Solution Dilution Calculator

About the Solution Dilution Calculator

The dilution equation C₁V₁ = C₂V₂ is arguably the most-used formula in laboratory science. It expresses the conservation of solute: the amount of solute in the stock aliquot (C₁ × V₁) equals the amount in the final diluted solution (C₂ × V₂). This simple relationship lets you solve for any one of the four variables when the other three are known.

Every scientist — from first-year chemistry students to senior researchers — uses this equation regularly for preparing dilutions from stock solutions. Whether diluting concentrated acid for a titration, making working solutions from a protein stock, diluting a PCR primer to working concentration, or preparing drug solutions for cell culture, C₁V₁ = C₂V₂ is the essential calculation.

This calculator solves for any of the four variables (C₁, V₁, C₂, or V₂), shows the dilution factor, the volume of diluent to add, and provides a visual diagram of the dilution process. It supports multiple concentration and volume units, making it quickly useful regardless of your field or the units in your protocol.

When This Page Helps

The C₁V₁ = C₂V₂ equation is simple, but unit mix-ups and arithmetic errors are common under time pressure. This calculator eliminates those mistakes and shows the diluent volume directly.

How to Use the Inputs

1. Select which variable you want to solve for (V₁, V₂, C₁, or C₂).
2. Enter the three known values in the input fields.
3. Select the appropriate concentration and volume units for your system.
4. Read the calculated result and diluent volume.
5. Use the visual diagram to understand the dilution process.
6. Use preset buttons for common laboratory dilution scenarios.

Example Calculation

Tips & Best Practices

• Always add the measured stock volume to a container already containing some diluent, then bring to final volume.
• For volumetric precision, use a volumetric flask to bring the solution to exactly V₂.
• Double-check that C₂ < C₁ — you can only dilute down, not up.
• When diluting acids, add acid to water slowly with stirring to dissipate the heat of mixing.
• For critical preparations, verify the final concentration with a refractometer, pH meter, or spectrophotometer.

The Physics Behind C₁V₁ = C₂V₂

The dilution equation is a statement of mass conservation. The number of moles of solute doesn't change during dilution — you're only adding solvent. Since moles = concentration × volume, the product C × V before dilution must equal C × V after. This holds for ideal solutions where mixing is perfectly additive.

Common Laboratory Applications

In molecular biology, C₁V₁ = C₂V₂ is used to dilute primers from 100 µM stock to 10 µM working solutions, dilute antibodies for Western blots, prepare agarose gel solutions, and set up PCR reaction mixes. In analytical chemistry, it's used to prepare calibration standards from a certified reference material stock. In pharmacology, it generates dose-response curves from a drug stock.

Minimizing Dilution Error

The biggest source of dilution error is measuring very small volumes of stock. If V₁ comes out to 0.5 µL, consider using a two-step dilution instead: first dilute to an intermediate concentration, then dilute again to the final target. This keeps all pipetting volumes in the accurate range of your equipment (typically >1 µL for micropipettes, >1 mL for glass pipettes).

Frequently Asked Questions

• Does C₁V₁ = C₂V₂ work for any concentration unit?

  Yes, as long as both concentrations use the same unit. Molarity, mg/mL, %, ppm — any consistent unit works because the equation is based on conservation of solute mass.

• Do the volume units need to match?

  Yes. Both V₁ and V₂ must be in the same unit (both mL, both L, etc.). The units cancel in the equation, but they must be consistent.

• When does this equation not apply?

  C₁V₁ = C₂V₂ assumes volume additivity (V_total = V₁ + V_diluent). For solutions where mixing causes significant volume contraction (like ethanol + water), the final volume may differ slightly from the expected V₂.

• What if I need a concentration higher than my stock?

  You can't dilute to a higher concentration. If C₂ > C₁, you need a more concentrated stock or a different approach (like dissolving additional solute).

• Is it "add acid to water" or "water to acid"?

  Always add concentrated acid to water, never the reverse. Adding water to concentrated acid causes violent boiling and spattering because the exothermic dissolution superheats the small water volume.

• How accurate is a dilution?

  Accuracy depends on your volume measurement tools. Micropipettes (±0.5–1%), volumetric flasks (±0.05%), and graduated cylinders (±1–3%) each contribute uncertainty.