Molarity Dilution Calculator
Solve C1V1 = C2V2 for any one of the four values: stock or final concentration in M, mM, µM or nM, or stock or final volume in L, mL or µL. How it works
Use the Molarity Dilution Calculator
About the Molarity Dilution Calculator
To dilute a 1.0 M stock to 0.1 M in a 1,000 mL final volume you need 100 mL of stock, because C1V1 = C2V2 gives V1 = 0.1 × 1,000 / 1.0. Pick the value to solve for, type the other three in M, mM, µM or nM and L, mL or µL, and the page returns it with the moles of solute, 0.1 mol in this example.
Stock volume for 1,000 mL of final solution from a 10 M stock
| Final concentration (C2) | Stock volume (V1) | Moles of solute |
|---|---|---|
| 0.1 M | 10 mL | 0.1 mol |
| 0.5 M | 50 mL | 0.5 mol |
| 1 M | 100 mL | 1 mol |
| 2 M | 200 mL | 2 mol |
V1 = C2 × V2 / C1 with C1 = 10 M and V2 = 1,000 mL. Add solvent to the 1,000 mL mark after the stock.
The four forms of the equation, checked with 2 M, 50 mL, 0.5 M and 200 mL
| Solve for | Formula | Result | Moles of solute |
|---|---|---|---|
| V1 | C2 × V2 / C1 | 50 mL | 0.1 mol |
| C1 | C2 × V2 / V1 | 2 M | 0.1 mol |
| C2 | C1 × V1 / V2 | 0.5 M | 0.1 mol |
| V2 | C1 × V1 / C2 | 200 mL | 0.1 mol |
Each row leaves one of the four values blank and solves it from the other three. The moles are the same in every row because the four values are consistent.
Methodology
Adding solvent does not change the amount of solute, so moles before and after dilution are equal and C1 × V1 = C2 × V2. The page solves the unknown as the product on one side divided by the known value on the other, and reports moles as C × V / 1000 with C in M and V in mL. Values typed in mM, µM, nM, L or µL are converted to M and mL by powers of ten first, and the answer is converted back to the unit chosen for it.
How to use this tool
- Press C1, V1, C2 or V2 under Solve for to choose the unknown. V1 is selected at first.
- Type the other three values and pick each one’s unit: M, mM, µM or nM for concentrations, L, mL or µL for volumes. Each must be above 0.
- Read the solved value and the moles of solute. They update as you type; there is no button to press.
- Measure V1 of stock and add solvent until the total volume is V2.
Frequently asked questions
- How do I calculate a dilution with C1V1 = C2V2?
- Multiply the stock concentration by the stock volume, set that equal to the final concentration times the final volume, and solve for the unknown. To make 500 mL of 0.25 M from a 2 M stock, V1 = 0.25 × 500 / 2 = 62.5 mL of stock, which holds 0.125 mol. Measure 62.5 mL of stock and add solvent until the total is 500 mL.
- How much stock do I need for a 10-fold dilution?
- One tenth of the final volume. A 5 M stock diluted to 0.5 M in 250 mL needs 25 mL of stock, because C1 / C2 = 5 / 0.5 = 10 and so V1 = V2 / 10. Type the concentrations and the final volume rather than the ratio.
- Can I use mM, µM, liters or microliters?
- Yes. Each of the four values has its own unit menu, M, mM, µM or nM and L, mL or µL, and the units may differ between fields. To make 500 µL of 100 µM from a 10 mM stock, the page gives V1 = 5 µL. A percent or mg/mL concentration has to be converted to molarity before you type it.
- What happens if the final concentration is higher than the stock?
- A dilution cannot raise a concentration. The page still returns the number and adds a warning that the values describe concentrating, not diluting. With a 0.1 M stock, a 1 M target and 1,000 mL final volume it returns a stock volume of 10,000 mL, ten times the final volume, which is the sign that C1 and C2 are swapped or the stock is too weak.
- What are the moles of solute the page shows?
- The amount of solute that is the same before and after the dilution: C × V / 1000, with C in M and V in mL. In the default example it is 1.0 × 100 / 1000 = 0.1 mol. It is taken from the side of the equation you typed, so it does not change with the value you solve for.
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