Dilution Calculator
Choose the unknown — stock volume, stock concentration, final concentration or final volume — and enter the other three with their units. You get the answer, the working, the dilution factor and how much diluent to add. Free, no sign-up.
Results
41.7 mL
Stock volume (V₁)
12.0×
Dilution factor (C₁ ÷ C₂)
458 mL
Diluent to add (V₂ − V₁)
The working
C₁V₁ = C₂V₂
V₁ = C₂V₂ ÷ C₁
V₁ = (1.00 M × 500.0 mL) ÷ 12.0 M = 41.67 mL
Dilution factor = 12 ÷ 1 = 12.0
How to make it
Measure 41.7 mL of the stock solution and add 458 mL of diluent, for a final volume of 500 mL. That is 1 part stock to 11.0 parts diluent. For accurate work, put the stock in a volumetric flask and add diluent up to the mark rather than adding a measured volume of diluent; the two volumes do not always add exactly.
How to Use the Dilution Calculator
- 1. Pick the unknown. The usual question is the stock volume (V₁): how much concentrated solution to take. The other three terms can be solved for too.
- 2. Enter the three known terms with their units. Concentrations can be in molar units (M to nM), mass concentrations (g/L, mg/mL, µg/mL …), percent or fold (×). Volumes can be in µL, mL or L. The stock and final concentrations may use different units of the same kind, for example M and mM.
- 3. Read the answer. The calculator shows the working with your numbers, the dilution factor, and the volume of diluent to add.
- 4. Follow the recipe. It gives the volumes to measure out; for accurate work make up to the final volume in a volumetric flask.
The Dilution Equation
Equation
C₁ × V₁ = C₂ × V₂
Stock volume
V₁ = C₂ × V₂ / C₁
Dilution factor
DF = C₁ / C₂ = V₂ / V₁
Diluent to add
V₂ − V₁
C₁ and V₁ are the concentration and volume of the stock; C₂ and V₂ are those of the diluted solution. The equation works because diluting adds solvent but no solute, so the amount of solute — concentration times volume — is the same before and after. Any concentration unit will do provided C₁ and C₂ use the same one, and likewise for the volumes; the calculator converts for you within a kind of unit.
Worked Examples
Diluting concentrated acid (the default inputs). To make 500.0 mL of 1.00 M HCl from a 12.0 M stock: V₁ = (1.00 M × 500.0 mL) ÷ 12.0 M = 41.67 mL, so take 41.7 mL of the stock and add about 458 mL of water. The dilution factor is 12.0, or 1 part stock to 11.0 parts water.
Mixed units. How much 2.5 M NaCl stock is needed for 20.0 mL of 150 mM? Convert 150 mM to 0.150 M, then V₁ = (0.150 M × 20.0 mL) ÷ 2.5 M = 1.2 mL — the calculator does the conversion and prints it in the working.
Finding the new concentration. If 25.0 mL of 2.00 M sodium hydroxide is diluted to 100.0 mL, then C₂ = (2.00 M × 25.0 mL) ÷ 100.0 mL = 0.500 M.
Add acid to water, and make up to the mark
When diluting a concentrated acid or base, add the stock slowly to most of the water, never the reverse, because the mixing releases heat. For quantitative work, put the stock in a volumetric flask and fill to the calibration line rather than adding a measured volume of diluent: volumes are not always exactly additive, and the difference is noticeable for some mixtures such as ethanol and water.
Dilution Factor and Common Mistakes
- A 1:10 dilution is not the same as a ten-fold dilution. Ratio notation varies: some labs mean 1 part stock plus 9 parts diluent (a ten-fold dilution, DF = 10), others 1 part plus 10. State the dilution factor and the volumes to avoid ambiguity.
- Mixing up V₂ and the diluent volume. V₂ is the final volume; the diluent is V₂ − V₁.
- Mixing kinds of concentration. You cannot take a stock in g/L to a target in mol/L without the molar mass. Convert first with the Molarity Calculator.
- Going the wrong way. If the answer for C₂ is higher than C₁, the 'stock' is actually the weaker solution.
Frequently Asked Questions
- What is the C1V1 = C2V2 formula?
- It is the dilution equation: the stock concentration times the stock volume equals the final concentration times the final volume. It holds because the amount of solute does not change when only solvent is added. Solve it for whichever term is unknown.
- How do I calculate how much water to add?
- Find V₁ from C₁V₁ = C₂V₂, then subtract it from the final volume: diluent = V₂ − V₁. For 41.67 mL of stock in a 500.0 mL final volume, add about 458 mL of water. With a volumetric flask, add the stock first and fill to the mark.
- What is the dilution factor?
- The dilution factor is the initial concentration divided by the final one, C₁ ÷ C₂, which equals the final volume divided by the stock volume. A 12.0 M stock diluted to 1.00 M has a dilution factor of 12.0.
- Can I use different units for the stock and the diluted solution?
- Yes, provided both concentrations are the same kind: M with mM, or mg/mL with µg/mL. The calculator converts one to the other before applying the equation. It will not mix molar and mass units, because that needs a molar mass.
- Does this work for percent solutions and fold concentrations?
- Yes. Percent (%) and fold (×) are treated as plain concentration units: 10× buffer diluted to 1× in 50 mL needs 5 mL of stock. For a percent solution that you make from scratch, use the Percent Solution Calculator.
- What is a serial dilution?
- A serial dilution repeats the same dilution step in sequence, each tube becoming the stock for the next, so the dilution factors multiply. The Serial Dilution Calculator plans the volumes and concentrations of each step.