The Dilution Formula Every Lab Uses (And How to Not Mess It Up)
C1V1 = C2V2 is one of the first formulas anyone learns in a wet lab, and also one of the most common sources of small, expensive mistakes ā a mislabeled stock concentration or a unit mismatch can throw off an entire experiment.
The formula, plainly
Where Cā and Vā are your stock (starting) concentration and volume, and Cā and Vā are your target (final) concentration and volume. Because the total amount of solute doesn't change when you dilute ā you're only adding solvent ā this equation always balances.
Where mistakes actually happen
- Unit mismatches ā mixing mM and M, or mL and L, in the same calculation without converting first
- Solving for the wrong variable ā confusing "volume of stock needed" with "volume of diluent to add" (they're different numbers ā diluent volume = Vā ā Vā)
- Serial dilution confusion ā treating a multi-step serial dilution as if it were one single dilution step
- Rounding stock concentration ā using a rounded label concentration (e.g., "10 mM" when the actual prepared stock was 9.8 mM) compounds error across a whole dilution series
| You know | Solving for | Rearranged formula |
|---|---|---|
| Cā, Cā, Vā | Vā (stock volume needed) | Vā = (Cā Ć Vā) / Cā |
| Cā, Vā, Vā | Cā (resulting concentration) | Cā = (Cā Ć Vā) / Vā |
| Cā, Vā, Cā | Vā (final volume) | Vā = (Cā Ć Vā) / Cā |
š” The step people forget
Once you know Vā (the volume of stock to use), the volume of diluent to add is Vā ā Vā, not Vā. A common error is adding the full target volume of diluent on top of the stock volume, overshooting the intended final volume.
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