Dilution calculator (C₁V₁ = C₂V₂)
This dilution calculator solves C₁V₁ = C₂V₂ for whichever value you are missing: how much stock to use, the final volume, or a concentration. It converts units, then tells you how much solvent to add.
- Solve for V₁, V₂, C₁ or C₂
- M, mM, µM, nM, mg/mL, µg/mL, % or X
- Dilution factor and solvent volume included
Last updated
How to use the dilution calculator
- Choose the value you need. Most often it is V₁, the volume of stock to measure out.
- Enter the other three values and pick a unit for each. C₁ and C₂ can be different units of the same kind, such as mM and µM.
- Read the answer, the dilution factor and how much solvent to add to reach the final volume.
- Measure the stock, then add solvent (water or buffer) up to the final volume and mix.
The dilution formula
Diluting adds solvent but not solute, so the amount of solute before and after is the same. Concentration times volume is that amount, which gives the dilution equation.
C₁ × V₁ = C₂ × V₂
C₁ and V₁ are the stock concentration and the volume of stock you use. C₂ and V₂ are the final concentration and the final total volume. Rearranged: V₁ = C₂V₂ ÷ C₁, V₂ = C₁V₁ ÷ C₂, C₁ = C₂V₂ ÷ V₁ and C₂ = C₁V₁ ÷ V₂. Any units work as long as both concentrations use the same unit and both volumes use the same unit.
Worked example
You need 100 mL of 0.1 M hydrochloric acid and have a 1.0 M stock.
- Write what you know: C₁ = 1.0 M, C₂ = 0.1 M, V₂ = 100 mL.
- Solve for V₁: V₁ = C₂ × V₂ ÷ C₁ = 0.1 M × 100 mL ÷ 1.0 M = 10 mL.
- Solvent to add: 100 mL − 10 mL = 90 mL.
Measure 10 mL of the 1.0 M stock and make it up to 100 mL. That is a 10-fold (1:10) dilution. With acids, add the acid to the water, not the water to the acid.
Dilution factor and ratios
The dilution factor is C₁ ÷ C₂, which is the same as V₂ ÷ V₁. A 1:10 dilution means 1 part stock in 10 parts total (1 part stock plus 9 parts solvent). Some kits and cleaning labels write ratios as stock to solvent instead, so 1:9 there means the same as 1:10 here; check which one your instructions use.
| Dilution (stock : total) | Stock for 100 mL | Solvent for 100 mL |
|---|---|---|
| 1:2 | 50 mL | 50 mL |
| 1:5 | 20 mL | 80 mL |
| 1:10 | 10 mL | 90 mL |
| 1:100 | 1 mL | 99 mL |
| 1:1,000 | 0.1 mL (100 µL) | 99.9 mL |
Serial dilutions
For a very large dilution, dilute in steps. Each step multiplies the dilution factor: three 1:10 dilutions in a row give 10 × 10 × 10 = a 1:1,000 dilution. To get 1 µM from a 1 M stock (1,000,000-fold), six 1:10 steps or three 1:100 steps are far more accurate than measuring 0.1 µL of stock.
Common questions
How do you calculate a dilution?
Use C₁V₁ = C₂V₂ and solve for the missing value. To make 100 mL of 0.1 M from a 1.0 M stock: V₁ = 0.1 × 100 ÷ 1.0 = 10 mL of stock, plus 90 mL of solvent.
How do I make a 1:10 dilution?
Mix 1 part stock with 9 parts solvent, so the stock is one tenth of the total. For 10 mL, use 1 mL of stock and 9 mL of solvent.
What is the dilution factor?
The final volume divided by the stock volume, or the stock concentration divided by the final concentration. 10 mL of stock made up to 100 mL is a dilution factor of 10.
Can I use C₁V₁ = C₂V₂ with mg/mL or percent?
Yes. Any concentration unit works if C₁ and C₂ use the same one. Diluting a 70% solution to 10% in 350 mL needs 10 × 350 ÷ 70 = 50 mL of the 70% stock.
How do you dilute from mM to µM?
Convert so both are in the same unit first. 10 mM is 10,000 µM, so 20 mL of 50 µM needs 50 × 20 ÷ 10,000 = 0.1 mL (100 µL) of the 10 mM stock.
Is V₂ the volume of water I add?
No. V₂ is the final total volume. The water to add is V₂ − V₁, assuming the volumes add up, which is close enough for most dilute solutions.
Sources
- OpenStax Chemistry 2e, 3.3 Molarity. The dilution equation C₁V₁ = C₂V₂, with worked examples for final concentration and stock volume
See the methodology page for how Studyfigure builds and checks its calculators.