Dilution Calculator
How much stock do you need, or how concentrated is it after topping up? Solve C₁V₁ = C₂V₂ for any one value, in any volume or concentration unit.
C₁V₁ = C₂V₂
Solve for
V₁
Stock volume to take
mL
1 sig figs: 20
≡
Same value in
20,830 µL · 2.083 × 10⁻⁵ m³ · 20.83 cm³
- Rearrange: V₁ = C₂V₂ ÷ C₁
- Substitute: C₁ = 12 M, C₂ = 1 M, V₂ = 250 mL (converted to SI units first).
- Result: V₁ = 20.8333 mL, rounded to 1 significant figures because the least precise input has 1.
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0/1500
Why C₁V₁ = C₂V₂ works
Moles of solute = concentration × volume. Adding water increases the volume but adds no solute, so the product C × V is the same before and after. Set them equal and solve for the unknown.
Making the dilution
- Calculate V₁, the volume of stock to take.
- Measure it with a pipette or measuring cylinder into a volumetric flask of volume V₂.
- Add solvent to the mark, stopper and invert to mix. For concentrated acids, put some water in the flask first.
Frequently asked questions
What is the dilution formula?
C₁V₁ = C₂V₂. The number of moles of solute does not change when you add solvent, so concentration × volume before equals concentration × volume after.
How do I dilute 12 M HCl to 1 M?
For 250 mL of 1.0 M: V₁ = 1.0 × 250 ÷ 12 = 20.8 mL of stock, made up to 250 mL with water. Always add acid to water, not water to acid.
Can I use mL instead of litres?
Yes, as long as V₁ and V₂ use the same unit (and C₁, C₂ the same unit). The ratio is what matters. The unit menus here convert anything automatically.
What is a dilution factor?
The ratio V₂ ÷ V₁ (or C₁ ÷ C₂). Taking 1 mL and making it up to 10 mL is a 1:10 dilution, dilution factor 10.
How do serial dilutions work?
Repeat the same dilution several times. Three 1:10 steps give 1:1000 overall; multiply the factors. Each step is one C₁V₁ = C₂V₂ calculation.