Common molar dilutions
Each row uses M1V1 = M2V2 to find V1. The diluent volume is V2 minus V1.
| Dilution | Stock (M1) | Target (M2) | Final volume (V2) | Stock to transfer (V1) | Diluent to add |
|---|---|---|---|---|---|
| 1:10 dilution | 1.0 M | 0.10 M | 100 mL | 10 mL | 90 mL |
| 1:100 dilution | 1.0 M | 10 mM | 100 mL | 1.0 mL | 99 mL |
| 1:5 dilution | 0.50 M | 0.10 M | 250 mL | 50 mL | 200 mL |
| Concentrated HCl | 12 M | 1.0 M | 500 mL | 41.7 mL | 458.3 mL |
| Stock to working solution | 10 mM | 50 µM | 10 mL | 50 µL | 9.95 mL |
Dilution factor and molarity
The dilution factor is M1 divided by M2. It is also V2 divided by V1.
A 1:10 dilution has a dilution factor of 10. One part of stock becomes 10 parts of final solution.
For a multi-step dilution, multiply the dilution factors of the steps.
To dilute a concentrated acid, add the acid slowly to the water. Do not add water to the acid.
How to use this calculator
- Select the unknown: stock molarity, stock volume, final molarity, or final volume.
- Enter the other three values.
- Select the molarity unit and the volume unit.
- Calculate the stock volume to transfer and the diluent to add.
Formula and variables
M₁V₁ = M₂V₂
| Symbol | Meaning | Unit |
|---|---|---|
| M₁ | stock molarity | M, mM, µM, nM, pM, fM |
| V₁ | stock volume to transfer | L, mL, µL, nL |
| M₂ | final molarity | M, mM, µM, nM, pM, fM |
| V₂ | final solution volume | L, mL, µL, nL |
Worked example
To make 1.0 L of 0.10 M solution from a 1.0 M stock, V1 = (0.10 × 1.0) / 1.0 = 0.10 L. Add 0.90 L of water to reach the final volume.
Interpretation
A physical dilution has final concentration no greater than stock concentration and final volume no smaller than the stock aliquot.
Common mistakes
- Do not enter more than one unknown.
- Use concentration units from the same dimension.
- Do not target a concentration above the stock.
Frequently asked questions
What is a molar dilution?
A molar dilution lowers the molarity of a solution when you add solvent. The moles of solute stay the same.
What is the molar dilution formula?
Use M1V1 = M2V2. M1 and V1 describe the stock. M2 and V2 describe the diluted solution.
Do the stock and final molarity need the same unit?
Yes. Both values use the selected molarity unit. Convert one value first if they differ, for example 10 mM = 10000 µM.
How much diluent should I add?
Add diluent until the solution reaches the final volume. The planning value is V2 minus V1.
Can a dilution make a more concentrated solution?
No. The final concentration cannot exceed the stock concentration in a dilution workflow.
Can I use scientific notation?
Yes. Enter values such as 6.022e23 or 1.0e-6 in a numeric field.
How should I round the result?
Keep extra digits during the calculation. Round the final result to the precision required by your data.