Dilution Calculator (C₁V₁ = C₂V₂)Free online science calculator — instant results, no sign-up
Find the volume of stock solution needed for a target dilution.
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About the Dilution Calculator (C₁V₁ = C₂V₂)
The Dilution Calculator (C₁V₁ = C₂V₂) finds the volume of stock solution needed to prepare a specified volume of a lower-concentration solution. Enter the stock concentration and target concentration in mol/L and the target volume in liters to calculate the stock volume needed and the nominal solvent volume to add.
- Stock concentration (mol/L)
- The concentration of the starting solution in moles per liter (mol/L), with a default of 6.
- Target concentration (mol/L)
- The desired concentration of the diluted solution in moles per liter (mol/L), with a default of 0.5.
- Target volume (L)
- The desired final volume of the diluted solution in liters (L), with a default of 1.
Formula and method
C₁V₁ = C₂V₂; V₁ = (C₂ × V₂) / C₁; V_solvent = V₂ − V₁.
- C₁Stock solution concentration in mol/L.
- V₁Volume of stock solution needed in L.
- C₂Target concentration after dilution in mol/L.
- V₂Target final solution volume in L, including both stock solution and solvent.
- V_solventNominal volume of solvent to add in L, calculated as the final volume minus the stock volume.
Dilution conserves the amount of dissolved solute, so the calculator equates C₁V₁ and C₂V₂ and solves for V₁. With the default inputs, V₁ = (0.5 mol/L × 1 L) / (6 mol/L) = 0.0833 L, rounded to four decimal places. Subtracting the unrounded stock volume from 1 L gives a nominal solvent volume of 0.9167 L, also rounded to four decimal places.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Stock concentration6 mol/L
- Target concentration0.5 mol/L
- Target volume1 L
Results
- Stock volume needed0.0833 L
- Solvent to add0.9167 L
- FormulaC₁V₁ = C₂V₂
How to use the Dilution Calculator (C₁V₁ = C₂V₂)
- 1Enter the stock concentration in mol/L; use 6 for the default example.
- 2Enter the target concentration in mol/L; use 0.5 for the default example.
- 3Enter the target final volume in L; use 1 for the default example.
- 4Read the results: stock volume needed is 0.0833 L and nominal solvent to add is 0.9167 L.
- 5For accurate preparation, measure the required stock volume and add compatible solvent to reach a total final volume of 1 L, following the chemical's handling and mixing precautions.
Reading your result
The 'Stock volume needed' row is the amount of the original 6 mol/L solution required: 0.0833 L for the default example. The 'Solvent to add' row is the nominal difference between the final volume and stock volume: 0.9167 L. The 'Formula' row shows C₁V₁ = C₂V₂, the conservation relationship used to obtain these results. The target volume is the total prepared solution volume, not the solvent volume alone.
Limitations
The calculation assumes the same solute is conserved during dilution, the solvent contributes none of that solute, and no reaction, precipitation, or loss changes its amount. Stock concentration and target volume must be positive, and target concentration must be nonnegative and no greater than the stock concentration for dilution alone to work. The solvent subtraction assumes additive volumes; real mixtures can contract or expand, so precise preparation requires adding solvent to a final-volume mark rather than relying on separately measured volumes summing exactly. Results are limited by stock-concentration accuracy, measurement precision, temperature effects, and display rounding. This tool does not determine chemical compatibility or safe mixing procedures.
Common questions
Why does the default dilution need only 0.0833 L of stock solution?+
The required stock volume is the target concentration multiplied by the final volume and divided by the stock concentration: (0.5 × 1) / 6 = 0.0833 L after rounding. Diluting that amount to a total of 1 L gives the target concentration, subject to measurement and rounding limits.
Should I add the stock solution to 1 L of solvent?+
No. The default 1 L is the final solution volume, including the stock. The nominal solvent amount is 0.9167 L; for accurate preparation, add solvent until the total solution volume reaches 1 L.
Can this calculator prepare a target concentration greater than the stock concentration?+
Not by dilution. A target concentration above the stock concentration would produce a stock volume larger than the target final volume and a negative solvent amount, indicating that a more concentrated stock or a different preparation method is needed.
Can I enter concentrations in percent instead of mol/L?+
Not directly into this calculator's mol/L inputs. Convert both concentrations to mol/L first; percent conversions depend on whether the percentage is mass-based or volume-based and may require molar mass and density.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
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Results are estimates for informational purposes and are not financial, medical or legal advice.