What is the dilution equation?

The dilution equation is C1 × V1 = C2 × V2, where C1 and V1 are the stock concentration and volume, and C2 and V2 are the final concentration and volume after dilution.

How do I work out the stock volume needed?

Rearrange to V1 = (C2 × V2) ÷ C1. For example, to make 100 mL of 2 M from a 10 M stock, V1 = (2 × 100) ÷ 10 = 20 mL of stock, topped up to 100 mL.

What units should I use?

Any units work as long as they match on both sides — use the same concentration unit (M, %, mg/mL) and the same volume unit (mL or L) throughout.

How much solvent do I add?

Solvent to add equals the final volume minus the stock volume (V2 − V1). The tool shows this automatically when you solve for a volume.

Why does the solute amount stay constant?

Diluting only adds solvent — you do not add or remove solute. Concentration × volume equals the total amount of solute, so that product is the same before and after, which is exactly what C1V1 = C2V2 states.

What is a dilution factor?

It is the ratio of final volume to stock volume, V2 ÷ V1, or equivalently C1 ÷ C2. A 1:10 dilution factor means one part stock to nine parts solvent, reducing the concentration tenfold.

Is this suitable for serial dilutions?

Yes — apply the equation one step at a time. Each step's diluted solution becomes the stock for the next, so you can chain calculations to reach very low concentrations accurately.

Dilution Calculator (C1V1 = C2V2)

Dilution calculator

When you dilute a concentrated stock solution, the amount of solute stays the same, so C1 × V1 = C2 × V2. This calculator relates the stock concentration and volume (C1, V1) to the diluted final concentration and volume (C2, V2), for lab work, chemistry classes and preparing solutions.

How it works

Because diluting only adds solvent, the total amount of solute is unchanged, giving the dilution equation. The tool rearranges it to solve for whichever value you leave blank:

Solve for	Formula
Stock concentration C1	C1 = (C2 × V2) ÷ V1
Stock volume V1	V1 = (C2 × V2) ÷ C1
Final concentration C2	C2 = (C1 × V1) ÷ V2
Final volume V2	V2 = (C1 × V1) ÷ C2

Keep units consistent on both sides — same concentration unit (M, %, mg/mL) and same volume unit (mL or L). When you solve for a volume, it also shows the solvent to add = V2 − V1.

Example

Make 100 mL of a 2 M solution from a 10 M stock, solving for V1:

V1 = (2 × 100) ÷ 10 = 20 mL of stock

Then add 100 − 20 = 80 mL of solvent to reach 100 mL total. All in your browser, nothing uploaded.