Molarity Calculator

A mole is a fixed number of particles (6.022 × 10²³), and the molar mass tells you how many grams one mole weighs. So dividing grams by the molar mass counts the moles, and dividing moles by the litres of solution gives the molarity. Every other answer here is the same sum turned around.

The formula

moles n = mass m ÷ molar mass MM
molarity M = moles n ÷ volume V (in litres)
so molarity M = mass ÷ (molar mass × volume)
mass m = molarity × volume × molar mass
volume V = mass ÷ (molar mass × molarity)
molar mass MM = mass ÷ (molarity × volume)
mass concentration (g/L) = molarity × molar mass
% w/v = g/L ÷ 10 (grams per 100 mL)
ppm (mg/L) = g/L × 1,000
dilution: C₁ × V₁ = C₂ × V₂, water to add = V₂ − V₁

Worked example

Molarity (the default): 5.844 g of sodium chloride (58.44 g/mol) made up to 100 mL. Moles: 5.844 ÷ 58.44 = 0.1 mol. Volume: 100 mL = 0.1 L. Molarity: 0.1 ÷ 0.1 = 1 M. The same strength is 1 × 58.44 = 58.44 g/L, 58.44 ÷ 10 = 5.844% w/v and 58.44 × 1,000 = 58,440 ppm (mg/L).

Mass to weigh out: 500 mL of 0.25 M NaCl. 0.25 × 0.5 = 0.125 mol, and 0.125 × 58.44 = 7.305 g.

Volume to make: 10 g of sodium hydroxide (40.00 g/mol) at 0.5 M. 10 ÷ 40 = 0.25 mol, and 0.25 ÷ 0.5 = 0.5 L (500 mL).

Molar mass: 9.807 g in 1 L gives a 0.1 M solution. 0.1 × 1 = 0.1 mol, and 9.807 ÷ 0.1 = 98.07 g/mol (sulfuric acid, H₂SO₄).

Molar mass from a formula: Ca(OH)₂ has 1 Ca, 2 O and 2 H. 40.078 + 2 × 15.999 + 2 × 1.008 = 40.078 + 31.998 + 2.016 = 74.092 ≈ 74.09 g/mol. For the hydrate CuSO₄·5H₂O: 63.546 + 32.06 + 4 × 15.999 + 5 × 18.015 = 63.546 + 32.06 + 63.996 + 90.075 = 249.677 g/mol.

Dilution: 500 mL of 0.1 M from a 1 M stock. V₁ = 0.1 × 500 ÷ 1 = 50 mL of stock, then add 500 − 50 = 450 mL of water. Dilution factor 1 ÷ 0.1 = 10.

% w/v to molarity: 0.9% saline is 0.9 g per 100 mL = 9 g/L, and 9 ÷ 58.44 = 0.154 M (154 mM).

How to make the solution

1. Weigh the mass the calculator gives.
2. Dissolve it in less water than the final volume (about three quarters).
3. Pour into a volumetric flask (or measuring cylinder), rinse the beaker into it, then top up to the line.
4. Mix well. Molarity is per litre of finished solution, so don't add the solid to the full volume of water.

For a hydrate (like CuSO₄·5H₂O) use the molar mass including the water, because the water is part of what you weigh. For acids and other chemicals bought as a liquid, use the dilution helper with the stock's strength instead. Always follow the safety sheet: add acid to water, not water to acid.

Common compounds (from rounded standard atomic weights)

Standard atomic weights used (rounded)

The formula tool uses rounded textbook values based on the IUPAC conventional and abridged standard atomic weights, for elements from hydrogen to bismuth (except technetium and promethium). They have not been checked against the official IUPAC table here. For elements whose weight varies in nature (like H, Li, B, C, N, O, S, Cl), real samples can differ slightly in the last digit. Some common ones:

Notes

• 1 M = 1,000 mM = 1,000,000 µM = 10⁹ nM. 1 mg/mL is the same as 1 g/L.
• % w/v means grams per 100 mL of solution, so 1% w/v = 10 g/L.
• ppm here is mg per litre. That equals parts per million by mass only for dilute water solutions (density about 1 g/mL). For other solvents or strong solutions, ppm by mass differs.
• g/L, mg/mL, % w/v and ppm need the molar mass to turn into molarity. To find the molar mass itself, give the concentration in M, mM, µM or nM.
• Molarity changes slightly with temperature because the volume does. For very exact work, make the solution at the temperature you will use it.