Dilution Calculator
Diluting a stock solution to a target concentration uses one of the most useful equations in the lab. Enter any three values and this calculator returns the fourth.
Formula
C₁V₁ = C₂V₂
- C₁, V₁ = concentration and volume of the stock
- C₂, V₂ = concentration and volume you want
- Units only need to match on each side
500 mL of 0.1 M from 2 M stock: V₁ = (0.1 × 500) ÷ 2 = 25 mL
The Dilution Equation
C₁V₁ = C₂V₂
Where C₁ and V₁ are the concentration and volume of stock, and C₂ and V₂ those of the final solution.
To make 500 mL of 0.5 M from a 5 M stock: V₁ = (0.5 × 500) ÷ 5 = 50 mL of stock, made up to 500 mL.
The equation works because the quantity of solute does not change — only the volume it occupies.
Make Up To, Not Add To
In that example you add 450 mL of diluent, but the reliable instruction is "make up to 500 mL" rather than "add 450 mL".
Mixing volumes is not always additive: 50 mL of ethanol plus 50 mL of water gives slightly less than 100 mL, because the molecules pack together more closely. For accuracy, dilute to a mark in a volumetric flask.
Serial Dilution and the Acid Rule
Very large dilution factors are unreliable in one step, because measuring a tiny stock volume accurately is hard. A 1:1,000,000 dilution is far better done as three successive 1:100 steps.
Safety: when diluting concentrated acids, always add acid to water, never the reverse. The reaction is strongly exothermic, and adding water to concentrated acid can boil it and spit.
Quick Reference
| Stock | Target | Stock volume | Dilution |
|---|---|---|---|
| 1 M | 0.1 M | 50 mL | 1:10 |
| 2 M | 0.1 M | 25 mL | 1:20 |
| 5 M | 0.5 M | 50 mL | 1:10 |
| 10 M | 1 M | 50 mL | 1:10 |
| 10 M | 0.1 M | 5 mL | 1:100 |
Frequently Asked Questions
- How do I dilute a stock solution?
- Use C1V1 = C2V2. For 500 mL of 0.5 M from 5 M stock, take 50 mL of stock and make it up to 500 mL.
- Should I add acid to water or water to acid?
- Always acid to water. Dilution is strongly exothermic, and adding water to concentrated acid can cause it to boil and spit dangerously.
- Why "make up to" rather than "add"?
- Because volumes are not always additive when liquids mix. Diluting to a mark in a volumetric flask gives the correct final concentration.
- What is serial dilution?
- Reaching a very large dilution factor through several smaller steps. It is far more accurate than trying to measure a minute volume of stock in one go.