Case 1
- Stock concentration C₁
- 10
- Target concentration C₂
- 2
- Final volume V₂
- 100
20.000
Open with these valuesSolution Dilution Calculator
20.000volume units
Result: 20.000 volume unitsThe answer is V₁, the volume of concentrated stock you measure out — not the solvent you add. For 100 mL of a 2× solution from a 10× stock: V₁ = 2 × 100 ÷ 10 = 20 mL of stock, topped up with 80 mL of solvent. Concentrations in one unit, volumes in another.
The numbers at a glance
Held fixed: Stock concentration C₁ 10.0000, Target concentration C₂ 2.0000.
| Final volume V₂ | Result |
|---|---|
| 0.000 | 0.000 |
| 25.000 | 5.000 |
| 50.000 | 10.000 |
| 75.000 | 15.000 |
| 100.000Your value | 20.000 |
| 125.000 | 25.000 |
| 150.000 | 30.000 |
| 175.000 | 35.000 |
| 200.000 | 40.000 |
Worked examples
Case 2
- Stock concentration C₁
- 1
- Target concentration C₂
- 0.1
- Final volume V₂
- 250
25.000
Open with these valuesCase 3
- Stock concentration C₁
- 100
- Target concentration C₂
- 25
- Final volume V₂
- 1000
250.000
Open with these valuesHow it's calculated
V₁ = (C₂ × V₂) ÷ C₁
- StepEnter both concentrations in the same unit — molar, percent, mg/mL or a fold like 10×.
- StepEnter the final volume you want, in mL or L.
- ResultMeasure out V₁ of stock, then top up to the final volume with solvent.
What this number means
The answer is the stock, not the solvent
V₁ is the volume of concentrated stock you measure out. The solvent to top up with is V₂ − V₁: for 100 mL of a 2× solution from a 10× stock that is 20 mL of stock and 80 mL of solvent.
C₁V₁ = C₂V₂ is conservation of solute
The amount of solute is the same before and after; the solvent only spreads it through more volume. C₁ and V₁ belong to the stock, C₂ and V₂ to the finished solution.
Any units, as long as they match
Both concentrations share one unit — molar, percent, mg/mL, or a fold such as 10×. The final volume you enter fixes the unit the answer comes back in.
Diluting cannot make a solution stronger
Ask for a target above the stock concentration and V₁ comes out larger than the final volume. That is the arithmetic saying the same thing.
Commonly misread
V₁ is 20 mL, so I add 20 mL of solvent to my stock.
The 20 mL is the stock itself. Top it up to the final volume of 100 mL, which takes 80 mL of solvent.
For 75 units at C₂ = 0.15 from a 2× stock I need 11.25.
That is C₂ × V₂ without the division by C₁. V₁ = 0.15 × 75 ÷ 2 = 5.625, leaving 69.375 to top up with.
The concentrations have to be in mol/L.
Any unit works as long as both carry the same one; percent and mg/mL are just as valid. Only the volume unit decides how the answer reads.
Reference table
| C₁, C₂, V₂ | Solvent to add | Stock volume V₁ |
|---|---|---|
| 2, 0.15, 75 | 69.375 | 5.625 |
| 10, 2, 100 | 80 | 20.000 |
| 1, 0.1, 250 | 225 | 25.000 |
| 5, 1, 500 | 400 | 100.000 |
| 100, 25, 1000 | 750 | 250.000 |
| 12, 12, 30 | 0 — no dilution at all | 30.000 |
Questions
How do I calculate a dilution?
Use C₁V₁ = C₂V₂ and solve for the stock volume: V₁ = (C₂ × V₂) ÷ C₁. To make 100 mL of a 2× solution from a 10× stock you need 20 mL of stock.
Does the result include the solvent I add?
No. The result is V₁, the concentrated stock you measure out; the solvent to add is the final volume minus V₁, so 100 − 20 = 80 mL in the example above.
What does C₁V₁ = C₂V₂ mean?
It says the amount of solute is the same before and after: adding solvent spreads the same material through more volume. C₁ and V₁ belong to the concentrated stock, C₂ and V₂ to the finished solution.
Which units should I use?
Any, as long as you are consistent. Both concentrations share one unit — molarity, percent, mg/mL, or a fold such as 10× — and the volume you enter fixes the unit the answer comes back in.
Can I make a solution stronger by diluting it?
No. If you ask for a target concentration above the stock concentration, V₁ comes out larger than the final volume, which is the arithmetic saying the same thing. You would have to evaporate solvent or add solute instead.
Sources and last check
Information, not professional advice.