Dilution Calculator (M1V1 = M2V2)
Use the dilution equation M1V1 = M2V2 to find a missing concentration or volume when preparing a diluted solution from a stock.
Solve for
M
M
mL
Solved from M1V1 = M2V2
- 1
Preserved moles: C2 × V2
2 M × 100 mL = 200 - 2
V1 = (C2 × V2) ÷ C1
200 ÷ 10 M = 20
How does this calculator work?
Apply M1V1 = M2V2 to dilutions. Pick the unknown — stock concentration, stock volume, final concentration, or final volume — enter the other three, and the calculator solves for it. It also reports the solvent to add (V2 − V1) and the dilution factor (C1 / C2) so you can prepare the solution accurately.
Formula
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.
Frequently asked questions
It is the dilution equation: the concentration and volume of the concentrated stock (M1, V1) multiply to the same value as the concentration and volume of the diluted solution (M2, V2), because the amount of solute stays constant.
Add V2 − V1 of solvent. Measure out V1 of stock, then add solvent until the total volume reaches V2. This calculator reports that difference directly.
Yes. The equation is a ratio, so any concentration unit (M, mg/mL, %) works as long as both concentrations match, and any volume unit works as long as both volumes match.
Also known as
TG we-Calculate Editorial Team. (2026). Dilution Calculator (M1V1 = M2V2) [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/dilution-calculator
TG we-Calculate Editorial Team. "Dilution Calculator (M1V1 = M2V2)." TG we-Calculate. 2026. https://we-calculate.com/calculator/dilution-calculator.
TG we-Calculate Editorial Team, "Dilution Calculator (M1V1 = M2V2)," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/dilution-calculator
@misc{wecalculate_dilution_calculator, title = {Dilution Calculator (M1V1 = M2V2)}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/dilution-calculator}}, year = {2026}, note = {TG we-Calculate} }
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