Your result will appear here
Fill in the fields and press Calculate.
Diluting a concentrated stock solution to a lower working concentration is one of the most routine tasks in any lab, and it all comes down to a single equation: C₁V₁ = C₂V₂. The amount of solute doesn't change when you add solvent — only the volume does.
Pick the value you need, enter the three you know, and the calculator returns the fourth.
Dilution Calculator: step-by-step worked example
- Solve for
- Stock volume V₁
- Stock concentration C₁
- 12 mol/L
- Final concentration C₂
- 1 mol/L
- Final volume V₂
- 500 mL
- 1
The amount of solute is conserved
C₁ × V₁ = C₂ × V₂
1 × 500 = 500 mmol
- 2
Stock volume needed
V₁ = C₂ × V₂ ÷ C₁
500 ÷ 12 = 41.6667 mL
- 3
Solvent to add
Solvent = V₂ − V₁
500 − 41.6667 = 458.3333 mL
- 4
Dilution factor
DF = C₁ ÷ C₂ = V₂ ÷ V₁
12 ÷ 1 = 12 ×
- Stock solution (V₁)41.6667 mL8.3%
- Solvent (water)458.3333 mL91.7%
Good to know: Both concentrations must share a unit, and both volumes must share a unit. Safety: when diluting concentrated acid, always add acid to water, never water to acid.
Dilution Calculator — how it works
The dilution equation
C₁ and V₁ are the concentration and volume of the concentrated stock; C₂ and V₂ are the concentration and volume of the final, diluted solution.
| Solve for | Formula |
|---|---|
| Stock volume V₁ | (C₂ × V₂) ÷ C₁ |
| Stock concentration C₁ | (C₂ × V₂) ÷ V₁ |
| Final concentration C₂ | (C₁ × V₁) ÷ V₂ |
| Final volume V₂ | (C₁ × V₁) ÷ C₂ |
How much diluent to add
The most common question is "how much stock and how much water?" Solve for V₁ (the stock you need), then the diluent to add is simply V₂ − V₁. For a 100 mL final volume needing 20 mL of stock, you add 80 mL of solvent.
Keep the units consistent
The two concentrations must share a unit (both M, both %, both mg/mL) and the two volumes must share a unit (both mL, both L). The equation is a ratio, so it doesn't matter which units you pick — only that each pair matches.
Where it helps
Preparing working solutions from a concentrated stock, making serial dilutions, or reconstituting reagents to a spec. To first work out a stock concentration from mass, use a molarity calculator.
Worked example
You have a 10 M HCl stock and need 100 mL of 2 M HCl. Solve for V₁: V₁ = (C₂ × V₂) ÷ C₁ = (2 × 100) ÷ 10 = 20 mL. So you measure 20 mL of the 10 M stock and add 80 mL of water to reach 100 mL total — never the other way around when handling strong acids: add acid to water.
Stock volume needed for a 1:N dilution (C₁V₁ = C₂V₂)
| Dilution | 10 mL final | 100 mL final | 1 L final |
|---|---|---|---|
| 1:2 | 5 mL | 50 mL | 500 mL |
| 1:4 | 2.5 mL | 25 mL | 250 mL |
| 1:5 | 2 mL | 20 mL | 200 mL |
| 1:10 | 1 mL | 10 mL | 100 mL |
| 1:20 | 0.5 mL | 5 mL | 50 mL |
| 1:50 | 0.2 mL | 2 mL | 20 mL |
| 1:100 | 0.1 mL | 1 mL | 10 mL |
| 1:200 | 0.05 mL | 0.5 mL | 5 mL |
| 1:500 | 0.02 mL | 0.2 mL | 2 mL |
| 1:1000 | 0.01 mL | 0.1 mL | 1 mL |
Stock volume = final volume ÷ dilution factor; make up the rest with diluent.
Frequently asked questions
What is the C1V1 = C2V2 formula?+
It states that the moles of solute are conserved during dilution: concentration × volume before equals concentration × volume after. Rearranged, it solves for any one of the four values.
How much water should I add to dilute a solution?+
Solve for the stock volume V₁ you need, then the water to add is the final volume minus V₁. For 100 mL needing 20 mL of stock, add 80 mL of water.
Do the units have to match?+
The two concentrations must use the same unit and the two volumes must use the same unit, but you can mix systems between the pairs. The formula is a ratio, so consistent pairs are all that matters.
What is a dilution factor?+
It is the ratio of final volume to stock volume (V₂ ÷ V₁), or equivalently C₁ ÷ C₂. A 1:10 dilution means one part stock to nine parts diluent, a factor of 10.
Can I use this for serial dilutions?+
Yes — apply the calculator once per step, using each step’s result as the stock for the next. Serial dilutions multiply the factors, so three 1:10 steps give a 1:1000 total dilution.
About this page
- Publisher:
- Kalkoro — Teknolojig Bilişim Teknolojileri A.Ş., İstanbul
- Written by:
- Ahmet Tur — Editor (Math, date & time, unit conversion, physics & chemistry, everyday tools)
- Reviewed by:
- Kübra Yıldız — Editor
Parameters come from official sources; the last update date is shown at the bottom of the page.
Spotted a wrong result? Use the "Report a bug" button at the top of the page; every report is reviewed.
How we calculate and our accuracy policy →
Results are for information only. For official matters the relevant authority's calculation prevails.
Last updated: