“Concentration” is four different numbers wearing one name — percent by mass, percent by volume, grams per litre, ppm — and recipes, labels and lab protocols each mean a different one. This concentration calculator computes all of them from the same two measurements (how much solute, how much mixture), and adds the conversion laboratories ask for most: turning a percentage on a reagent bottle into molarity, using the solution’s density and the solute’s molar mass.
The Percent Family, Disentangled
Three percents circulate and labels rarely say which. Percent w/v (weight/volume): grams of solute per 100 mL of solution — the default of pharmacies and this calculator’s percent mode: 5 g dissolved and made up to 500 mL is 5 ÷ 500 × 100 = 1.0 percent w/v, also 10 g/L and 10,000 ppm (as mg/L). Percent w/w: grams per 100 g of solution — the reagent-bottle standard, used in the molarity mode. Percent v/v: millilitres per 100 mL, the language of alcoholic drinks and liquid-liquid mixes. Same word, three denominators; the first question about any percentage is “of what, per what?”
Percent to Molarity: The Bottle Conversion
Concentrated acids are sold by percent and used by molarity, and the bridge is density: molarity = (percent w/w × density × 10) ÷ molar mass. The factor 10 converts percent (per 100 g) and density (per mL) into grams of solute per litre. The classic worked example is reagent hydrochloric acid: 37 percent w/w, density 1.19 g/mL, molar mass 36.46 g/mol → (37 × 1.19 × 10) ÷ 36.46 = 12.08 mol/L — the “12 M concentrated HCl” of every laboratory’s muscle memory, derived rather than recalled. Sulfuric acid the same way (98 percent, 1.84, 98.08) lands at about 18.4 M, matching its fearsome reputation.
ppm and Its Neighbours
Parts per million is the dialect of dilute solutions: 1 ppm = 1 mg of solute per litre of solution (for water-density liquids), so the g/L figure multiplied by 1,000 reads directly in ppm. Below it sits ppb (µg/L), the unit of trace contaminants and drinking-water standards; above it, percent (1 percent = 10,000 ppm — the conversion that makes the 1 percent saline example above double as a 10,000 ppm solution). Environmental and clinical work lives at ppm and below, food and pharmacy at percent, and stock solutions at g/L or molarity; a fluent chemist converts between them without noticing, which is the skill this page drills.
Mass Concentration vs Molar Concentration
Two of the hub’s perennial questions reduce to this distinction. Mass concentration (g/L) asks how much stuff; molar concentration (mol/L) asks how many particles — and reactions count particles. Converting between them needs exactly one fact: the molar mass, which is why the grams-to-moles tool is this calculator’s sibling. A 10 g/L sodium chloride solution is 10 ÷ 58.44 = 0.171 M; the same 10 g/L of glucose is 10 ÷ 180.16 = 0.0555 M. Same mass concentration, threefold different molarity — the reason protocols that say only “10 g/L” are complete recipes while protocols that need reaction ratios must speak in moles.
Making Solutions to a Target
The calculator inverts cleanly by hand: to make a litre of 1 percent w/v, dissolve 10 g and dilute to the mark (not into a litre of solvent — volumes are not additive, and “dilute to volume” is the volumetric flask’s whole purpose). For a target molarity from a percent stock, compute the stock’s molarity here, then use the dilution relation (stock volume = target moles ÷ stock molarity). Temperature nibbles at all of it — volumes expand measurably between a cold store room and a warm bench — which is why analytical standards state their reference temperature and why routine work wisely ignores the third decimal.
Common Mistakes
Reading a w/w label as w/v (for dense acids the error exceeds 15 percent). Using solution volume where solution mass belongs. Forgetting that ppm-as-mg/L assumes water-like density — in a dense brine or an oil, ppm by mass and mg/L part company. Mixing up “dissolve in 500 mL” with “dilute to 500 mL”: the first gives a weaker solution than the second, every time. And quoting percent to three decimals from a two-decimal measurement — precision theatre that the extra digits cannot support.
Related Tools
The concentration family continues in the Chemistry Calculators hub — the Bleach Dilution Calculator applies percent-to-ppm thinking to sanitation, and the Mixing Ratio Calculator handles proportion-based mixing.
Frequently Asked Questions
How do you calculate percent concentration?
Percent (w/v) = grams of solute ÷ millilitres of solution × 100. Five grams made up to 500 mL is 1.0 percent. Percent (w/w) uses grams of solution in the denominator; percent (v/v) uses millilitres of solute.
How do you convert percent to molarity?
Molarity = (percent w/w × density in g/mL × 10) ÷ molar mass. Reagent HCl at 37 percent, density 1.19 and molar mass 36.46 gives (37 × 1.19 × 10) ÷ 36.46 ≈ 12.08 M.
How many ppm is a 1 percent solution?
10,000 ppm — one percent is one part per hundred, and scaling to parts per million multiplies by 10,000. The same 1 percent w/v solution is also 10 g/L.
What is the difference between g/L and molarity?
g/L (mass concentration) counts grams; molarity counts moles — particles. Divide g/L by the molar mass to get molarity: 10 g/L of NaCl is 0.171 M, while 10 g/L of glucose is only 0.0555 M.
Why do I need density to convert percent to molarity?
Percent w/w is per gram of solution, while molarity is per litre. Density is the exchange rate between mass and volume for that specific solution — without it the conversion has a missing dimension.
Is ppm the same as mg/L?
For dilute aqueous solutions, yes, to excellent approximation, because a litre of the solution weighs about a kilogram. In dense or non-aqueous liquids, ppm by mass and mg/L diverge and must be distinguished.