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chemistry

Solution Dilution Calculator

Calculate the volume or concentration needed when diluting a stock solution using the C₁V₁ = C₂V₂ equation.

Reviewed by Christopher FloiedPublished Updated

This free online solution dilution calculator provides instant results with no signup required. All calculations run directly in your browser — your data is never sent to a server. Enter your values below and see results update in real time as you type. Perfect for everyday calculations, homework, or professional use.

Minimum: 0

Concentration of the stock (concentrated) solution.

Volume of stock to use (leave blank to solve for this).

Minimum: 0

Desired final concentration after dilution.

Desired final total volume.

Results

Stock Volume Needed (V₁)

10

Solvent to Add

90

How to Use This Calculator

1

Enter your input values

Fill in all required input fields for the Solution Dilution Calculator. Most fields include unit selectors so you can work in your preferred unit system — metric or imperial, whichever matches your problem.

2

Review your inputs

Double-check that all values are correct and that you have selected the right units for each field. Incorrect units are the most common source of calculation errors and can produce results that are off by factors of 2, 10, or more.

3

Read the results

The Solution Dilution Calculator instantly computes the output and displays results with units clearly labeled. All calculations happen in your browser — no loading time and no data sent to a server.

4

Explore parameter sensitivity

Try adjusting individual input values to see how the output changes. This is a quick and effective way to develop intuition about how different parameters influence the result and to identify which inputs have the largest effect.

When to Use This Calculator

  • •Use the Solution Dilution Calculator when you need accurate results quickly without the risk of manual computation errors or unit conversion mistakes.
  • •Use it to verify calculations made by hand or in spreadsheets — an independent check can catch errors before they lead to costly decisions.
  • •Use it to explore how changing input parameters affects the output — a quick way to develop intuition and identify the most influential variables.
  • •Use it when collaborating with others to ensure everyone is working from the same numbers and applying the same assumptions.

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About Solution Dilution Calculator

The solution dilution calculator uses the fundamental dilution equation C₁V₁ = C₂V₂ to determine how much stock solution to use when preparing a diluted solution of a desired concentration and volume. This equation is one of the most frequently used relationships in chemistry, biology, and clinical laboratories. It applies to any dilution scenario where the amount of solute is conserved — no chemical reaction occurs, and the solute simply becomes spread through a larger volume of solvent. Whether you are diluting a concentrated acid for a titration, preparing a working-strength buffer from a 10× stock, or making serial dilutions for a bioassay, this calculator gives you the exact volumes needed.

The Math Behind It

The dilution equation derives from the conservation of solute: the moles of solute in the concentrated solution equal the moles in the diluted solution. Since moles = concentration × volume, we get C₁V₁ = C₂V₂. This holds regardless of the concentration unit (M, %, mg/mL) as long as the same unit is used on both sides. The equation assumes ideal mixing — no volume change upon mixing — which is a good approximation for dilute aqueous solutions but less accurate for concentrated solutions or mixtures of organic solvents where molecular interactions cause volume contraction or expansion. When preparing the diluted solution, always add the measured volume of stock to a volumetric container and then bring the total volume up to V₂ with solvent, rather than adding V₂ worth of solvent to V₁ worth of stock (which would give a final volume greater than V₂). Serial dilutions are a sequence of dilution steps used to achieve very low concentrations: a 1:10 serial dilution repeated three times gives a final dilution of 1:1000.

Formula Reference

Dilution Equation

C₁V₁ = C₂V₂

Variables: C₁ = initial concentration; V₁ = initial volume; C₂ = final concentration; V₂ = final volume

Worked Examples

Example 1: Diluting HCl

Dilute 10 M HCl to make 100 mL of 1 M HCl.

Step 1:C₁V₁ = C₂V₂ → 10 × V₁ = 1 × 100.
Step 2:V₁ = 100 / 10 = 10 mL.
Step 3:Add 10 mL stock HCl to a flask, then add water to 100 mL total.

Use 10 mL of 10 M HCl and add 90 mL of water.

Common Mistakes & Tips

  • !Adding solvent equal to V₂ on top of V₁, making the final volume V₁ + V₂ instead of V₂.
  • !Mixing concentration units (e.g., using M on one side and % on the other).
  • !Adding water to concentrated acid instead of acid to water, which can cause violent boiling.

Related Concepts

Molarity

Molarity is the most common concentration unit used in dilution calculations.

Concentration

General concentration calculations for different units.

Used in These Calculators

Calculators that build on or apply the concepts from this page:

Concentration Calculator

Mass Percent Calculator

Molarity Calculator

Frequently Asked Questions

Does C₁V₁ = C₂V₂ work for any concentration unit?

Yes, as long as you use the same unit on both sides. It works for molarity, mass/volume, parts per million, percentage, etc.

Why should I add acid to water, not water to acid?

Adding water to concentrated acid generates intense localized heat that can cause the water to flash-boil and splatter acid. Adding acid to water distributes the heat over a larger volume, making it much safer.

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