Use this free molarity calculator, also called a molar concentration calculator, to find the molarity of a solution from the mass dissolved, the molar mass and the volume. Switch to Mass to Weigh to find how many grams you need for a solution of a chosen molarity, to Dilution to work out how much stock and water you need with C₁V₁ = C₂V₂, or to Convert Units to change between M, mM, µM, nM and pM. Choose grams, milligrams or kilograms for the mass and liters, milliliters or microlitres for the volume. Type a formula such as NaCl and the molar mass is filled in for you. Every answer shows the working, and tables list the grams to weigh for common solutions. It is free and instant, and your numbers stay in your browser.
What is molarity?
Molarity (symbol M), also called molar concentration, is the concentration of a solution measured in moles of dissolved substance per liter of solution. A 1 M solution has 1 mole of the substance in every liter. It is the most common concentration unit in chemistry labs, because it tells you directly how many particles are in a given volume.
The molarity formula
Moles (n) = mass in grams ÷ molar mass in g/mol
Put together, M = mass ÷ (molar mass × volume in liters). Turned around, the mass to weigh out is mass = M × V × molar mass, and the volume is V = mass ÷ (M × molar mass).
How to calculate molarity
Divide the mass you dissolved by the molar mass to get the moles, then divide by the volume in liters. If you dissolve 5.85 g of sodium chloride (molar mass 58.44 g/mol) and make the solution up to 250 mL, you have 5.85 ÷ 58.44 = 0.1001 mol in 0.25 L, which is a molarity of 0.4004 M. Do not know the molar mass? Type the formula in the calculator, or use the Molar Mass Calculator.
How much to weigh out
To make a solution of a chosen molarity, multiply the molarity by the volume in liters to get the moles, then multiply by the molar mass. For 500 mL of a 0.5 M sodium chloride solution that is 0.5 × 0.5 = 0.25 mol, or 14.61 g. Dissolve it in some water, then add water up to the 500 mL mark so the final volume is right.
Diluting a stock solution
When you dilute a solution the amount of solute does not change, only the volume, so C₁ × V₁ = C₂ × V₂. To make 500 mL of 1 M solution from a 12 M stock, you need V₁ = 1 × 500 ÷ 12 = 41.67 mL of stock and 458.3 mL of water.
Safety note: when diluting concentrated acids, always add the acid slowly to the water, never the water to the acid, and wear eye protection and gloves.
mM, µM and nM
Lab solutions are often weak, so concentrations are written in smaller units. A millimolar (mM) is a thousandth of a molar, a micromolar (µM) a millionth and a nanomolar (nM) a billionth. To change a unit, move one step per factor of 1,000: 5 mM is 0.005 M, and 250 µM is 0.00025 M. The Convert Units tab does it for you and shows every unit at once.
From mg/mL to molarity
A concentration in mg/mL is the same number as g/L. Divide it by the molar mass to get mol/L. For example, 10 mg/mL of sodium chloride is 10 g/L ÷ 58.44 g/mol = 0.1711 M, or 171.1 mM.
Molarity or molality?
Molarity is moles per liter of solution, while molality (symbol m) is moles per kilogram of solvent. The volume of a liquid changes a little with temperature, so molarity changes too, but molality does not. For dilute water solutions at room temperature the two numbers are close.
pH from molarity
For a strong acid that gives one hydrogen ion per molecule, such as hydrochloric acid, the pH is −log₁₀ of the molarity. A 0.01 M solution has a pH of 2, and a 0.1 M solution a pH of 1. Weak acids and acids with more than one hydrogen need extra steps, so this shortcut does not apply to them.
