Calculators
Dilution Calculator
Solve C₁V₁ = C₂V₂ with compatible concentration and volume units.
Dilution Calculator tool
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About This Tool
A dilution lowers a solution's concentration by increasing its final volume while keeping the amount of dissolved solute represented by the aliquot unchanged. For a simple dilution, that conservation relationship is C₁V₁ = C₂V₂. This calculator solves any one of the four quantities and also reports the concentration dilution factor and the nominal difference between final volume and stock aliquot. It is useful for classroom problems and routine planning when the simple dilution model applies.
How To Use It
- Choose the concentration or volume you want to solve for.
- Enter the other three positive values and select each unit. The calculator converts compatible molar, mass-per-volume, and volume scales automatically.
- Read the solved value and dilution factor. If you are preparing a solution, distinguish final solution volume from an instruction to add a fixed volume of solvent.
- Apply suitable significant figures and follow your laboratory or process procedure for actual preparation.
Examples
Make 100 mL of 0.25 M from 1.0 M stock
V₁ = C₂V₂/C₁ = 0.25 × 100 / 1.0 = 25 mL of stock. Bring the solution to 100 mL final volume.
Find final concentration
Diluting 10 mL of a 2.5 mg/mL stock to 250 mL gives C₂ = 2.5 × 10 / 250 = 0.10 mg/mL.
Find final volume
A 5 M stock aliquot of 20 mL diluted to 1 M requires V₂ = 5 × 20 / 1 = 100 mL final volume.
Useful Notes
Why C₁V₁ = C₂V₂ works
For a simple dilution, the amount of solute in the selected stock aliquot is conserved. When concentration is expressed per unit volume, C₁V₁ and C₂V₂ represent the same solute amount, so the products are equal.
Compatible units and conversion
C₁ and C₂ may use different scales within the same concentration basis, such as M with mM or g/L with mg/mL. The calculator also converts liters, milliliters, and microliters. It rejects incompatible bases such as molarity paired with mass per volume because converting those requires additional information such as molar mass.
Dilution factor
The concentration dilution factor is C₁/C₂, which equals V₂/V₁ for this model. A factor of 10 means the final concentration is one tenth of the stock concentration.
Final volume versus solvent added
If the calculation says use 25 mL stock and make to 100 mL final volume, that does not always mean precisely adding 75 mL solvent. In volumetric preparation, combine the stock aliquot and then bring the mixture to the specified final volume.
When the simple model is inappropriate
C₁V₁ = C₂V₂ assumes conserved solute and compatible concentration definitions. It does not model chemical reactions, density-driven mass-percent conversions, purity corrections, dissociation equilibria, serial dilution uncertainty, or volume changes that require a more specific procedure.
FAQ
What is the dilution formula?
For a simple dilution, C₁V₁ = C₂V₂, where C₁ and V₁ describe the stock aliquot and C₂ and V₂ describe the final diluted solution.
Is M1V1 = M2V2 the same formula?
Yes when concentration is molarity: M₁V₁ = M₂V₂ is the molarity-specific form of C₁V₁ = C₂V₂.
Do the volumes have to be in liters?
No. Both volume values only need to use the same unit, such as both mL or both L.
Can I mix mM and M directly?
Yes. Select the unit beside each concentration and the calculator converts compatible scales automatically. It will not mix unlike bases such as M and mg/mL.
Is final volume equal to stock plus solvent volume?
The arithmetic difference V₂ − V₁ is useful as a nominal estimate, but accurate solution preparation commonly means bringing the mixture to the final target volume rather than assuming perfectly additive liquid volumes.