Dilution Calculator (C1V1 = C2V2)

Dilution Calculator tells you how to make a weaker solution from a stronger stock. When you add solvent, the amount of dissolved substance stays the same, so the stock concentration times the volume of stock you take equals the final concentration times the final volume. Enter any three of those four and the fourth is worked out, with the working shown, and the page writes the result as a recipe: take this much stock, add this much solvent, to make this much — a one-in-so-many dilution. Concentrations can be molar (M, mM, µM, nM) or mass per volume (g/L, mg/mL, mg/L, µg/mL and % w/v); both concentrations always use the same kind, and you can mix units within it, such as a 1 M stock diluted to 50 mM. The page opens with 1 M stock diluted to 200 mL at 50 mM: 10 mL of stock and 190 mL of water.

1. Choose whether your concentrations are molar or mass per volume.
2. Fill in three of the four values with their units — usually the stock concentration, the final concentration and the final volume.
3. Leave the fourth empty; it is worked out and highlighted.
4. Follow the recipe under the answer: measure the stock, then make it up to the final volume with solvent.

• The solvent to add assumes volumes simply add up, which is close enough for dilute water solutions. For concentrated acids, alcohols or other mixtures that shrink or swell when mixed, make the solution up to the final volume in a volumetric flask instead.
• When diluting concentrated acids, add the acid slowly to the water, never water to the acid.
• Both concentrations must be the same kind. To go from a mass concentration to a molar one, use the molarity calculator with the compound’s molar mass.
• Diluting can only lower a concentration: the page refuses a final concentration higher than the stock, or a stock volume bigger than the final volume.
• For a serial dilution, run the calculation once per step, using each step’s result as the next stock.
• The calculation runs in your browser. Nothing you enter is sent or saved.

That is a 1 in 10 dilution. For 50 mL of 100 mM, take 5 mL of the 1 M stock and add 45 mL of solvent. Enter 1 M, 100 mM and 50 mL here to check.

Concentration times volume is the amount of solute. Diluting adds only solvent, so the amount before (C1 × V1) equals the amount after (C2 × V2).

Choose mass per volume and % w/v. For 500 mL, take 45 mL of the 10% stock and make it up to 500 mL — 455 mL of water.

How many times weaker the final solution is: the final volume divided by the stock volume. A 1 in 20 dilution is one part stock in twenty parts total, not twenty parts water.