Dilution formula
The dilution equation is C1·V1 = C2·V2, where C is concentration and V is volume. Solving for the final volume gives V2 = C1·V1 ÷ C2. To check the resulting molarity, use the molarity calculator.
The logic behind it is conservation of solute: adding solvent changes the volume but not the number of moles already dissolved. Since moles equal concentration times volume, that product must be identical before and after, which is exactly what C1·V1 = C2·V2 states.
How to use this calculator
Enter the stock concentration (C1) and stock volume (V1), then the target concentration (C2). The calculator returns the final total volume V2 and how much solvent to add. Keep C1 and C2 in the same units. For mass-based dilutions see the mass percent calculator.
The most common bench mistake is treating V2 as the volume of solvent rather than the total final volume. Always dilute to V2, not with V2 — add the stock to a flask and top up to the mark.
Worked example
To dilute 50 mL of 2 M HCl down to 0.5 M: V2 = (2 × 50) ÷ 0.5 = 200 mL. So you add 150 mL of water to the original 50 mL.
Note the dilution factor here is 4, matching the drop from 2 M to 0.5 M and the rise from 50 mL to 200 mL. With concentrated acids, add the acid to water rather than the reverse. Very dilute solutions are easier to describe in parts per million than in molarity.
Frequently asked questions
- What is C1V1 = C2V2?
- It is the dilution equation: the moles of solute stay constant, so initial concentration × volume equals final concentration × volume.
- What units should I use?
- Concentrations must match each other (e.g. both in M), and the volume answer comes out in the same unit as V1.
- How much solvent do I add?
- Subtract the stock volume V1 from the final volume V2; the difference is the solvent to add.
- Why must C2 not be zero?
- Dividing by a target concentration of zero is undefined — a zero-concentration solution would need infinite volume.
- Can I use this for percent or mg/mL concentrations?
- Yes, as long as both C1 and C2 use the same unit. The equation only requires that concentration be proportional to the amount of solute per volume, so %w/v, mg/mL and ppm all work — just never mix two different concentration units in one calculation.