Molarity Calculator

Molarity (M) is the number of moles of solute per liter of solution. It is the most commonly used concentration unit in research chemistry and is often written as mol/L or simply M.

The core formula is: mass (g) = concentration (mol/L) × volume (L) × MW (g/mol)

Molarity depends on the molecular weight (MW) of the solute — also called molar mass. MW tells you how many grams equal one mole of the substance. For example, NaCl has a MW of 58.44 g/mol, meaning 58.44 g of NaCl equals exactly 1 mole.

Common sub-units: millimolar (mM, 10⁻³ M), micromolar (μM, 10⁻⁶ M), and nanomolar (nM, 10⁻⁹ M). Drug research often works in the nM–μM range, while buffer preparation typically uses mM–M concentrations.

Need to work with reaction quantities instead? Try the stoichiometry calculator for equivalents, reagent tables, and yield calculations.

Preparing a solution at a target molarity requires careful technique. The most common mistake is adding solute to a pre-measured volume of solvent — this produces an incorrect concentration because the solute displaces volume.

Correct procedure:

1. Calculate the required mass using the molarity formula
2. Weigh the solute on an appropriate balance (analytical for mg, microbalance for μg)
3. Dissolve the solute in approximately 80% of the final volume
4. Ensure complete dissolution before proceeding
5. Bring to the final volume (QS — “quantum sufficit”) using a volumetric flask or graduated cylinder
6. Mix thoroughly

Key: “Dissolve in 80% volume, then bring to final volume” — not “add to final volume of solvent.”

The dilution equation C1 × V1 = C2 × V2 relates the concentration and volume of a stock solution (C1, V1) to the concentration and volume of the diluted solution (C2, V2).

This equation works because the number of moles of solute remains constant during dilution — you are only adding more solvent (diluent).

Key constraints:

• C2 must be less than C1 (you cannot dilute to a higher concentration)
• V1 must be less than V2 (stock volume is a portion of the final volume)
• Diluent volume = V2 − V1

Worked example: To make 10 mL of 1 mM from a 10 mM stock: V1 = (1 × 10) / 10 = 1 mL. Add 1 mL stock to 9 mL diluent.

For more complex dilution workflows including DMSO tracking and reconstitution, see the dedicated dilution calculator.

A serial dilution creates a series of progressively more dilute solutions by repeatedly diluting a portion of the previous solution. This is the standard technique for creating dose-response curves, standard curves, and titration series.

Common dilution schemes:

• 1:10 (10-fold): Transfer 10 μL to 90 μL diluent. Creates log-scale concentration series.
• 1:2 (2-fold): Transfer 50 μL to 50 μL diluent. Common in ELISA and dose-response assays.
• 1:3 (3-fold): Transfer 33 μL to 67 μL diluent. Balances resolution and range.

Error propagation: Pipetting errors accumulate across steps. A 5% pipetting error at each step compounds to approximately 26% cumulative error by tube 6. This is why later tubes in a serial dilution are less reliable — always label tubes before starting and mix thoroughly at each step.

Chemistry uses multiple concentration units. The most common in research:

• Molarity (M): moles of solute per liter of solution. The standard.
• Percent (%w/v, %w/w, %v/v): Always specify which type. 10% w/v means 10 g per 100 mL. Never use bare “%” without specifying the type.
• Normality (N): N = n × M, where n is the number of equivalents per mole. 1 M H₂SO₄ = 2 N because sulfuric acid donates 2 protons. Still used in titration and acid-base chemistry.
• Parts per million (ppm): mg/L for dilute aqueous solutions. Common in environmental and water quality testing.