Dilution Calculator
C1V1 = C2V2, solved by the dilution calculator for whichever term you are missing. It also gives the diluent to add, which is the number you actually pour.
Notice: For general informational purposes only. Hazardous substances, including cleaning products and pesticides, must be mixed, used and stored in accordance with the manufacturer's label. Mixing certain products can release toxic gases.
V1 - stock volume
- How to make it This is the number you actually pour. Note it is the diluent to add, not the final volume. A 1:10 dilution means 1 part stock to 9 parts diluent, giving 10 parts total.
- take 50 ml of stock and add 450 ml of diluent
- The equation Both sides are the amount of solute, which does not change when you add solvent. That is the whole principle.
- 10 x 50 = 1 x 500
- Dilution factor Written as 1:10, meaning one part stock to 10 parts total.
- 10-fold
- Ratio to pour Stock to diluent. This is the other convention and the two get confused constantly: 1:10 means one part in ten total to most people and one part to ten parts to others. Say which you mean.
- 1 : 9
- Diluent to add
- 450 ml
- Final volume
- 500 ml
| Final concentration | Stock needed | Diluent | Factor |
|---|---|---|---|
| 5 | 250 ml | 250 ml | 2-fold |
| 2 | 100 ml | 400 ml | 5-fold |
| 1 | 50 ml | 450 ml | 10-fold |
| 0.2 | 10 ml | 490 ml | 50-fold |
| 0.1 | 5 ml | 495 ml | 100-fold |
- C1 and C2 must be in the same units as each other, and V1 and V2 in the same units as each other. The equation does not care which units, because they cancel. It only needs each pair to match.
- This assumes volumes are additive, which is very nearly true for dilute aqueous solutions and not true for concentrated ones. Mixing 50 ml of ethanol with 50 ml of water gives about 96 ml, not 100.
How the Dilution Calculator works
Dilution is one equation: C1V1 = C2V2. The concentration of the stock times the volume of stock you use equals the concentration you want times the final volume you want.
The reason it holds is worth seeing, because it makes the equation obvious rather than something to memorize. Both sides are the amount of solute: concentration times volume is how much stuff is dissolved. Adding solvent does not change how much solute is present; it only spreads it through more volume. So the amount before equals the amount after, and that is the equation.
Worked through: you have a 10 M stock and want 500 ml at 1 M. Rearranged, V1 = C2V2/C1 = (1 x 500)/10 = 50 ml. Take 50 ml of stock and add 450 ml of diluent.
That last step is the one people get wrong. The equation gives you V1 and V2: the stock volume and the final volume. The amount of diluent to add is V2 minus V1. Adding 500 ml of water to 50 ml of stock gives 550 ml at 0.91 M, not 500 ml at 1 M. In laboratory usage the instruction "dilute to 500 ml" means bring the total up to 500, and "add 450 ml" means add that much; the two are different operations and the phrasing matters.
The units are more forgiving than they look. C1 and C2 can be anything (molar, percent, mg/ml, parts per million) provided they are the same as each other. V1 and V2 likewise. They cancel on both sides, which is why the equation does not need to know what you are working in. What it will not survive is mixing molar on one side with percent on the other.
Ratio notation is a genuine ambiguity and causes real errors. "1:10" means one part in ten total to most people in a laboratory, so 1 ml of stock made up to 10 ml. To others, particularly in trades and cleaning, it means one part stock to ten parts diluent, giving 11 parts total. The difference is 10% and in some contexts it matters a great deal. This calculator gives both forms explicitly rather than picking one.
For large dilution factors, one step is the wrong method. To go 10,000-fold you would need 0.1 ml of stock in a liter, and measuring 0.1 ml accurately is where all the error is. A serial dilution does it in stages (four successive 10-fold steps), keeping every volume in a range the equipment measures well. The errors still compound across the steps, but each one is far smaller than the single-step pipetting error would have been.
One assumption worth knowing about. The arithmetic treats volumes as additive, which is very nearly true for dilute aqueous solutions and false for concentrated ones. Mixing 50 ml of ethanol with 50 ml of water gives about 96 ml, not 100, because the molecules pack together more tightly than they do apart. For anything where that matters, concentrations are prepared by mass rather than by volume, and the equation is applied to masses instead.
Dilution Calculator FAQ
What is the dilution formula?
C1V1 = C2V2: stock concentration times stock volume equals final concentration times final volume. Both sides are the amount of solute, which does not change when you add solvent. Rearrange for whichever term you are missing.
How much water do I add to dilute a solution?
V2 minus V1, the final volume less the stock volume. For 500 ml at 1 M from a 10 M stock you need 50 ml of stock, so you add 450 ml of water. Adding 500 ml to the 50 ml of stock would give 550 ml at the wrong concentration.
What does a 1:10 dilution mean?
It depends who is saying it, which is why it causes errors. In most laboratory usage it means one part in ten total: 1 ml made up to 10 ml. In trades and cleaning it often means one part stock to ten parts diluent, giving 11 parts total. Always state which convention you mean.
When should I use a serial dilution?
Whenever the factor is large enough that one step would need a very small stock volume, which is past about 100-fold. A 10,000-fold dilution in one step needs 0.1 ml in a liter, and measuring that is where the error lives. Four successive 10-fold steps keep every volume in a range the equipment handles accurately.