The dilution equation
The amount of solute stays the same, so concentration times volume before equals concentration times volume after.
To make 100 mL of 1 M from 5 M stock you need 20 mL of stock, because 5 × 20 = 1 × 100.
Worked example
Start with 5 M stock and want 100 mL at 1 M. V1 = 1 × 100 / 5 = 20 mL of stock.
Top it up to 100 mL, so the diluent is 80 mL. The dilution factor is 5, which is also 100 / 20.
Final volume, not water added
V2 is the total volume after diluting. If you add 20 mL of stock to 80 mL of water, V2 is 100 mL, not 80.
The diluent row does that subtraction for you, so the two volumes always add up to the final volume.
Units cancel
Both concentrations use the same unit and both volumes use the same unit, so the units cancel on each side.
That means mM with mL works exactly like M with L. Only the ratio matters, which is why no conversion is needed.
Inputs for the dilution equation calculator
Stock concentration
The strength of the solution you are starting from.
Target concentration
The strength you want. It cannot be higher than the stock, because diluting only weakens.
Final volume
The total volume after diluting, not the amount of diluent added.
CALCULATOR QUESTIONS
Dilution equation calculator questions
How do I make 100 mL of 1 M from 5 M stock?
Take 20 mL of the 5 M stock and make it up to 100 mL with diluent, so you add 80 mL.
What does C1V1 = C2V2 mean?
The amount of solute is unchanged by diluting, so the concentration times the volume is the same before and after.
Is the final volume the water I add?
No. It is the total after diluting. Adding 20 mL of stock to 80 mL of water gives a final volume of 100 mL.
Do I need to convert units?
Not if both concentrations share a unit and both volumes share a unit, because they cancel. Mixing mg/mL with M does need converting first.