Dilution Calculator (C₁V₁ = C₂V₂)

Use the dilution equation C₁V₁ = C₂V₂ to calculate the final volume needed when diluting a solution to a target concentration.

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How to Use

  1. 1
    Enter initial concentration and volume

    Input C₁ (the stock solution concentration) and V₁ (the volume of stock you will use) in any consistent units such as mol/L and mL.

  2. 2
    Enter the known final value

    Provide either C₂ (the desired final concentration) or V₂ (the desired final volume), leaving the unknown field blank.

  3. 3
    Calculate the missing variable

    Click Calculate to solve C₁V₁ = C₂V₂ for the unknown. The result tells you either how much stock to take or what total volume to prepare.

About

The dilution equation C₁V₁ = C₂V₂ is one of the most frequently used tools in the chemistry laboratory. It follows directly from the conservation of moles: when a solution is diluted by adding solvent, the total moles of solute remain constant, so the product of concentration and volume is preserved. This simple relationship underlies everything from preparing saline solutions in hospitals to calibrating spectrophotometric standards.

In practice, dilution calculations arise whenever chemists need to bring a concentrated stock solution down to a working concentration. Stock solutions are prepared at high concentration for stability and storage efficiency, then diluted to the exact concentration needed for each experiment. Accurate dilution is critical in analytical chemistry, where even small errors in concentration propagate through calibration curves and quantitative results.

Beyond single dilutions, the concept extends to serial dilution — the workhorse technique of microbiology, immunology, and toxicology for spanning large concentration ranges. Understanding dilution arithmetic also builds intuition for more advanced topics such as buffer preparation, enzyme kinetics assays, and HPLC mobile phase preparation. This calculator eliminates arithmetic errors so you can focus on the chemistry.

FAQ

What is the dilution equation and when does it apply?
The dilution equation C₁V₁ = C₂V₂ states that the number of moles of solute before dilution equals the number of moles after, because dilution only adds solvent without changing the amount of solute. It applies whenever a solution is diluted by adding pure solvent. It does not apply to mixing two solutions of different solutes, to chemical reactions, or to situations involving evaporation.
What is a serial dilution and when is it used?
A serial dilution involves applying the same dilution factor repeatedly, each time using the diluted product as the new starting solution. Serial dilutions are used in microbiology to reduce cell counts to countable numbers, in pharmacology to prepare dose-response curves, and in analytical chemistry to prepare calibration standards spanning several orders of magnitude. Each step multiplies the total dilution factor; three consecutive 1:10 dilutions produce a 1:1000 total dilution.
How do I prepare a 1 mol/L NaCl solution from a 5 mol/L stock?
Using C₁V₁ = C₂V₂: (5 mol/L) × V₁ = (1 mol/L) × (target volume). To prepare 100 mL of 1 mol/L NaCl, you need V₁ = (1 × 100) / 5 = 20 mL of stock. Pipette 20 mL of the 5 mol/L stock into a 100 mL volumetric flask and add distilled water up to the 100 mL mark while mixing thoroughly.
What units should I use in the dilution equation?
Both concentration values must be in the same units (mol/L, g/L, μg/mL, etc.) and both volume values must be in the same units (mL, L, μL, etc.). The units cancel algebraically, so the specific choice does not matter as long as they match on both sides. Mixing mol/L with g/L, or mL with L on different sides, is the most common source of error in dilution calculations.
What is the difference between dilution factor and dilution ratio?
The dilution factor (DF) is the ratio of the final volume to the volume of stock used: DF = V₂/V₁. A dilution factor of 10 means you added enough solvent to make the total volume ten times greater than the stock taken. The dilution ratio (e.g., 1:10) expresses the parts of stock to total parts. These terms are sometimes used interchangeably but the distinction matters when reporting protocols; always clarify which convention you are using.
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