The dilution formula (M₁V₁ = M₂V₂) is used to calculate how to prepare a less concentrated solution from a more concentrated stock solution. It's one of the most practical formulas in chemistry labs.
M₁V₁ = M₂V₂
Moles before = Moles after
Units: M or mol/L
The concentration of the concentrated stock solution
Units: L or mL (must match V₂)
Volume of concentrated solution needed
Units: M or mol/L
The desired concentration after dilution
Units: L or mL (must match V₁)
Total volume of diluted solution
V₁ = (M₂ × V₂) / M₁
Most common use case
M₂ = (M₁ × V₁) / V₂
Check dilution result
M₁V₁ = M₂V₂
(6.0 M)(V₁) = (1.5 M)(500 mL)
V₁ = (1.5 M × 500 mL) / 6.0 M = 125 mL
Answer: Take 125 mL of 6.0 M HCl and add water to make 500 mL total
⚠️ Always add acid to water, never water to acid!
V₁ and V₂ must be in the same units! Use both in mL or both in L.
V₂ is the TOTAL final volume, not the amount of water to add. Add water until you reach V₂.
M₁ is always the more concentrated solution. M₂ is always less concentrated.
M₁V₁ = M₂V₂, where M₁ and V₁ are the molarity and volume of the concentrated solution, and M₂ and V₂ are the molarity and volume of the diluted solution.
Yes! As long as V₁ and V₂ are in the same units. You can use mL, L, or any volume unit.
The number of moles of solute stays constant during dilution. Since n = M × V, and n₁ = n₂, then M₁V₁ = M₂V₂.