💧 Dilution Calculator (C₁V₁ = C₂V₂)

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Enter details

Pick what you want to find. The box for that quantity is ignored, so you can leave any number in it.
Any unit (M, %, mg/mL) — use the same for C₂.

Fill in the details and click Calculate to see your results.

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📘 About the Dilution (C₁V₁ = C₂V₂)

Diluting a solution adds solvent but not solute, so concentration × volume stays the same: C₁V₁ = C₂V₂ (written M₁V₁ = M₂V₂ for molarity). Choose what you want to find and enter the other three values.

The concentrations can be in any unit — molarity, percent or mg/mL — as long as C₁ and C₂ use the same one. The calculator also tells you how much solvent to add.

🧮 Formula

Dilution equation
C₁V₁ = C₂V₂
Stock volume needed
V₁ = C₂V₂ ÷ C₁
Solvent to add
V₂ − V₁

Where

  • C₁ = concentration of the stock solution
  • V₁ = volume of stock used
  • C₂ = concentration after dilution
  • V₂ = total volume after dilution
Volumes add approximately for dilute aqueous solutions; for concentrated acids the final volume can be slightly less than V₁ + water.

✏️ Worked examples

100 mL of 0.1 M from 1 M stock

You enter
FindVolume of stock needed (V₁)
Stock concentration (C₁)1
Final concentration (C₂)0.1
Final volume (V₂)100 mL
You get
Stock volume V₁ (mL)10
Stock concentration C₁1
Final concentration C₂0.1
Final volume V₂ (mL)100
Solvent to add (mL)90

Take 10 mL of the stock and add 90 mL of water.

Try this example →

Diluting 25 mL of 2 M to 500 mL

You enter
FindFinal concentration (C₂)
Stock concentration (C₁)2
Volume of stock (V₁)25 mL
Final volume (V₂)500 mL
You get
Stock volume V₁ (mL)25
Stock concentration C₁2
Final concentration C₂0.1
Final volume V₂ (mL)500
Solvent to add (mL)475

The new concentration is 0.1 M.

Try this example →

🧭 How to use this calculator

What you enter

  • FindPick what you want to find. The box for that quantity is ignored, so you can leave any number in it.
  • Stock concentration (C₁)Any unit (M, %, mg/mL) — use the same for C₂.
  • Volume of stock (V₁) (mL)
  • Final concentration (C₂)
  • Final volume (V₂) (mL)

What you get

  • Stock volume V₁ (mL)
  • Stock concentration C₁
  • Final concentration C₂
  • Final volume V₂ (mL)
  • Solvent to add (mL)

💡 Safety tip: acid to water

When diluting a concentrated acid, always add the acid slowly to the water, never water to the acid. The heat released can make water boil and spit if it is added to concentrated acid.

❓ Frequently asked questions

What is the dilution formula?

C₁V₁ = C₂V₂ (or M₁V₁ = M₂V₂ for molarity).

Do the volumes have to be in litres?

No. Use any volume unit as long as V₁ and V₂ match.

What is a dilution factor?

V₂ ÷ V₁ (or C₁ ÷ C₂). Diluting 10 mL to 100 mL is a 10× dilution.

How much water do I add?

V₂ − V₁. For 10 mL of stock made up to 100 mL, add 90 mL.