How it works
Diluting a solution does not change the amount of solute, only the volume it is spread through. So concentration × volume is the same before and after: C1V1 = C2V2.
Concentrations can be in any unit (M, mM, %, mg/mL, ppm) as long as C1 and C2 use the same one. Volumes are shown in mL but any matching unit works.
The solvent to add is V2 − V1. In practice, add stock to a flask and fill to the final volume mark, since volumes of some liquids are not perfectly additive.
Formula
C₁ × V₁ = C₂ × V₂
Questions people ask
How do I make 100 mL of 0.1 M from a 1 M stock?
V1 = 0.1 × 100 ÷ 1 = 10 mL of stock, topped up with 90 mL of solvent to 100 mL total.
What is a dilution factor?
The ratio C1 ÷ C2, or V2 ÷ V1. A 1:10 dilution means one part stock in ten parts total, a dilution factor of 10.
How do serial dilutions work?
Repeat the same dilution several times. Three successive 1:10 dilutions give 1:1,000 overall, which is more accurate than measuring a tiny volume of stock once.