The dilution equation
C₁ × V₁ = C₂ × V₂
Rearrange to find any one value: V₁ = C₂V₂ ÷ C₁, C₂ = C₁V₁ ÷ V₂, and so on.
Example
You have a 2 M stock solution and need 200 mL of 0.5 M.
- V₁ = (0.5 × 200) ÷ 2 = 50 mL of stock
- Water to add: 200 − 50 = 150 mL
- Dilution factor: 200 ÷ 50 = 4 (a 1:4 dilution)
Serial dilutions
For very weak solutions, dilute in steps. Three 1:10 dilutions in a row give a total dilution of 1:1,000, which is easier and more accurate than measuring a tiny amount of stock into a huge volume.
Everyday dilutions
The same math works for mixing cleaning concentrates, plant fertilizer or drink syrups: if a label says "dilute 1:4", mix 1 part concentrate with 3 parts water. Always follow product safety directions.
Making a solution from a solid instead? Use the molarity calculator.
Last reviewed October 2026.
Frequently asked questions
What is the dilution formula?
C₁V₁ = C₂V₂. The amount of solute stays the same when you add solvent, so the starting concentration times the starting volume equals the final concentration times the final volume.
How much water do I add?
Subtract the stock volume from the final volume: water to add = V₂ − V₁. To make 200 mL of 0.5 M from a 2 M stock, take 50 mL of stock and add 150 mL of water.
Can I use percentages or other concentration units?
Yes, as long as C₁ and C₂ use the same unit. The formula works with molarity, percent, mg/mL, ppm or any other concentration, because the units cancel.
What is a dilution factor?
The dilution factor is the final volume divided by the stock volume, or the stock concentration divided by the final concentration. A 1:10 dilution (dilution factor 10) means 1 part stock to 9 parts solvent, 10 parts in total.
Why can't C₂ be higher than C₁?
Adding solvent can only make a solution weaker. If the target concentration is higher than the stock, you would need to add more solute or evaporate solvent instead.