Molarity Calculator
Find the mass of solute, the volume, the molarity or the molar mass of a solution, or work out a dilution with C₁V₁ = C₂V₂. Units convert automatically.
Concentration units can be molar (M, mM, µM, nM) or mass based (g/L, mg/mL, µg/mL, % w/v). C₁ and C₂ must be the same kind.
How to use the Molarity Calculator
- Choose a tab: Molarity for preparing a solution, or Dilution for diluting a stock.
- Pick what to solve for. That field turns green and shows the answer.
- Enter the other values and choose their units. Pick a compound preset to fill the molar mass.
- Press Calculate to see the result with the formula, moles and mass concentration.
- For dilutions, read the stock volume and the amount of solvent to add, and use Copy to save the recipe.
Molarity formula
Molarity (M) = moles of solute ÷ liters of solution, and moles = mass ÷ molar mass. Combined:
M = mass (g) ÷ (molar mass (g/mol) × volume (L))
Rearranged, mass = M × V × molar mass, volume = mass ÷ (molar mass × M) and molar mass = mass ÷ (M × V). The calculator converts every unit to grams, liters and mol/L before applying the formula.
Worked examples
- Mass needed: to make 250 mL of 0.5 M NaCl (58.44 g/mol): 0.5 × 0.250 × 58.44 = 7.305 g NaCl, made up to 250 mL with water.
- Molarity: 10 g of glucose (180.156 g/mol) in 500 mL: 10 ÷ 180.156 = 0.0555 mol; 0.0555 ÷ 0.5 L = 0.111 M (111 mM).
- Dilution: to make 100 mL of 250 mM from a 2 M stock: V₁ = 0.25 × 100 ÷ 2 = 12.5 mL of stock plus 87.5 mL of water (an 8× dilution).
The dilution equation C₁V₁ = C₂V₂
When you dilute a solution, the amount of solute does not change, so the stock concentration times the stock volume equals the final concentration times the final volume. Any one of the four values can be found from the other three. Use the same kind of concentration unit on both sides – both molar or both mass per volume – while volumes can be in any unit.
Concentration unit conversions
| Unit | Equals |
|---|---|
| 1 M (molar) | 1 mol/L = 1,000 mM = 1,000,000 µM |
| 1 mM | 0.001 M = 1 mmol/L = 1,000 µM |
| 1 µM | 10⁻⁶ M = 1,000 nM |
| 1 g/L | 1 mg/mL = 1,000 µg/mL = 0.1 % w/v |
| 1 % w/v | 1 g per 100 mL = 10 g/L |
| g/L → M | divide by molar mass (g/mol) |
Frequently asked questions
How do you calculate molarity?
Divide the moles of solute by the volume of solution in liters. If you know the mass, first convert it to moles by dividing by the molar mass: M = mass ÷ (molar mass × volume).
How do I make a 1 M solution?
Weigh out the molar mass of the compound in grams (for NaCl, 58.44 g), dissolve it in less than 1 L of water, then add water until the total volume is exactly 1 L. Always make up to the final volume rather than adding the solid to 1 L of water.
What is C1V1 = C2V2?
It is the dilution equation. The concentration and volume of the stock (C₁, V₁) multiplied together equal the concentration and volume after dilution (C₂, V₂), because the amount of solute stays the same.
What is the difference between molarity and molality?
Molarity is moles per liter of solution, while molality is moles per kilogram of solvent. Molality does not change with temperature, but molarity is more common in the lab because volumes are easy to measure.
How do I convert mM to M?
Divide by 1,000. For example 250 mM = 0.25 M. To go from µM to mM, also divide by 1,000.
Where do I find the molar mass?
Add up the atomic masses of every atom in the formula, or use our Molar Mass Calculator. For hydrates, include the water molecules, for example CuSO₄·5H₂O is 249.69 g/mol.