Molarity Calculator | M = n/V

The Molarity Calculator solves for any variable in the fundamental concentration equation M = n/V, finding molarity from moles and volume, moles from concentration and volume, or volume from moles and concentration. A built-in dilution mode handles the lab workhorse equation C₁V₁ = C₂V₂ for preparing working solutions from stock concentrations.

• ›Three-way solve: click which variable to find, molarity, moles, or volume, and enter the other two.
• ›Unit flexibility: volume input accepts mL, L, or µL, no manual conversion needed.
• ›Dilution mode: C₁V₁ = C₂V₂ with four-way solve for any of the four unknowns, plus dilution factor output.
• ›Step-by-step working: every calculation shows the substitution and arithmetic so you can verify the result.

What Is Molarity?

Molarity (symbol M) is the most widely used measure of solution concentration in chemistry. It is defined as the number of moles of solute dissolved in exactly one litre of solution, not solvent. The unit is mol/L, commonly written as M (molar). A 1.0 M NaCl solution contains 1.0 mole of sodium chloride in every litre of the final solution.

Molarity is preferred over mass-based concentrations (like percent by mass) because it directly counts molecules, which is what matters in chemical reactions. The stoichiometry of a reaction is always expressed in moles, so working in molarity allows direct conversion from volume to moles without knowing the density of the solution.

• ›Molarity is temperature-dependent, volume changes with temperature, so M changes slightly.
• ›Molality (mol/kg solvent) is temperature-independent and used for colligative property calculations.
• ›At low concentrations (dilute solutions), molarity ≈ molality numerically.
• ›Standard solutions are often prepared at exactly 25°C to ensure precise volume.

The Dilution Equation C₁V₁ = C₂V₂

When you dilute a solution, you add more solvent but the number of moles of solute stays constant. This conservation of moles gives the dilution equation: C₁V₁ = C₂V₂, where C₁ and V₁ are the initial concentration and volume, and C₂ and V₂ are the final values. This equation can be solved for any of the four variables by simple rearrangement.

The dilution factor (DF) describes how much the concentration has been reduced: DF = C₁/C₂ = V₂/V₁. A 1:10 dilution means 1 part stock in 10 parts final solution, giving DF = 10. Serial dilutions (repeated 1:10 dilutions) are commonly used in microbiology for bacterial counts and in ELISA assays for antibody titrations.

• ›Both concentrations must be in the same units (both mol/L, or both mg/mL, etc.).
• ›Both volumes must be in the same units (both mL, or both L).
• ›C₁V₁ = C₂V₂ works for any concentration unit, molar, mass/volume, percent.
• ›For serial dilutions, apply the equation repeatedly: first dilution output becomes the next input.

Concentration Units in Chemistry

While molarity (mol/L) is the standard in most lab contexts, other concentration units are used for specific applications:

• ›Molality (m): mol solute / kg solvent. Used for boiling point elevation and freezing point depression calculations. Temperature-independent.
• ›Normality (N): equivalents of solute per litre. Used in acid-base and redox titrations. 1 M H₂SO₄ = 2 N (two protons per molecule).
• ›Mass percent (% w/w): grams solute per 100 g solution. Common for concentrated commercial reagents (e.g. 37% HCl).
• ›ppm / ppb: µg/mL (ppm) and ng/mL (ppb), used for trace analytes in environmental and clinical chemistry.

Preparing Solutions in the Lab

The correct procedure for preparing a solution of known molarity is critical for reproducibility. Always add solute to less than the target volume of solvent, dissolve completely, then transfer to a volumetric flask and make up to exactly the target volume. Never add the target volume of water directly to a mass of solute in a beaker, the final volume will be slightly off due to volume of mixing.

• ›Use a calibrated volumetric flask, not a beaker or Erlenmeyer, for accurate volume.
• ›For concentrated acids: add acid slowly to water, never water to acid (exothermic).
• ›Check solution density if preparing from a concentrated reagent (e.g. 37% HCl): use ρ × %purity ÷ M_r.
• ›Allow the solution to equilibrate to the reference temperature before making up to volume.