Dilution Calculator (C1V1 = C2V2)
Free dilution calculator solves C1V1 = C2V2 for stock volume, final volume or concentration. Find how much stock and diluent to mix, with the formula shown.
Updated 2026-06-14 · Free · No sign-up · Runs privately in your browser
Show the formula & steps
How the Dilution Calculator Works
This calculator uses the fundamental dilution equation to find any one of the four variables when you know the other three. Pick what you want to solve for — stock volume, final volume, or either concentration — enter the known values, and it returns the answer plus the amount of diluent (solvent) you need to add.
The Formula
The dilution equation expresses conservation of solute:
C1 × V1 = C2 × V2
Where:
- C1 = concentration of the stock (starting) solution
- V1 = volume of stock solution used
- C2 = concentration of the final (diluted) solution
- V2 = total volume of the final solution
The most common task is finding the stock volume:
V1 = (C2 × V2) ÷ C1
The amount of solvent to add is simply the difference:
Diluent = V2 − V1
Concentrations can be in molarity, percent, or mass-per-volume, as long as C1 and C2 use the same unit and V1 and V2 use the same unit.
Worked Example
You have a 10 M stock acid and need 100 mL of a 1 M solution:
- V1 = (C2 × V2) ÷ C1 = (1 × 100) ÷ 10 = 10 mL of stock
- Diluent = V2 − V1 = 100 − 10 = 90 mL of solvent
So you measure 10 mL of the 10 M stock and add 90 mL of water (or buffer) to reach 100 mL of 1 M solution.
Common Dilutions
| Stock (C1) | Final (C2) | Final volume (V2) | Stock to use (V1) | Diluent |
|---|---|---|---|---|
| 10 M | 1 M | 100 mL | 10 mL | 90 mL |
| 100% | 70% | 500 mL | 350 mL | 150 mL |
| 5 mg/mL | 0.5 mg/mL | 10 mL | 1 mL | 9 mL |
| 2 M | 0.1 M | 250 mL | 12.5 mL | 237.5 mL |
Tips for Accurate Dilutions
- Add stock to diluent, not the other way around, when working with strong acids to control the exothermic reaction.
- For serial dilutions, treat each diluted solution as the stock for the next step and repeat the calculation.
- Always verify your units match before mixing. A mismatch between mL and L is the most common dilution error.
Frequently asked questions
What is the dilution formula C1V1 = C2V2?+
It states that the amount of solute is conserved during dilution. C1 is the stock (starting) concentration, V1 is the stock volume used, C2 is the final concentration and V2 is the final volume. Because solute does not disappear, C1 × V1 always equals C2 × V2.
How do I find how much stock solution to use?+
Rearrange the equation to V1 = (C2 × V2) / C1. For example, to make 100 mL of 1 M solution from a 10 M stock, V1 = (1 × 100) / 10 = 10 mL of stock, topped up with 90 mL of solvent.
How much diluent (water) do I add?+
The diluent volume is the final volume minus the stock volume: V2 − V1. In the example above you add 100 − 10 = 90 mL of solvent to the 10 mL of stock to reach 100 mL total.
Do the concentration units have to match?+
Yes. C1 and C2 must use the same unit (both molarity, both percent, or both mg/mL), and V1 and V2 must share a unit. As long as each pair is consistent, the equation gives the correct answer regardless of which units you choose.
Can this calculator do serial dilutions?+
Each step of a serial dilution is one C1V1 = C2V2 calculation. Solve for the stock volume of the first step, then treat that diluted solution as the new stock for the next step and repeat to build a dilution series.