About this calculator
Choose the quantity you want to solve for, enter the other three, and the calculator applies C₁V₁ = C₂V₂. It also shows how much solvent (water) to add.
Use the same unit for both concentrations and the same unit for both volumes.
Worked examples
Real numbers, worked out by the same calculator. Press “Use these numbers” to try one above.
Make 100 mL of 1 M from 10 M stock
- Volume of stock solution (V₁)
- 10
- Solvent (water) to add
- 90
Using C₁V₁ = C₂V₂, the volume of stock solution is 10.
Show the working
- The amount of dissolved substance stays the same when you add solvent, so C₁ × V₁ = C₂ × V₂.
- Rearranged: V₁ = C₂ × V₂ ÷ C₁.
- Check: 10 × 10 = 100 and 1 × 100 = 100.
- Solvent to add = V₂ − V₁ = 100 − 10 = 90.
10 mL of 5 M made up to 250 mL
- Final concentration (C₂)
- 0.2
- Solvent (water) to add
- 240
Using C₁V₁ = C₂V₂, the final concentration is 0.2.
Show the working
- The amount of dissolved substance stays the same when you add solvent, so C₁ × V₁ = C₂ × V₂.
- Rearranged: C₂ = C₁ × V₁ ÷ V₂.
- Check: 5 × 10 = 50 and 0.2 × 250 = 50.
- Solvent to add = V₂ − V₁ = 250 − 10 = 240.
Final volume from 20 mL of 2% diluted to 0.5%
- Final volume (V₂)
- 80
- Solvent (water) to add
- 60
Using C₁V₁ = C₂V₂, the final volume is 80.
Show the working
- The amount of dissolved substance stays the same when you add solvent, so C₁ × V₁ = C₂ × V₂.
- Rearranged: V₂ = C₁ × V₁ ÷ C₂.
- Check: 2 × 20 = 40 and 0.5 × 80 = 40.
- Solvent to add = V₂ − V₁ = 80 − 20 = 60.
The dilution equation
Adding solvent does not change how much dissolved substance there is, only how spread out it is. So concentration × volume stays the same: C₁ × V₁ = C₂ × V₂, where 1 is the stock solution and 2 is the diluted one.
Making a dilution
Measure the stock volume V₁, put it in a container and add solvent until the total volume is V₂. The amount of solvent to add is V₂ − V₁. To make 100 mL of a 1 M solution from 10 M stock, use 10 mL of stock and add 90 mL of water.
Units and safety
Any concentration unit works (molar, percent, mg/mL) as long as C₁ and C₂ use the same one, and the same goes for volumes. When diluting concentrated acids, always add the acid to the water, never the other way round.
Frequently asked questions
What is C1V1 = C2V2?
The dilution equation: concentration × volume is the same before and after adding solvent.
How much water do I add?
Final volume minus the stock volume.
Can I use percent or mg/mL?
Yes, as long as both concentrations share a unit.
What if C₂ is bigger than C₁?
You would be concentrating, not diluting. The calculator flags it.
Formulas tested against hand-worked answers. Last reviewed 29 September 2026. These calculators do arithmetic only; they are not financial, tax or legal advice.