Dilution Calculator (M1V1 = M2V2)

Kaava

How this is calculated

The dilution equation states that the moles of solute are conserved when you dilute a solution: the concentration times the volume of the stock (C1 × V1) equals the concentration times the volume of the final, diluted solution (C2 × V2). Choose which of the four quantities is unknown, then enter the remaining three. The calculator rearranges the equation to solve for the missing value — for example V1 = C2 × V2 / C1 to find how much stock you need, or C2 = C1 × V1 / V2 to find the resulting concentration.

Concentrations are entered in molarity (M) and volumes in millilitres (mL), but any consistent pair of units works because the relationship is a ratio: as long as both concentrations share one unit and both volumes share another, the result is correct. The "solvent to add" value is V2 − V1, the amount of pure solvent (such as water) you mix into the stock aliquot to reach the final volume. The dilution factor C1 / C2 tells you how many times more concentrated the stock is than the final solution.

The equation assumes volumes are additive and that temperature and any volume-change-on-mixing effects are negligible — good approximations for dilute aqueous solutions. Division by zero is guarded: solving for V1 requires a non-zero C1, solving for C1 requires a non-zero V1, and so on. A negative "solvent to add" means the requested final volume is smaller than the stock aliquot, which is not a true dilution.