The one formula
1 mg/mL is the same as 1 g/L, so dividing by the molar mass in g/mol gives moles per liter:
molarity (M) = concentration (mg/mL) ÷ molar mass (g/mol)
Going the other way, multiply: mg/mL = M × molar mass.
Examples
- A salt: NaCl has a molar mass of 58.44 g/mol. A 5.844 mg/mL solution is 5.844 ÷ 58.44 = 0.1 M.
- A protein: a 50,000 g/mol (50 kDa) protein at 1 mg/mL is 1 ÷ 50,000 = 0.00002 M = 20 µM.
- Back to mass: 250 mM glucose (180.16 g/mol) is 0.25 × 180.16 = 45.0 mg/mL.
Other units that mean the same thing
- mg/mL = g/L
- µg/mL = mg/L, which is about 1 ppm in dilute water solutions
- 1% w/v = 1 g per 100 mL = 10 mg/mL
- 1 M = 1,000 mM = 1,000,000 µM
So 10 ppm of a compound with a molar mass of 100 g/mol is 10 mg/L ÷ 100 = 0.1 mM, or 100 µM.
Common mistakes
- Using the anhydrous molar mass for a hydrate. CuSO₄·5H₂O weighs 249.69 g/mol, not 159.61. Use the formula on the bottle.
- Mixing up kDa and Da. 66 kDa is 66,000 g/mol.
- Molar mass of a salt form. Drugs are often sold as hydrochloride or sodium salts, which weigh more than the free compound.
Tools
The Concentration Converter converts between M, mM, µM, mg/mL, µg/mL, ppm and % w/v once you give it the molar mass or formula. Find the molar mass with the Molar Mass Calculator, and work out how much to weigh for a solution with the Molarity Calculator.