How the dilution formula works
A dilution keeps the amount of substance the same and spreads it through more liquid, so concentration × volume is equal before and after. OpenStax calls C1V1 = C2V2 the dilution equation and notes that any units can be used as long as they cancel.[1]
V1 = C2 × V2 ÷ C1 · C2 = C1 × V1 ÷ V2
V2 = C1 × V1 ÷ C2 · C1 = C2 × V2 ÷ V1
diluent to add = V2 − V1
Worked dilution examples
Each row solves for the stock volume, then subtracts it from the final volume to get the diluent.
| Stock (C1) | Target (C2) | Final volume (V2) | Take stock (V1) | Add diluent | Factor |
|---|---|---|---|---|---|
| 10 mg/mL | 2 mg/mL | 5 mL | 1 mL | 4 mL | 5× |
| 50 mg/mL | 10 mg/mL | 10 mL | 2 mL | 8 mL | 5× |
| 100 mg/mL | 1 mg/mL | 10 mL | 0.1 mL | 9.9 mL | 100× |
| 1 mg/mL | 0.1 mg/mL | 1 mL | 0.1 mL | 0.9 mL | 10× |
| 20 % | 5 % | 100 mL | 25 mL | 75 mL | 4× |
| 1 mol/L | 0.25 mol/L | 50 mL | 12.5 mL | 37.5 mL | 4× |
Dilution factor chart
A dilution factor of N means 1 part stock in N parts total. For every 10 mL of final solution:
| Dilution factor | Stock | Diluent | Final strength |
|---|---|---|---|
| 2× | 5 mL | 5 mL | C1 ÷ 2 |
| 4× | 2.5 mL | 7.5 mL | C1 ÷ 4 |
| 5× | 2 mL | 8 mL | C1 ÷ 5 |
| 10× | 1 mL | 9 mL | C1 ÷ 10 |
| 20× | 0.5 mL | 9.5 mL | C1 ÷ 20 |
| 50× | 0.2 mL | 9.8 mL | C1 ÷ 50 |
| 100× | 0.1 mL | 9.9 mL | C1 ÷ 100 |
Percent solutions and mg/mL
Percent weight-in-volume is grams per 100 mL,[2] so a 20% w/v stock is 200 mg/mL and 5% is 50 mg/mL. Because C1V1 = C2V2 only needs matching units, you can work in percent directly: 25 mL of 20% made up to 100 mL gives 5%. To turn a percent or a label total into mg/mL, use the concentration calculator.
Common dilution mistakes
- Adding V2 of diluent. V2 is the final total. Add V2 − V1, not V2.
- Mixing units. C1 and C2 must share a unit, and so must V1 and V2; convert mcg to mg first with mg to mcg.
- Reading “1:10” two ways. Here a factor of 10 means 1 part stock in 10 parts total (1 + 9). Some labs write 1:9 for the same thing; check which your protocol means.
- Expecting to concentrate. Adding liquid can only lower the concentration; C2 above C1 is an input error.
How we checked these numbers
Every result on this page comes from the same code as the calculator, and the known answers below are run as tests before each release.
| Input | Expected | Basis |
|---|---|---|
| C1 10, C2 2, V2 5 → V1 | 1 (add 4) | C1V1 = C2V2 |
| C1 10, V1 1, V2 5 → C2 | 2 | C1V1 = C2V2 |
| C1 50, V1 2, C2 10 → V2 | 10 | C1V1 = C2V2 |
| V1 2, C2 5, V2 10 → C1 | 25 | C1V1 = C2V2 |
Known limits.
- Assumes no solute is lost, added or reacted; the equation conserves the amount of substance.
- Volumes are treated as additive; for some liquid mixtures the final volume differs slightly.
- For medicines, follow the label or your pharmacist; this tool does arithmetic only.
Download the data. Dilution factor chart (CSV)
Change log.
- : Calculator and charts published.
Frequently asked questions
How do you calculate a dilution?
Use C1 × V1 = C2 × V2. Rearranged for the stock volume, V1 = C2 × V2 ÷ C1. Then add V2 − V1 of diluent.
How much diluent do I add?
The final volume minus the stock volume: to make 5 mL from 1 mL of stock, add 4 mL.
What is a 1 in 10 dilution?
1 part stock in 10 parts total, for example 1 mL of stock plus 9 mL of diluent. The concentration falls to one tenth.
Can C1 and C2 be in different units?
No. Use the same unit for both concentrations and the same unit for both volumes, or convert first.