What Is a Dilution Calculator?
A dilution calculator uses the relationship C₁V₁ = C₂V₂ to figure out how a stock (concentrated) solution relates to a diluted solution. Because the total amount of solute doesn't change when you add solvent, the concentration multiplied by the volume stays constant before and after dilution. Enter any three of the four values and this tool solves for the fourth.
How to Use the Dilution Calculator
- Choose which value you want to solve for: C₁, V₁, C₂, or V₂.
- Pick a consistent concentration unit (used for both C₁ and C₂) and volume unit (used for both V₁ and V₂).
- Enter the three known values.
- Read the result, along with the formula shown with your numbers plugged in.
The Dilution Formula (M1V1 = M2V2)
This formula works regardless of which concentration unit you use — molarity (mol/L), mg/mL, percent (%), or any other consistent unit — as long as C₁ and C₂ share the same unit, and V₁ and V₂ share the same unit.
Worked Example
You have 10 mL of a 5 mol/L stock solution (C₁ = 5 mol/L, V₁ = 10 mL) and want to dilute it down to a final concentration of 1 mol/L (C₂ = 1 mol/L).
Rearranging: V₂ = (C₁ × V₁) ÷ C₂ = (5 × 10) ÷ 1 = 50 mL
You need a final total volume of 50 mL — so add 40 mL of solvent to your 10 mL of stock solution.
Understanding Serial Dilution
A serial dilution repeats this same process multiple times in a row, using the output of one dilution step as the input (C₁, V₁) for the next. Serial dilutions are common in microbiology, chemistry, and pharmacology when you need to reach a very low final concentration that would be hard to measure accurately in a single step.
Common Mistakes to Avoid
- Mixing units — e.g., entering C₁ in mol/L and C₂ in mmol/L will give a wrong answer, since the formula assumes matching units on each side.
- Confusing "volume of solvent added" with "final total volume" — V₂ in this formula is the total volume of the diluted solution, not just the amount of solvent added.
- Forgetting that this formula only works for simple dilution (adding solvent), not for reactions that consume or produce solute.
Frequently Asked Questions
It's the dilution equation stating that concentration multiplied by volume before dilution equals concentration multiplied by volume after dilution, since the total moles (or mass) of solute doesn't change — only the volume of solvent does.
Yes — it works with molarity, mg/mL, percent concentration, or any other consistent unit, as long as C₁ and C₂ are expressed in the same unit as each other, and V₁ and V₂ are expressed in the same unit as each other.
Preparing reagents from concentrated stock solutions, diluting samples for spectrophotometry, preparing standard curves, and performing serial dilutions in microbiology for colony counting are all common lab applications.
Dilution decreases concentration by adding solvent (increasing volume without adding more solute), while concentrating a solution increases its concentration, typically by removing solvent (for example through evaporation) or adding more solute.
Yes — calculate one dilution step at a time, then use the resulting C₂ and V₂ from one step as the C₁ and V₁ for the next step in your dilution series.