How much stock for this dilution?
Enter any three of the stock concentration, stock volume, final concentration and final volume. The calculator finds the fourth and tells you how much solvent to add.
- Stock volume (V₁)
- 10 mL
To make 100 mL at 0.1 from a stock at 1, use 10 mL of stock.
- Solvent to add
- 90 mL
- Dilution factor
- 10
Stock volume (V₁): 10 mL. To make 100 mL at 0.1 from a stock at 1, use 10 mL of stock.
How to calculate
Solves the dilution equation C₁V₁ = C₂V₂ for the stock volume, the final volume or either concentration, and gives the solvent to add and the dilution factor.
Example with the default inputs (Stock concentration (C₁) 1, Final concentration (C₂) 0.1, Final volume (V₂) 100 mL): To make 100 mL at 0.1 from a stock at 1, use 10 mL of stock.
Formula: C₁ × V₁ = C₂ × V₂; solvent to add = V₂ − V₁; dilution factor = C₁ ÷ C₂ = V₂ ÷ V₁.
- Both concentrations use the same unit (mol/L, mmol/L, % or mg/mL). The volumes may be in any units.
- Only solvent is added, so the amount of solute does not change.
- Volumes add up: the final volume is the stock volume plus the solvent volume. For mixtures such as alcohol and water this is only approximate.
Worked examples
Each example is checked against the calculator on every build.
- Stock concentration (C₁) 1, Final concentration (C₂) 0.1, Final volume (V₂) 100 mL gives Stock volume (V₁) 10 mL, Solvent to add 90 mL, Dilution factor 10.Source: hand calculation in content.mdx: V₁ = 0.1 × 100 ÷ 1 = 10 mL; solvent = 100 − 10 = 90 mL; factor = 1 ÷ 0.1 = 10
- Stock concentration (C₁) 12, Stock volume (V₁) 25 mL, Final volume (V₂) 250 mL gives Final concentration (C₂) 1.2, Dilution factor 10.Source: hand calculation in content.mdx: C₂ = 12 × 25 ÷ 250 = 1.2 M
- Stock concentration (C₁) 70, Stock volume (V₁) 100 mL, Final concentration (C₂) 25 gives Final volume (V₂) 280 mL, Solvent to add 180 mL, Dilution factor 2.8.Source: hand calculation in content.mdx: V₂ = 70 × 100 ÷ 25 = 280 mL; solvent = 280 − 100 = 180 mL
How it works
Diluting adds solvent but no solute. The amount of solute, concentration × volume, is the same before and after:
- C₁ × V₁ = C₂ × V₂
Rearranged for each value:
- V₁ = C₂ × V₂ ÷ C₁
- V₂ = C₁ × V₁ ÷ C₂
- C₁ = C₂ × V₂ ÷ V₁
- C₂ = C₁ × V₁ ÷ V₂
C₁ and C₂ must be in the same unit; the unit then cancels. Volumes are converted to liters first (1 mL = 0.001 L, 1 US fluid ounce = 29.5735295625 mL, 1 US gallon = 3.785411784 L).
The calculator also gives:
- solvent to add = V₂ − V₁, shown only when V₂ is larger than V₁. When V₂ equals V₁ there is nothing to add, and when V₂ is smaller the final solution is stronger than the stock, which is not a dilution.
- dilution factor = C₁ ÷ C₂ = V₂ ÷ V₁.
Assumptions
- Both concentrations are in the same unit, and all values are above zero.
- The volumes of stock and solvent add up to the final volume. This is exact enough for dilute water solutions; for alcohol and water, fill up to the final volume instead of adding a measured volume of solvent.
Worked examples by hand
100 mL of 0.1 M from a 1 M stock. V₁ = 0.1 × 100 ÷ 1 = 10 mL. Solvent = 100 − 10 = 90 mL. Dilution factor = 1 ÷ 0.1 = 10.
25 mL of 12 M hydrochloric acid made up to 250 mL. C₂ = 12 × 25 ÷ 250 = 1.2 M. Dilution factor = 12 ÷ 1.2 = 10.
100 mL of 70% alcohol diluted to 25%. V₂ = 70 × 100 ÷ 25 = 280 mL. Solvent = 280 − 100 = 180 mL. Dilution factor = 70 ÷ 25 = 2.8.
Other questions people ask
What is the dilution formula?
C₁ × V₁ = C₂ × V₂. C₁ and V₁ are the concentration and volume of the stock solution, and C₂ and V₂ are the concentration and volume after diluting. Adding solvent does not change the amount of solute, so concentration times volume stays the same.
How much stock solution do I need?
V₁ = C₂ × V₂ ÷ C₁. For 100 mL of 0.1 M from a 1 M stock: 0.1 × 100 ÷ 1 = 10 mL of stock, then add 90 mL of solvent.
What units can I use?
Any concentration unit, as long as C₁ and C₂ are in the same one: mol/L, mmol/L, percent, or mg/mL. The volumes may be in different units; the calculator converts them.
What is a dilution factor?
How many times the solution is diluted: C₁ ÷ C₂, which equals V₂ ÷ V₁. Diluting 10 mL of stock to 100 mL is a 10-fold dilution, often written 1:10.
How do I dilute an acid safely?
Add the acid slowly to the water, never water to acid, and wear eye protection. The mixing gives off heat, and water added to concentrated acid can boil and spatter.