Solution Dilution Calculator
Apply the C₁V₁ = C₂V₂ relationship
Dilutions assume that the amount of solute remains constant when you mix a concentrated stock with solvent. Expressed in MathML, the conservation step is . Solving for the unknown stock volume yields , while the solvent you must add is simply . The calculator evaluates both expressions and rounds results sensibly for lab pipettes.
Worked example: Buffer dilution
Suppose your lab keeps a 5× Tris buffer stock and you need 750 mL of a 1× working solution. Enter C₁ = 5, C₂ = 1, and V₂ = 750. The tool reports that V₁ = 150 mL of stock is required, meaning you will add 600 mL of water to reach the final volume. Because the units cancel, you can perform the same calculation with liters or microliters.
Compare common dilution scenarios
These example rows illustrate how V₁ and solvent change for different lab situations. Adjust the inputs above to match your protocol and refer to the table for quick sanity checks.
| Scenario | C₁ → C₂ | Target volume | Stock volume V₁ | Solvent to add |
|---|---|---|---|---|
| Cell culture media | 10× → 1× | 1.0 L | 100 mL | 900 mL |
| DNA staining solution | 2% → 0.5% | 200 mL | 50 mL | 150 mL |
| ELISA wash buffer | 1 M → 50 mM | 500 mL | 25 mL | 475 mL |
Tips for reliable dilutions
Always mix volumes at the same temperature because density changes can skew precision in high-concentration stocks. Use calibrated volumetric flasks when possible, rinse pipettes with the solution you are measuring, and label both the intermediate and final solutions. For serial dilutions, repeat the calculation for each step or explore the Antibody Titer Dilution Calculator for automated sequences.
If you need to prepare solutions starting from solid reagents, combine this page with the Molar Mass Calculator and Molarity Calculator to check that your concentrations align. For specialty applications such as essential oils or agricultural sprays, review the Essential Oil Dilution Calculator and Pesticide Dilution Calculator for contextual safety notes.