Dilution Calculator
Work out any part of C1V1 = C2V2. Enter the three values you know and the calculator solves for the fourth, including how much solvent to add.
How the dilution formula works
When you dilute something you add more solvent, but you do not add or remove any of the dissolved substance. The amount of solute before and after is identical. That single idea gives you the formula.
C1V1 = C2V2
Concentration multiplied by volume gives you moles, so both sides of that equation are just "moles of solute" written two different ways. C1 and V1 describe the concentrated stock you start with. C2 and V2 describe the diluted solution you finish with.
The units do not have to be liters and mol/L. They only have to match on both sides. If C1 and C2 are both in percent, the formula still works. If V1 and V2 are both in milliliters, it still works. That flexibility is why the same equation shows up in chemistry, biology, and pharmacy.
Worked example
You have a 2.0 M stock of hydrochloric acid. You need 500 mL of 0.10 M acid. How much stock do you measure out?
Step 1. Label what you know.
C1 = 2.0 M, C2 = 0.10 M, V2 = 500 mL, V1 = unknown
Step 2. Rearrange for V1.
V1 = C2V2 ÷ C1
Step 3. Put the numbers in.
V1 = (0.10 M × 500 mL) ÷ 2.0 M = 25 mL
Step 4. Find the solvent to add.
500 mL − 25 mL = 475 mL
So you measure 25 mL of stock into a 500 mL volumetric flask and top up to the mark. Note that you top up to 500 mL rather than adding exactly 475 mL, because mixing can change the total volume slightly.
Dilution factor
The dilution factor tells you how many times weaker the solution became:
Dilution factor = V2 ÷ V1 = C1 ÷ C2
In the example above, 500 ÷ 25 = 20, so it is a 20-fold dilution. You may also see this written as 1:20.
Be careful with that colon notation, because two conventions exist. In most laboratory and medical work, 1:20 means 1 part stock plus 19 parts solvent, giving 20 parts in total and a 20-fold dilution. Some older texts use it to mean 1 part stock plus 20 parts solvent, which is a 21-fold dilution. If a protocol matters, check which convention it uses.
Serial dilutions
Sometimes you need a solution so weak that measuring the stock directly is impractical. Diluting 1 microliter into a liter is not something a pipette can do accurately. The answer is to dilute in stages.
In a serial dilution you dilute, then take some of that result and dilute again. The dilution factors multiply:
Total factor = factor 1 × factor 2 × factor 3 …
Three 10-fold steps in a row give 10 × 10 × 10 = 1000, so a 1000-fold dilution overall. Five 10-fold steps give 100,000-fold. Mix each tube thoroughly before drawing from it, and use a fresh pipette tip every step, because carryover on a tip is the usual reason a serial dilution drifts off target.
Common dilutions at a glance
| Written as | Stock : solvent | Factor | Strength left |
|---|---|---|---|
| 1:2 | 1 part + 1 part | 2 | 50% |
| 1:5 | 1 part + 4 parts | 5 | 20% |
| 1:10 | 1 part + 9 parts | 10 | 10% |
| 1:100 | 1 part + 99 parts | 100 | 1% |
| 1:1000 | 1 part + 999 parts | 1000 | 0.1% |
Safety: acid into water, never the reverse
Diluting a concentrated acid releases a surprising amount of heat. If you pour water onto concentrated acid, the first drops can boil on contact and spit acid out of the container.
Always add the acid slowly into the water, stirring as you go. The larger volume of water absorbs the heat and spreads it out. A common way to remember it is "do what you oughta, add acid to water." Wear eye protection, and for concentrated sulfuric acid use an ice bath.
Mistakes worth avoiding
- Mixing units across the equation. C1 in molarity and C2 in percent will give nonsense. Convert first.
- Adding the solvent volume instead of topping up. V2 is the final total volume, not the amount of solvent you add.
- Asking for a concentration higher than the stock. Dilution can only make a solution weaker. If C2 is above C1 you need a more concentrated stock.
- Forgetting to mix between serial steps. An unmixed tube gives every later step the wrong starting point.
- Diluting in the storage bottle. Use a volumetric flask, then transfer.
Frequently asked questions
What is the dilution formula?
The dilution formula is C1V1 = C2V2. C1 and V1 are the concentration and volume of the stock solution, and C2 and V2 are the concentration and volume of the diluted solution you want. The units just need to match on both sides.
How much solvent do I add?
Subtract the stock volume from the final volume. If you need 500 mL of final solution and the calculation says to use 25 mL of stock, you add solvent up to the 500 mL mark, which is about 475 mL.
What does a 1:10 dilution mean?
In most lab and medical protocols a 1:10 dilution means one part stock plus nine parts solvent, giving ten parts in total. The result is ten times weaker than the stock. A few older texts use it to mean one part stock plus ten parts solvent, so check the source if precision matters.
How do I calculate a serial dilution?
Multiply the individual dilution factors together. Three successive 10-fold dilutions give a total factor of 10 x 10 x 10, which is 1000, so the final solution is 1000 times weaker than the stock.
Can I use percent instead of molarity?
Yes. C1V1 = C2V2 works with any concentration unit as long as you use the same unit for C1 and C2. Percent, molarity, parts per million, and milligrams per milliliter all work.
Why do I add acid to water and not water to acid?
Diluting concentrated acid gives off a lot of heat. Adding water to acid can make the first drops boil and splash acid out of the container. Adding acid slowly into a larger volume of water spreads that heat safely.
Related terms
Next: the molarity calculator works out the concentration of a solution you make from scratch.