Solution Dilution Calculator

Quickly compute accurate solution dilutions using the classical C1V1 = C2V2 equation. This professional tool serves chemists, biologists, and lab technicians who need to prepare solutions at a target concentration. It supports molar, mass/volume, and percent units, performs instant validation, and outputs a clear, step-by-step recipe.

Calculator

Choose what to solve for

Tip: For standard dilutions, choose “V1” to compute how much stock to pipette for a desired final volume V2.

Unit type: auto

Results

Computed variable —
Diluent to add —
Dilution factor (DF = C1 / C2) —
Ratio (stock : diluent) —
Enter values to see your step-by-step dilution recipe.

Data Source and Methodology

Authoritative source: IUPAC Compendium of Chemical Terminology (Gold Book), 2nd ed. (1997) — “dilution” (updated 2014). Direct link. All calculations apply the conservation-of-mass relationship for solutions.

Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da questa fonte.

For additional background, see: D. C. Harris, “Quantitative Chemical Analysis,” 10th ed., W. H. Freeman (2020).

The Formula Explained

Primary equation (LaTeX): \( C_{1} \cdot V_{1} = C_{2} \cdot V_{2} \)

Solving for stock volume: \( V_{1} = \dfrac{C_{2} \cdot V_{2}}{C_{1}} \)

Diluent volume: \( V_{\text{diluent}} = V_{2} - V_{1} \)

Dilution factor: \( \mathrm{DF} = \dfrac{C_{1}}{C_{2}} \)

Units must be consistent in type for C1 and C2 (molar with molar, mass/volume with mass/volume, or the same percent basis).

Glossary of Variables

C1Stock concentration of the initial solution (e.g., M, mM, mg/mL, % w/v, % v/v).
C2Desired final concentration at which the solution should be prepared.
V1Volume of stock solution to pipette.
V2Total final volume after adding stock and diluent.
DFDilution factor, defined as C1/C2 (dimensionless).
DiluentThe amount of solvent/buffer to add: V2 − V1.

How It Works: A Step-by-Step Example

Scenario: Prepare 10 mL of 100 µM solution from a 10 mM stock.

  1. Enter C1 = 10 mM, C2 = 100 µM, V2 = 10 mL. Choose “Solve for V1”.
  2. Convert units internally to a common base (molar): 10 mM = 0.010 M; 100 µM = 0.0001 M.
  3. Apply the equation: \( V_{1} = \dfrac{C_{2} \cdot V_{2}}{C_{1}} = \dfrac{0.0001 \cdot 10\,\text{mL}}{0.010} = 0.1\,\text{mL} = 100\,\mu\text{L} \).
  4. Diluent volume: \( V_{2} - V_{1} = 10\,\text{mL} - 0.1\,\text{mL} = 9.9\,\text{mL} \).
  5. Recipe: Pipette 100 µL of stock, then add diluent to a final volume of 10 mL.

DF = C1/C2 = 10 mM / 0.1 mM = 100 → a 1:99 (stock:diluent) ratio.

Frequently Asked Questions (FAQ)

Why must C1 and C2 have the same type of unit?

Because the equality C1×V1 = C2×V2 requires consistent dimensions. You may freely mix scales within a type (e.g., mM with µM), but not different physical bases (e.g., % v/v with % w/v).

Can this tool create a serial dilution?

This page focuses on single-step dilutions. For serial dilutions, repeat the calculation step-wise or use a dedicated serial-dilution workflow.

What precision should I use for pipetting?

Choose a pipette volume within its optimal operating range and round to practical increments. Always follow your lab’s SOPs.

How do I interpret the dilution factor (DF)?

DF = C1/C2. A DF of 50 means one part stock with 49 parts diluent (1:49). The tool also shows the exact stock:diluent ratio.

What if the computed V1 exceeds V2?

The requested C2 is higher than C1. Simple dilution cannot achieve this. Prepare a more concentrated stock or adjust your target.

Is percent w/v the same as mg/mL?

1% (w/v) is 1 g per 100 mL, equivalent to 10 mg/mL. However, this tool treats percent and mass/volume as separate types to prevent accidental unit mixing.

Do you support scientific notation?

Yes. You can enter numbers like 1e-3 or 2.5e2 in any numeric field.

Strumento sviluppato da Ugo Candido,. Contenuti verificati da,.
Ultima revisione per l'accuratezza in data: .