What the dilution equation does
Diluting a solution means adding solvent so that the same amount of solute is spread through a larger volume. The amount of solute does not change, only its concentration does. That conservation of moles is captured by the dilution equation C1V1 = C2V2, which is used daily in teaching labs, cell culture, and any workflow that starts from a concentrated stock.
This calculator takes the stock concentration, the volume of stock you take, and the concentration you want, and returns the total final volume. It also reports the solvent to add, which is the final volume minus the stock volume. If you instead know the final volume you need, rearrange the equation to V1 = C2V2 / C1 to get the stock volume, then check it by entering that volume here.
Formula and variables
V2 = C1 × V1 / C2
- C1 is the initial (stock) concentration in mol/L. Any concentration unit works if C2 uses the same one.
- V1 is the volume of stock, entered in mL.
- C2 is the desired final concentration.
- V2 is the final total volume in mL. The dilution factor is C1/C2 or equivalently V2/V1.
Worked example
You have a 2.0 M stock and take 25 mL of it. You want a 0.50 M solution.
- V2 = (2.0 × 25) / 0.50 = 50 / 0.50 = 100 mL.
- Solvent to add = 100 − 25 = 75 mL.
- Dilution factor = 2.0 / 0.50 = 4, so the stock is diluted 1 part in 4.
The calculator shows “Final Volume: 100.00 mL” and “Solvent to add: 75.00 mL”. In the reverse case, to make 250 mL of 0.10 M from a 5.0 M stock you need V1 = 0.10 × 250 / 5.0 = 5.0 mL; entering 5, 5 and 0.1 returns 250 mL.
Common mistakes and how to interpret the result
- Adding the stock to a fixed volume of solvent. Solvent to add is V2 − V1 only when volumes are additive; in practice, dilute to the mark in a volumetric flask.
- Mixing units. C1 and C2 must share a unit, and V1 is read here as mL.
- Entering a target higher than the stock. The result then implies a smaller volume, and the tool warns you because that is a concentration step, not a dilution.
- Forgetting safety order. When diluting concentrated acids, add the acid slowly to water, never the reverse.