Dilution Calculator
C1V1 = C2V2, without the algebra.
Dilution Calculator
C₁V₁ = C₂V₂, so V₁ = (C₂ × V₂) / C₁
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What This Calculator Does
The Dilution Calculator solves the standard dilution equation for the volume of stock you need. Enter the stock concentration, the concentration you want, and the final volume, and it returns the stock volume, the diluent volume, and the dilution factor.
How It Works
Dilution conserves the amount of solute: concentration times volume is constant, so C₁V₁ = C₂V₂. Rearranging gives the stock volume. The diluent is whatever remains of the final volume once the stock is added. The dilution factor is the stock concentration divided by the target.
Example
To make 100 mL of 0.1 M solution from a 1 M stock, you need 0.1 × 100 / 1 = 10 mL of stock. Add roughly 80 mL of diluent first, then make up to the 100 mL mark, so the diluent volume is about 90 mL. The dilution factor is 10×.
Formula
C₁V₁ = C₂V₂V₁ = (C₂ × V₂) / C₁DF = C₁ / C₂A 10× dilution means one part stock to nine parts diluent.
Reading the Results
Stock solution needed
The volume of concentrated solution that contains exactly the target amount of solute. Measure it with a pipette or graduated cylinder, not by eye.
Dilution factor
How many times the solution is diluted. A factor of 10 means the final concentration is one tenth of the stock.
Sources and References
IUPAC — Compendium of Chemical Terminology (Gold Book)
Dilution and concentration definitions
Defines concentration in terms of amount of substance and volume, which is the basis of C₁V₁ = C₂V₂.
NIST — Standard Reference Materials for solution concentration
Gravimetric and volumetric preparation
Illustrates why final volume, not added solvent volume, defines the concentration.
References identify the method or data behind this calculator. Where a standard or tariff changes, the current edition applies, and the assumptions stated above take precedence over a remembered figure.
Frequently Asked Questions
Do I add the stock to the diluent or the other way round?
Add the stock to part of the diluent, mix, then make up to the final volume. The volumes are not perfectly additive, so adding all the diluent first often leaves you above the mark.
What does a 1:10 dilution mean?
It usually means one part stock plus nine parts diluent, for a total of ten parts and a dilution factor of 10. Some protocols write 1:10 to mean one part in ten total, which is the same thing; watch for 1:9 notation, which also gives a factor of 10.
Can I use this for a serial dilution?
Yes, but apply it one step at a time. Each transfer carries pipetting error, so a five-step 10× series can drift noticeably from the nominal final concentration.
Why can I not set the target above the stock?
Dilution only lowers concentration. To go up you would need to add solute, evaporate solvent, or use a more concentrated stock — none of which this equation models.