Dilution Calculations: C1V1 = C2V2 and When to Use It

The Formula

C1V1 = C2V2. That is it. Four variables, one equation, and it covers virtually every dilution problem in chemistry, biology, cleaning, pool maintenance, and agriculture.

C1 is the initial concentration of your stock solution. V1 is the volume of stock you need to measure out. C2 is the target concentration you want to end up with. V2 is the total final volume of your diluted solution.

The equation works because dilution does not create or destroy solute — it only adds solvent (usually water). The total amount of dissolved substance stays the same. Concentration × volume before = concentration × volume after.

Our dilution calculator solves for whichever variable you leave blank. Enter three, get the fourth.

Example 1: Lab Solution Prep

You have a stock solution of hydrochloric acid at 12 M (moles per liter) and need 500 mL of 1 M HCl for an experiment.

C1 = 12 M. C2 = 1 M. V2 = 500 mL. Solve for V1:

V1 = (C2 × V2) / C1 = (1 × 500) / 12 = 41.7 mL

Measure out 41.7 mL of the 12 M stock, pour it into a volumetric flask, and add water to the 500 mL line. You now have 500 mL of 1 M HCl. The molar mass calculator can help if you need to convert between molarity and grams per liter.

Example 2: Cleaning Product Dilution

A commercial cleaning concentrate says to dilute 1:10 for general cleaning. The bottle is 32 oz. How much cleaning solution can you make from the whole bottle?

A 1:10 ratio means 1 part concentrate to 10 parts total (not 1 to 10 added). So C1/C2 = 10. V1 = 32 oz. V2 = V1 × (C1/C2) = 32 × 10 = 320 oz of total solution. That is 2.5 gallons from one 32 oz bottle.

Example 3: Pool Chlorine

Your pool holds 15,000 gallons and you need 3 ppm free chlorine. Liquid chlorine (sodium hypochlorite) from the pool store is typically 12.5% concentration (about 125,000 ppm).

C1 = 125,000 ppm. C2 = 3 ppm. V2 = 15,000 gallons. Solve for V1:

V1 = (3 × 15,000) / 125,000 = 0.36 gallons = about 46 fluid ounces.

That is how much 12.5% liquid chlorine to add to bring a clean pool from zero to 3 ppm. Real pools have existing chlorine levels, organic demand, and sunlight degradation, so actual dosing needs testing and adjustment. But the dilution math is the starting point.

Common Mistakes

Mixing up V1 and V2. V2 is the total final volume, not the amount of solvent you add. If V2 is 500 mL and V1 is 41.7 mL, you add 458.3 mL of water to the stock — not 500 mL. In precise lab work, you pour the stock into the flask first, then add solvent up to the target volume mark.

Using mismatched units. C1 and C2 must be in the same concentration units (both molarity, both percent, both ppm). V1 and V2 must be in the same volume units (both mL, both liters, both gallons). Mix them and the answer is garbage.

Assuming it works for mixing two solutions. C1V1 = C2V2 only applies when you are diluting a concentrated solution with pure solvent. If you are mixing two solutions of different concentrations, you need a different equation: C1V1 + C2V2 = C3V3, where C3 and V3 are the resulting concentration and total volume.

When pH Gets Involved

Diluting acids and bases changes pH, but not linearly. Diluting a pH 2 acid by 10x gives pH 3, not pH 2.1. This is because pH is logarithmic — each unit represents a tenfold change in hydrogen ion concentration. The pH calculator converts between pH and concentration so you can see how dilution affects acidity.

Tools

The dilution calculator solves C1V1 = C2V2 for any variable. For converting between concentration formats (molarity vs grams per liter), the molar mass calculator gives you the molecular weight you need for the conversion. And for understanding what’s actually dissolving in your solution at the atomic level, start with the periodic table.