Molarity and dilution calculator
Leave one box empty and it solves for that value, with the work shown.
Need the molar mass? Use the molar mass calculator.
M1V1 = M2V2. Concentrations can be in any unit as long as M1 and M2 match.
How these formulas work
Molarity is moles of solute per liter of solution: M = n ÷ V. Convert milliliters to liters before using it, which the calculator does for you.
When you dilute a solution, the moles of solute stay the same, so M1V1 = M2V2. If you know three of the four values, the fourth follows. The solvent to add is V2 minus V1.
Worked examples
Making a solution. Dissolve 5.85 g of NaCl (58.44 g/mol) and add water to a total volume of 250 mL. Moles = 5.85 ÷ 58.44 = 0.100 mol, so molarity = 0.100 mol ÷ 0.250 L = 0.400 M.
Diluting a stock. To make 500 mL of 0.100 M HCl from a 2.00 M stock, use M₁V₁ = M₂V₂: V₁ = (0.100 M × 500 mL) ÷ 2.00 M = 25.0 mL of stock, then add water until the total volume is 500 mL.
Frequently asked questions
What is the difference between molarity and molality?
Molarity (M) is moles of solute per liter of solution. Molality (m) is moles of solute per kilogram of solvent. Molality doesn’t change with temperature, which is why it’s used for freezing-point and boiling-point problems.
What units do I use in M₁V₁ = M₂V₂?
Any volume unit works as long as both volumes use the same one. mL on both sides is fine, and the answer comes out in mL.
Do I add 475 mL of water in the example above?
Not exactly: you add water until the total volume reaches 500 mL, which is why labs use volumetric flasks. Volumes don’t always add perfectly when liquids mix.
Does dilution change the number of moles?
No. Dilution adds solvent only, so the moles of solute stay the same. That’s exactly why M₁V₁ (moles before) equals M₂V₂ (moles after).