C₁V₁ = C₂V₂ Dilution Calculator
Calculate the volume or concentration required to dilute a stock solution. Support for Molarity, mM, µM, and custom units.
Initial Solution (1)
Final Solution (2)
Understanding Dilutions
Make perfect lab solutions every time by understanding the core concepts of concentration.
Conservation of Mass
The C₁V₁ = C₂V₂ formula relies on the fact that adding solvent (like water) does not change the total number of moles of solute present in the solution.
Stock Solutions
Buy or prepare concentrated "stock" solutions (C₁) to save space. When you need a working solution (C₂), simply measure out V₁ and add solvent until you reach V₂.
Serial Dilutions
For extremely low concentrations, it\'s more accurate to perform a series of step-wise dilutions (e.g., 1:10, then 1:10 again to reach 1:100) rather than a single massive dilution.
Frequently Asked Questions
What is the dilution formula?
The dilution formula is C₁V₁ = C₂V₂ where C₁ is the initial concentration, V₁ is the initial volume, C₂ is the final concentration, and V₂ is the final volume. It states that the total amount of solute remains constant when you dilute a solution with more solvent.
How do I use this calculator for a 10x stock solution?
If you have a 10x stock solution and you want 1000 mL of a 1x solution: Set C₁ to 10x, C₂ to 1x, and V₂ to 1000 mL. Keep V₁ blank. The calculator will tell you to use 100 mL of the 10x stock (and therefore add 900 mL of water).
Does it matter what units I use?
Our calculator automatically handles unit conversions! Just make sure you select the correct units from the dropdown menus (e.g. mM vs µM). Internally, it converts concentrations to a base unit (like M) and volumes to a base unit (like L) to perform the math accurately.
When should I use this calculator?
This is an essential lab tool used when preparing working solutions from concentrated stock solutions, diluting samples for spectrophotometry, or scaling down biological assays in chemistry, biology, and pharmacology.
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