Molarity and dilution calculator
Three jobs in one tool: find molarity from moles and volume, find moles from molarity and volume, or plan a dilution with C1V1 = C2V2.
How this calculator works
Molarity is the number of moles of dissolved substance in each litre of the finished solution, written M or mol/L. The key phrase is "of solution", not "of solvent": it is the total volume after dissolving, which is why lab recipes say "make up to the mark" in a volumetric flask.
Diluting does not change how much solute you have, only how spread out it is. So moles before equal moles after, and since moles are concentration times volume, C1 × V1 = C2 × V2. Rearrange to find the final volume, then subtract the stock volume to see how much water to add.
The formula behind it
- M = n ÷ V (molarity = moles ÷ litres)
- n = M × V
- C1 × V1 = C2 × V2, so V2 = C1 × V1 ÷ C2
A worked example
Dilute 25 mL of 12 M hydrochloric acid to 1 M. V2 = 12 × 25 ÷ 1 = 300 mL, so add 275 mL of water. In the lab, always add acid to water rather than the other way around.
Questions people ask
Is molarity the same as molality?
No. Molarity is moles per litre of solution. Molality is moles per kilogram of solvent. They are close for dilute water solutions but not equal.
Why can I not dilute to a higher concentration?
Adding solvent only ever weakens a solution. To go stronger you would have to add more solute or evaporate some solvent.
Do the volume units in C1V1 = C2V2 matter?
Only that V1 and V2 use the same unit, and C1 and C2 use the same unit. The calculator reports V2 in whatever unit you entered for V1.
Why must I add acid to water?
Diluting strong acids releases a lot of heat. Pouring acid into a large amount of water spreads that heat safely. Water poured into acid can boil and spit.