Dilution Calculator

Quick Answer

Last updated: 2 November 2026 ·How we calculate this: the dilution equation C₁V₁ = C₂V₂

How This Dilution Calculator Works

Choose the value you want to find, then enter the other three. The calculator rearranges C₁V₁ = C₂V₂, converts the volumes to the same unit, and solves. It also shows how much solvent to add and the dilution factor, so you know exactly how to mix the solution.

How to Use the Dilution Calculator

1. Choose which value to solve for.
2. Enter the other three values.
3. Choose a unit for each volume.
4. Press Calculate.
5. Read the answer, the solvent to add and the dilution factor.

Core Formulas

• Dilution equation: C₁V₁ = C₂V₂
• Stock volume: V₁ = C₂V₂ ÷ C₁
• Final concentration: C₂ = C₁V₁ ÷ V₂
• Solvent to add: V₂ − V₁
• Dilution factor: C₁ ÷ C₂ = V₂ ÷ V₁

Why it works: the amount of solute is concentration × volume. When you add only solvent, the amount of solute does not change, so the product before mixing, C₁ × V₁, must equal the product after mixing, C₂ × V₂. That is why you can solve for any one of the four values when you know the other three. The two volumes just need to be in the same unit before you divide, which the calculator handles for you.

Key Terms

• Stock solution: a concentrated solution used to make weaker ones.
• Solute: the substance dissolved in a solution.
• Solvent: the liquid that dissolves the solute, often water.
• Concentration: the amount of solute per volume, such as mol/L (M).
• Serial dilution: a series of dilutions, each made from the one before.

Worked Example

You have a 1 M salt solution and need 500 mL at 0.1 M.

• V₁ = 0.1 × 500 ÷ 1 = 50 mL of stock
• Solvent = 500 − 50 = 450 mL
• Dilution factor = 1 ÷ 0.1 = 10×, or a 1:10 dilution

Real-Life Examples

• Lab work: make 100 mL of 0.5 M HCl from 6 M stock: about 8.33 mL of stock.
• Cleaning: dilute a 12% concentrate to 3%: 1 part concentrate to 4 parts total.
• Plant food: mix a liquid fertilizer at the label’s strength from a concentrate.
• Serial dilutions: repeat a 1:10 dilution to go from 1 M to 0.001 M in three steps.

Dilution Factor vs Dilution Ratio

• Dilution factor: final volume ÷ stock volume, such as 10×.
• 1:10 (part to whole): often means 1 part stock in 10 parts total.
• 1:9 (part to part): 1 part stock plus 9 parts solvent, which is the same 10× dilution. Check which style a recipe uses.

Stock Needed for 100 mL

Tips for Accurate Dilutions

• Add solvent up to the final volume in a volumetric flask, rather than adding a measured amount, for the best accuracy.
• Keep units the same for C₁ and C₂.
• For acids, add acid to water, not water to acid, for safety.
• Mix well before using the final solution.

Common Mistakes to Avoid

• Adding V₂ of solvent. V₂ is the total final volume, not the solvent amount.
• Mixing concentration units. Use the same unit for C₁ and C₂.
• Trying to concentrate. Adding solvent can only lower the concentration.
• Confusing 1:10 styles. Part to whole and part to part differ.
• Ignoring volume changes. Some liquids, like alcohol and water, shrink slightly when mixed.

Frequently Asked Questions

References & Sources