dilution releases heat and can spit if it goes the wrong way.

    Frequently asked questions

    Is the answer the volume to add?

    No, it is the final total volume. Subtract the starting volume to find how much solvent to add.

    Do the units have to be litres?

    No, only consistent. Millilitres on both sides give the same answer.

    Why does the formula work?

    Because diluting does not change the amount of solute. Concentration times volume gives that amount, so the two products match.

    Should I add acid to water or water to acid?

    Always acid to water. Dilution releases heat, and the other order can boil and spit.