Dilution calculator: C1V1 = C2V2 with units

A C1V1 = C2V2 calculator that shows its work

Diluting a solution means adding solvent, usually water, to lower its concentration. This dilution calculator solves C1V1 = C2V2: enter any three values and it returns the fourth, plus the volume of solvent to add. It also works as a concentration calculator for 1:N ratios, serial dilutions, solutions weighed from a powder and cleaning products mixed in a sprayer. Every result comes with the calculation steps.

How to use it

1. Pick a calculation type: “C₁V₁ = C₂V₂”, “1:N ratio”, “Serial dilution”, “From a solid” or “Product to dilute”.
2. In “C₁V₁ = C₂V₂”, fill in three of “Stock concentration C₁”, “Volume to take V₁”, “Target concentration C₂” and “Final volume V₂”, each with its unit. The blank field is calculated.
3. Read the result and the “Calculation steps”. “Copy link” gives an address that reopens the same calculation.

Why C1V1 = C2V2 works

Dilution adds solvent, never solute. The amount of solute you pipette, C1 × V1, ends up entirely in the final solution, C2 × V2. Rearrange for whatever is missing: V1 = C2 × V2 ÷ C1, or C2 = C1 × V1 ÷ V2.

Example: 5 mL of a 10 mg/mL stock made up to 50 mL gives 10 × 5 ÷ 50 = 1 mg/mL, and you add 45 mL of solvent. The dilution factor is 10.

The calculator rejects a target concentration higher than the stock: diluting cannot make anything stronger.

Units and conversions

Both concentrations must be in the same unit, and both volumes too. The calculator converts for you: 1 mg/mL = 1 g/L = 1,000 ppm; 0.9% (w/v, 0.9 g per 100 mL) = 9 g/L; 250 mmol/L = 0.25 mol/L. Here ppm means mg per liter, which holds for dilute water-based solutions.

Going between mol/L and g/L needs the molar mass, so fill in “Molar mass in g/mol (optional)”. With it, 9 g/L of sodium chloride (58.44 g/mol) reads as 0.154 mol/L. The “× (times)” unit is for buffers labeled 10× or 5×: 50 mL of 1× from a 10× stock takes 5 mL.

The 1:N notation is ambiguous

“Dilute 1:10” has two readings. In most labs it means 1 part in 10 parts total: 100 mL of stock per 1 L of final solution, so 900 mL of diluent. On many cleaning product labels it means 1 part product to 10 parts water: 1 L of concentrate plus 10 L of water, 11 L in all. A janitorial “1:64” follows the second reading: 1,000 ÷ 64 = 15.6 mL of concentrate per liter of water. In “1:N ratio”, choose the convention and the known volume; the tool also shows how the same mix is written in the other convention.

Serial dilutions

To reach very low concentrations, labs repeat the same dilution several times, for plate counts in microbiology or a standard curve. With a factor of 10, five tubes and 1 mL per tube, you move 0.1 mL from tube to tube into 0.9 mL of diluent, giving 10⁻¹ to 10⁻⁵.

Making a solution from a solid

Mass to weigh = C × V × M. For 250 mL of 1 mol/L Tris base (121.14 g/mol): 1 × 0.25 × 121.14 = 30.285 g. If the chemical is only 99% pure, divide by 0.99. Dissolve in less water than the final volume, then top up to the mark.

Around the house and garden

“Product to dilute” starts from the label dose, in mL per liter, mL per 10 L or %. A cleaner dosed at 20 mL per liter needs 100 mL for a 5 L sprayer. Always follow the product label, never mix two household cleaners (bleach with ammonia or with acid cleaners releases toxic gas), wear gloves and add the product to the water.

FAQ

Does V2 include V1?

Yes. V2 is the total volume after dilution, so you add V2 − V1 of solvent, not V2.

What does “2%” mean on a label?

Usually 2 mL of product per 100 mL of water, or 20 mL per liter. That is how the “% (mL per 100 mL)” unit is read here.

How do I convert mol/L to g/L?

Multiply by the molar mass: 0.15 mol/L sodium chloride is 0.15 × 58.44 = 8.766 g/L.

Is my data sent anywhere?

No. The calculation runs in your browser, and your last values stay on your device.