Dilution Calculator
Solve C₁V₁ = C₂V₂ for any one value, and get the volume of solvent to add.
Why C₁V₁ = C₂V₂ works
Drag the slider to pour solvent into 20 mL of a 1.00 M solution. The dots are solute particles: their number never changes, they just spread through more liquid. Concentration × volume stays fixed, and that product is the moles.
- Volume
- 20 mL
- Concentration
- 1.000 M
- Moles of solute
- 0.0200 mol
1.00 M × 20 mL = 1.000 M × 20 mL = 20 mmol, every time.
Serial dilutions
A 1:10 serial dilution repeats the same step: 1 mL of solution into 9 mL of solvent, mix, take 1 mL of that into the next 9 mL, and so on. After n steps the concentration is C₁ ÷ 10ⁿ. Three steps turn 1 M into 1 mM.
Starting from a solid instead of a stock? Use the molarity calculator to find the grams to weigh out.
Questions students ask
What is the dilution formula?
C₁V₁ = C₂V₂. C₁ and V₁ are the concentration and volume of the stock you take; C₂ and V₂ are the concentration and total volume after diluting. It works because adding solvent doesn’t change the number of moles of solute.
How much water do I add?
V₂ − V₁. To make 100 mL of 0.5 M from 2 M stock, take V₁ = 0.5 × 100 ÷ 2 = 25 mL of stock and add 75 mL of solvent (strictly: make up to 100 mL total).
Does it matter which units I use?
Only that both concentrations share one unit and both volumes share another. M, mM, %, mg/mL or ×-fold all work as long as C₁ and C₂ match.
How do I dilute concentrated acid safely?
Always add acid to water, slowly, never water to acid. The heat released can make water boil and spatter. Wear goggles and gloves.