Dilution Calculator: C1V1 = C2V2 for Stock Solutions

Diluting a stock adds solvent but leaves the amount of solute unchanged. Concentration times volume is that amount, so it has to be the same before and after, and that single fact is the whole of the dilution equation, C1V1 = C2V2.

How to use the calculator

1. Choose the concentration unit at the top: M, mM, µM, nM, mg/mL, µg/mL, ng/µL, % or × (for buffers sold as 10× or 5× stocks). C1 and C2 both use it.
2. Choose the volume unit: L, mL or µL. V1 and V2 both use it.
3. Fill in three of the four boxes (C1 stock, V1 stock volume, C2 final, V2 final volume) and leave the one you want empty. Each empty box shows "empty = solve".
4. Read the result. You get the missing value, the dilution factor, and, when the missing value is a volume, the diluent to add.

If none or more than one box is empty, the tool asks you to leave exactly one blank. A zero or negative number in any box brings up the warning that every value has to be above zero. It also warns when the final concentration comes out higher than the stock, since a dilution cannot do that. The unit menus only relabel the boxes; they do not convert numbers. If your stock is labeled in M and your target in mM, convert one of them before typing.

The dilution equation

C1 × V1 = C2 × V2

• C1 is the concentration of the stock.
• V1 is the volume of stock you pipette.
• C2 is the concentration you want at the end.
• V2 is the final total volume, stock plus diluent.

Rearranged, it gives each unknown: V1 = C2 × V2 ÷ C1, C1 = C2 × V2 ÷ V1, V2 = C1 × V1 ÷ C2 and C2 = C1 × V1 ÷ V2. Two more numbers follow from it:

• diluent to add = V2 - V1
• dilution factor = C1 ÷ C2, which equals V2 ÷ V1

Worked example with the default values

The calculator opens with a 10 mM stock, a 0.1 mM target and a final volume of 1 mL, with V1 left empty.

1. V1 = 0.1 mM × 1 mL ÷ 10 mM = 0.01 mL.
2. Diluent = 1 mL - 0.01 mL = 0.99 mL.
3. Dilution factor = 10 ÷ 0.1 = 100.

The tool shows "Volume of stock V1: 0.01 mL", "Diluent to add: 0.99 mL" and "Dilution factor: 1:100". At the bench, 0.01 mL is 10 µL: put 990 µL of buffer in a tube, add 10 µL of stock and mix. Switching the volume unit to µL and typing 1000 (or 1,000) for V2 gives the answer directly as 10 µL.

A 10× buffer

Set the concentration unit to ×. With C1 = 10, C2 = 1 and V2 = 500 mL, the tool returns V1 = 50 mL and 450 mL of water to add, a 1:10 dilution.

Common mistakes

• Adding V1 on top of V2. V2 is the total volume. Pipetting 10 µL of stock into a full 1 mL of buffer gives 1.01 mL and a slightly weaker solution.
• Mixing units. If C1 is in mg/mL and C2 in µg/mL, put both in the same unit first, because the tool uses one unit for both.
• Reading "1:100" two ways. Here it means one part stock in 100 parts total, which is the same as a dilution factor of 100. Some protocols use ratio notation, where 1:99 means one part stock plus 99 parts diluent. Check which one a method uses.
• Pipetting volumes that are too small. A V1 of a microliter or less is hard to measure accurately. Make an intermediate dilution first, or plan the whole series in the serial dilution calculator.
• Forgetting the stock's own solvent. A compound dissolved in DMSO and diluted 1:1000 leaves 0.1 percent DMSO in the final mix, which cell assays often need a matching control for.

Limits

The equation assumes the volumes simply add up and that nothing reacts or precipitates on mixing. That is close enough for buffers and aqueous stocks; ethanol and water, which shrink when mixed, are better made up to a final volume. It handles one step at a time. If you are starting from a solid rather than a stock, the molarity calculator gives the mass to weigh, and the ppm calculator turns mg/L figures into molarity first.

FAQ

What is the dilution equation?

The dilution equation is C1V1 = C2V2, where C1 and V1 are the stock concentration and the volume of stock used, and C2 and V2 are the final concentration and final total volume. It works because diluting adds solvent without changing the amount of solute.

How do I use C1V1 = C2V2?

Fill in the three values you know and solve for the fourth. To make 1 mL of 0.1 mM from a 10 mM stock, V1 = 0.1 × 1 ÷ 10 = 0.01 mL, or 10 µL. Keep both concentrations in the same unit and both volumes in the same unit.

What does a 1:100 dilution mean?

In this calculator, and in most lab usage, a 1:100 dilution means one part of stock in a total of 100 parts, so the concentration falls 100-fold. For 1 mL total, that is 10 µL of stock and 990 µL of diluent. A few protocols write the same mix as 1:99, counting stock to diluent.

How do I calculate how much diluent to add?

Subtract the stock volume from the final volume: diluent = V2 - V1. The calculator prints this line whenever it solves for V1 or V2.

Can C1V1 = C2V2 be used with mg/mL or percent?

Yes. Any concentration unit works as long as C1 and C2 are in the same one, which is why the calculator offers mg/mL, µg/mL, ng/µL, % and × as well as molar units. The volumes also have to share one unit.