Labs and kitchens alike keep concentrated stock solutions and dilute them as needed. This calculator applies the dilution equation, C₁V₁ = C₂V₂, to tell you how much stock to measure, how much solvent to add, and how strong the result will be. It works with molar, mass-per-volume, percent, ppm and fold (×) concentrations.
How to use the dilution calculator
- Under Solve for, pick the unknown: C₁ (stock), V₁ (stock volume), C₂ (final) or V₂ (final volume).
- Enter the other three values. Stock concentration (C₁) and Final concentration (C₂) accept M, mM, µM, nM, g/L, mg/mL, mg/L, µg/mL, µg/L, %, ppm, ppb or ×. Stock volume used (V₁) and Final total volume (V₂) accept mL, L, µL, fl oz, cups, quarts or gallons.
- Use Show the result in to choose the output unit. For a concentration, the default is the same unit as the one you entered.
- Read the stock volume, the solvent / diluent to add (V₂ − V₁), the dilution factor and the stock : diluent ratio. The steps show the rearranged equation with your numbers.
Dilution formula
The amount of solute does not change when you add solvent, so concentration times volume is the same before and after:
Worked example: a 0.1 M working solution from a 2 M stock
You need 500 mL of 0.1 M solution and have a 2 M stock.
V1 = 0.1 M × 500 mL ÷ 2 M = 25 mL of stock
Diluent: 500 mL − 25 mL = 475 mL
Dilution factor 2 ÷ 0.1 = 20, so the stock : diluent ratio is 1 : 19.
Notice that a 20-fold dilution is a 1 : 19 mix, not 1 : 20. The calculator reports both numbers so the label on your bottle cannot be misread. In practice, put some solvent in the container first, add the 25 mL of stock, then top up to the 500 mL mark. With concentrated acids, always add the acid to the water, never the reverse.
Use the same kind of unit on both sides
C₁ and C₂ must belong to the same family:
- Molar: M, mM, µM, nM
- Mass per volume: g/L, mg/mL, mg/L, µg/mL, µg/L
- Ratio: %, ppm, ppb (1% = 10,000 ppm)
- Fold strength: × (for buffers sold as 10× or 50× concentrates)
Mixing families, such as a molar stock with a g/L target, is rejected, because the conversion needs the solute’s molar mass. Convert one value first with the molarity calculator. Within a family you can mix freely: a 1 mM stock and a 50 µM target work fine.
Fold units make buffer prep quick. To make 1 L of 1× buffer from a 10× concentrate, use 100 mL of concentrate and 900 mL of water.
A household example: rubbing alcohol
To make 16 fl oz of 70% isopropyl alcohol from a 91% bottle, set C₁ = 91%, C₂ = 70% and V₂ = 16 fl oz. You need 12.31 fl oz of the 91% alcohol and about 3.69 fl oz of water, a dilution factor of only 1.3. Alcohol and water shrink slightly when mixed, so the most accurate method is to fill to the final volume rather than measure the water.
Serial dilutions
A large dilution is more accurate in steps. Starting from a 1 mM stock, transferring 1 mL into 9 mL of diluent (V₁ = 1 mL, V₂ = 10 mL) gives 0.1 mM. Repeat the step to work down:
| Step | Concentration | Total dilution |
|---|---|---|
| Stock | 1 mM | 1× |
| 1 | 0.1 mM (100 µM) | 10× |
| 2 | 10 µM | 100× |
| 3 | 1 µM | 1,000× |
Run the calculator once per step. The overall factor is the product of the step factors.
Why C₂ cannot exceed C₁
Diluting adds solvent and never removes solute, so the final concentration can only be equal to or lower than the stock. When you solve for a volume with C₂ larger than C₁, the calculator stops with a message rather than returning a meaningless volume. Likewise, when solving for a concentration, V₂ must be at least V₁. To make a stronger solution, start again from the solid or a more concentrated stock.
Frequently asked questions
How much 2 M stock do I need to make 500 mL of a 0.1 M solution?
V₁ = 0.1 M × 500 mL ÷ 2 M = 25 mL. Measure 25 mL of the stock and add solvent until the total reaches 500 mL, which takes about 475 mL. That is a 20-fold dilution.
What does a 1:10 dilution mean?
Most often it means 1 part of stock in 10 parts total, for example 1 mL of stock plus 9 mL of water, a dilution factor of 10. Some fields write it as 1 part stock to 10 parts diluent instead, so the calculator shows both the dilution factor and the stock-to-diluent ratio.
Can I enter C₁ in mol/L and C₂ in g/L?
No. Both concentrations must be the same kind of unit, because converting molar to mass concentration needs the molar mass. Prefixes within a kind are fine, such as mM to µM or g/L to mg/mL.
Why does the calculator say my final concentration is higher than the stock?
Adding solvent can only lower the concentration, so C₂ must not be larger than C₁. Check that you have not swapped the two values or picked different prefixes, such as mM for one and M for the other.
Does C₁V₁ = C₂V₂ work for percent solutions?
Yes, as long as both percentages are of the same type, for example both v/v or both w/v. Diluting 91% isopropyl alcohol to 70% needs 12.31 fl oz of the 91% for every 16 fl oz of finished solution.