Dilution Calculator (M1V1 = M2V2)
Solve M1V1 = M2V2 for whichever of the four values you leave blank.
What is Dilution?
Diluting a solution adds solvent without changing the amount of solute, so the number of moles stays the same: M₁V₁ = M₂V₂. Every dilution problem is that one equation with one unknown, whether the question asks how much stock to measure out, what volume to make up to, or what concentration results.
How it works
Leave exactly one of the four fields blank. The calculator checks that only one is missing, warns if too many or too few are filled, and solves the equation for the blank — showing the rearrangement it used. A dilution factor is also reported, since that is the number people compare between protocols.
- Enter what you know. Every field recalculates as you type — there is no submit button. Leave the quantity you want blank and the page solves for it.
- Read the answer and the working. The result appears above the fold; underneath it is the formula with your numbers substituted, so the arithmetic can be checked rather than trusted.
- Check the units and the size. Units are shown on every value and selectable per field, so a result in kJ, kPa or km/h is converted rather than assumed. Sanity-check the magnitude against a known landmark such as 1 g/cm³ for water.
Examples
A textbook problem with a known answer
Every tool here is checked against standard example problems — the molar mass of C6H12O6 is 180.16 g/mol, and free fall from 20 m takes about 2.02 s at g = 9.8 m/s².
A result you want to reason backwards from
Leave the quantity you already know blank instead: given the final answer, most tools recover the starting value — the mass needed for a target concentration, or the height a fall must have had.
Common mistakes
Forgetting that a formula is only as good as its subscripts
H2O and H2O2 are different compounds. The formula field shows its parse — element by element — so a mis-typed subscript is visible before it reaches the arithmetic.
Mixing units in the middle of a calculation
The most common source of a wrong answer is a value in grams next to a formula expecting kilograms, or Celsius next to a gas constant expecting kelvin. This category converts on the way in and labels what it used.
Frequently asked questions
How much 2 M stock do I need for 250 mL of 0.5 M?
62.5 mL. V₁ = (M₂V₂) ÷ M₁ = (0.5 × 0.25) ÷ 2 — load the example and the working appears with those numbers.
Why does the volume increase but the moles stay the same?
Because dilution adds only solvent. The solute particles are spread through a larger volume, which lowers the concentration but cannot change how many there are.
Do the units of concentration and volume matter?
They must be consistent between the two sides. If both concentrations are in the same unit and both volumes in the same unit, the equation works regardless of which units those are.