What is the C₁V₁ = C₂V₂ equation?

It states that the amount of solute is conserved during dilution. The concentration of the stock times its volume equals the concentration of the final solution times its volume, so you can solve for any one unknown if you know the other three.

Which units should I use?

Any units, as long as the two concentrations share a unit and the two volumes share a unit. If C₁ and C₂ are both in molar and V₂ is in millilitres, the V₁ result comes out in millilitres. The tool does not assume units.

How much diluent do I add?

You add diluent equal to the final volume minus the stock volume, V₂ minus V₁. Measure out the stock volume first, then top up to the final volume — do not simply add V₂ of diluent, which would over-dilute.

What is the dilution factor?

The dilution factor is C₁ divided by C₂, the ratio of stock to final concentration. A factor of 5 means a 1-in-5 dilution: one part stock to four parts diluent, giving a fifth of the original concentration.

Can I use this for serial dilutions?

Yes, one step at a time. Compute each step's stock volume against the next target concentration, then use that diluted solution as the stock for the following step. The same equation applies at every stage of a serial dilution.

Dilution Calculator (C₁V₁ = C₂V₂)

The dilution equation C₁V₁ = C₂V₂ is the workhorse of any lab that prepares solutions. It captures the simple fact that diluting a solution does not change the amount of solute present. This calculator solves for whichever variable you leave blank and tells you how much diluent to add, all in your browser.

How it works

Because the mass of solute is conserved, the product of concentration and volume is the same before and after dilution. Rearranging for each unknown:

V1 = (C2 × V2) / C1
C1 = (C2 × V2) / V1
C2 = (C1 × V1) / V2
V2 = (C1 × V1) / C2

Fill in three values, leave one blank, and the tool picks the right rearrangement. It also reports the dilution factor (C₁ ÷ C₂) and the diluent volume to add (V₂ − V₁) whenever both volumes are known or solved.

Example and tips

To make 50 mL of a 2 M solution from a 10 M stock, leave V₁ blank: the tool computes V1 = (2 × 50) / 10 = 10 mL of stock, a 5× dilution, with 40 mL of diluent added. The single most common mistake is adding the full final volume of diluent to the stock — always measure the stock first and then bring the total up to V₂. Keep your concentration units matched and your volume units matched, and the answer carries those same units.