Percent Solution Calculator

What percent w/v means

A percent weight per volume figure is grams of solute per 100 mL of final solution: % w/v = (mass in g / volume in mL) × 100. A 5% w/v glucose solution therefore holds 5 g of glucose in every 100 mL. The denominator is the volume of the finished solution, not the volume of solvent added at the start.

Strictly, mixing a mass with a volume makes the percentage a convention rather than a true ratio, but it is the convention used throughout biology, clinical work and reagent preparation because it maps directly onto what a balance and a volumetric flask measure.

Worked example

Physiological saline is 0.9% w/v NaCl. How much salt does 500 mL require?

• Rearrange: mass = % × volume / 100.
• mass = 0.9 × 500 / 100
• mass = 4.5 g
• Check the equivalences: 0.9% w/v = 9 g/L = 9 mg/mL.

For dilute aqueous solutions, where density is close to 1 g/mL, 1% w/v = 10 g/L = 10 mg/mL = 10000 ppm. Those four expressions describe the same solution.

Choosing between w/v, v/v, w/w and molarity

The three percent bases differ in what they measure. w/v is mass per volume and suits solids dissolved in liquid. v/v is volume per volume and suits liquid mixtures such as 70% ethanol. w/w is mass per mass, which makes it independent of temperature because neither quantity expands on heating; concentrated acids are usually specified this way.

Percent notation is preferable when molar mass is unknown or meaningless: protein preparations, agar, gelatin, stains and undefined mixtures. Use molarity when the chemistry depends on the number of particles, as with reaction stoichiometry, equilibrium constants, buffer calculations and enzyme kinetics. A 1% w/v solution of two different salts contains different numbers of ions.

Common mistakes

• Confusing w/v with w/w. The two coincide only when density is near 1 g/mL. For a dense solution such as concentrated sulfuric acid the two figures differ substantially.
• Assuming ppm equals mg/L. That equality relies on a solvent density of 1 g/mL. In organic solvents or dense brines, ppm as a mass ratio and mg/L as a mass per volume diverge.
• Filling to the mark too early. Dissolving the solute changes the volume. Dissolve in part of the solvent first, then make up to the final mark.
• Treating % v/v as additive. Ethanol and water contract on mixing, so 70 mL of ethanol plus 30 mL of water gives less than 100 mL. Make up to volume rather than adding measured volumes together.

Converting units first? Use the volume and mass conversion tables.