Solution Concentration Converter – One Value, Every Unit
A concentration label can arrive in almost any form: 37 % w/w HCl on a reagent bottle, 0.9 % w/v saline on an IV bag, 10 mg/dL calcium on a lab report or 2.5 µg/L lead in a water test. This converter takes the one number you have and shows it in molarity, mass concentration, mass percent, ppm, mEq/L, molality and mole fraction. It also shows exactly which extra number each conversion needs, so nothing is quietly assumed.
Four denominators, seven families
Concentration units differ in what they divide by. mol/L, eq/L, g/L, % w/v and % v/v divide by the volume of solution. % w/w, ppm and ppb divide by the mass of solution. Molality (mol/kg) divides by the mass of solvent only, and mole fraction divides by the total moles. Within one family the units are fixed multiples of each other, so mg/dL to mg/L is just a factor of ten. Crossing between families needs a bridge:
- Molar mass
Mturns grams into moles (g/L ↔ mol/L, % w/w ↔ mol/kg). - Solution density
ρturns a volume of solution into a mass (g/L ↔ % w/w). - The n-factor turns moles into equivalents (mol/L ↔ eq/L).
- The density of the pure liquid solute links g/L to % v/v.
The bridges form a tree, so there is exactly one route between any two units. The unit map draws that tree and marks each missing bridge, which is why a value with no density can still give you mol/L but not ppm.
Reading a reagent bottle: concentrated hydrochloric acid
Concentrated HCl is sold as about 37 % w/w with a density, or specific gravity, near 1.18 g/mL. To get its molarity, weigh a litre, take the solute share, then divide by the molar mass:
w = 37.0 % w/w = 0.3700
γ = 1000 × ρ × w = 1000 × 1.18 × 0.3700 = 436.6 g/L
c = γ / M = 436.6 ÷ 36.458 = 11.98 mol/LThe same litre holds 743.4 g of water, so its molality is 11.98 ÷ 0.7434 = 16.11 mol/kg. Molality comes out a third higher because the same 11.98 mol share only 0.7434 kg of water, while the litre of solution weighs 1.18 kg.
% w/w vs % w/v vs % v/v
A bare percent sign is ambiguous, so this tool always says which one it means. % w/w is grams of solute per 100 g of solution and can never exceed 100. % w/v is grams per 100 mL of solution, and a dense solution can pass 100: concentrated sulfuric acid at 98 % w/w and 1.84 g/mL is about 180 % w/v. % v/v, used for alcoholic drinks, compares the volume of pure solute before mixing with the final volume. A 40 % v/v spirit is only about 33 % ethanol by mass, because ethanol is lighter than water.
Why ppm equals mg/L only in dilute water
Strictly, ppm is mass per mass (mg/kg). Water analysts call mg/L "ppm" because one litre of dilute water weighs almost exactly one kilogram. That shortcut breaks for anything dense or concentrated.
mEq/L in clinical chemistry
Electrolytes are often reported in milliequivalents per litre, which counts charge rather than particles. Sodium and chloride carry one charge, so mEq/L equals mmol/L. Calcium and magnesium carry two, so a serum calcium of 10.0 mg/dL is 2.495 mmol/L but 4.990 mEq/L. Typing the ion as Ca 2+ sets the n-factor from the charge automatically.
Temperature: volume units drift, mass units don't
Liquids expand when they warm, so every volume-based unit (mol/L, g/L, % w/v, % v/v) changes slightly with temperature even though nothing is added or removed. Mass-based units (% w/w, ppm, mol/kg, mole fraction) stay fixed. That is why precise work and colligative-property equations use molality, and why the density you enter should be measured at the temperature you care about.