Solve any unknown in the dilution equation C1V1 = C2V2, with the volume of solvent to add to the stock solution.
Enter the values to see the result here.
Formula
Diluting does not change the amount of solute, only the volume it is spread in:
C1V1=C2V2
so V1=C2V2/C1, and the solvent to add is V2−V1. The dilution factor is C1/C2=V2/V1.
Worked example
Prepare 500 mL of 1.0 M hydrochloric acid from 12 M stock.
V1=C2V2/C1=1.0×500/12=41.7 mL.
Solvent to add: 500−41.7=458.3 mL.
Measure 41.7 mL of stock, pour it into about 400 mL of water in a flask, and make up to the 500 mL mark. The dilution factor is 12.
Common mistakes
Mixing units, for example C1 in mol/L with V1 in mL and V2 in L. Keep volumes in one unit.
Adding the calculated solvent volume to the stock and ending up with the wrong final volume when the liquids do not mix ideally. Top up to the final mark instead.
Entering a final concentration higher than the stock. Dilution can only lower it.
Pouring water onto concentrated acid. Add the acid slowly to the water.
Frequently asked questions
Can I use any units?
Yes, as long as both concentrations share one unit and both volumes share another. The result comes back in the same units you used, for example mol/L and mL, or percent and L.
How do I prepare the diluted solution safely?
Measure the stock volume, then add it to part of the solvent and top up to the final volume. For strong acids always add the acid to the water, never the reverse, because the mixing releases heat.
Does the equation work for any concentration unit?
Yes: molarity, percent, mg/mL, ppm or dilution factors all work, because the amount of solute stays constant and only the volume changes. It does not apply when solute is consumed or produced.