Solution Dilution Calculator
Calculate stock solution volume and the idealized solvent amount for a target concentration and final volume using C₁V₁ = C₂V₂.
Must be greater than 0
Concentration of the stock (concentrated) solution.
Minimum: 0
Desired final concentration after dilution.
Must be greater than 0
Desired final total volume (greater than zero).
Results
Stock Volume Needed (V₁)
10
Solvent to Add
90
Learn with a worked scenario
Stock volume for an ideal dilution using C₁V₁ = C₂V₂.
Question
Prepare a final 250 mL at 0.20 mol/L from a 2.0 mol/L stock.
- Solute amount is conserved: C₁V₁ = C₂V₂.
- V₁ = 0.20 × 250 / 2.0 = 25 mL.
- The simple volume difference is 250 − 25 = 225 mL.
Use 25 mL of stock and make up to a final 250 mL; idealized solvent difference 225 mL.
Precision: Volumes are rounded to at most 3 decimal places, with trailing zeros dropped; values below 0.001 are shown in scientific notation.
Load this example in the calculatorTry a variation
Double the final volume to 500 mL, keeping the 2.0 mol/L stock and the 0.20 mol/L target. How much stock do you need? Predict the answer before you reveal it.
Predict, then reveal
50 mL. V₁ = C₂V₂ / C₁ is proportional to the final volume, so doubling V₂ doubles V₁; the idealized solvent difference becomes 450 mL.
| Final volume | Stock volume |
|---|---|
| 250 mL | 25 mL |
| 500 mL | 50 mL |
| 1,000 mL | 100 mL |
Check the assumptions
- No reaction or solute loss occurs.
- Concentration units match and volume units match.
- Real preparation uses a final measured volume; mixing volumes may not add exactly.
Common mistake: Treating the desired final volume as the amount of solvent to add.
Method reference: OpenStax Chemistry: Molarity. These examples illustrate the method; they do not validate every possible input.
How to Use This Calculator
Enter your input values
Fill in all required input fields for the Solution Dilution Calculator. Follow the units and input format printed next to each field. Where a unit selector is available, choose the units that match your data.
Review your inputs
Double-check that all values are correct and match the units or format shown 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.
Read the results
The Solution Dilution Calculator computes the output in your browser and displays the results, with units clearly labeled, as soon as they are ready — no data sent to a server.
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 C₁V₁ = C₂V₂ to determine the stock volume needed for a desired final concentration and volume. Enter compatible amount-per-volume or mass-per-volume concentrations and use one volume unit throughout. The solute amount must be conserved, with no reaction or loss. The solvent difference is an idealized estimate; actual preparation should follow the relevant laboratory procedure and final-volume measurement.
The Math Behind It
Formula Reference
Dilution Equation
C₁V₁ = C₂V₂
Variables: C₁ = initial concentration; V₁ = initial volume; C₂ = final concentration; V₂ = final volume
Worked Examples
Example 1: A tenfold solution dilution
Use a 2.0 mol/L stock to obtain 250 mL at 0.20 mol/L.
Stock volume: 25 mL. Final solution volume: 250 mL; solvent addition is approximately 225 mL if volumes are additive.
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
Used in These Calculators
Calculators that build on or apply the concepts from this page:
Frequently Asked Questions
Does C₁V₁ = C₂V₂ work for any concentration unit?
Use matching amount-per-volume or mass-per-volume units, such as mol/L or mg/mL. Mass fractions, mass-based percentages and some ppm conventions require a mass balance or density conversion before using volume in this equation.
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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