Making 500 mL of a 0.1 M solution from a 2 M stock
V1 = (0.1 × 500) / 2 = 25 mL of stock, topped up with solvent to 500 mL total.
Solution dilution calculator (C₁V₁ = C₂V₂)
Result
Fill in the fields to see your result.
How it works
Diluting a solution adds solvent but not solute — the amount of dissolved substance stays the same before and after. Since amount equals concentration times volume, C1×V1 (before) must equal C2×V2 (after), which is the whole basis of the calculation.
The most common question is "how much stock do I measure out?" — that solves for V1 given the stock concentration, the target concentration and the final volume you want to make.
Formulas used
Dilution equation
C1 × V1 = C2 × V2
- C1
- Stock (starting) concentration
- V1
- Stock volume taken
- C2
- Target (final) concentration
- V2
- Final total volume
Worked examples
Checking the result of diluting 10 mL of stock to 200 mL
If the stock is 5 M, the resulting concentration is C2 = (5 × 10) / 200 = 0.25 M.
Assumptions and limits
- The solute amount is conserved — nothing is added or removed except solvent.
- Concentration and volume units are whatever you entered, as long as they are consistent across C1/C2 and V1/V2 respectively.
- Mixing volumes are assumed additive (no significant volume change on mixing), which is accurate for dilute aqueous solutions.
Frequently asked questions
How much solvent do I actually add?
Not V2 itself — you add V2 − V1, because the stock volume V1 you measure out already contributes to the final volume. Measure V1 of stock into your container, then add solvent up to the V2 mark, rather than adding a full V2 of solvent on top of V1.
Does this work for serial dilutions?
Yes, one step at a time: solve for V1 in the first dilution, then use its result (the new C2) as the C1 of the next dilution step, and so on.
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