Percent Concentration Converter (% w/v, % w/w, % v/v, ppm ↔ mol/L)
The reagent bottle reads 37%, the protocol calls for 12 mol/L, and another SOP writes 43.7% (w/v) — all three describe the same bottle of concentrated HCl. The difficulty with percent concentration is not the arithmetic, but the fact that “%” has three mutually incompatible definitions, and labels rarely specify which one is meant.
Three types of “%” — not just a decimal difference
| Notation | Definition | Who uses it |
|---|---|---|
| % (w/v) | grams of solute per 100 mL of solution | Default in biology labs — SDS, agarose, NaCl solutions |
| % (w/w) | grams of solute per 100 g of solution | Reagent bottle labels, industrial chemicals; concentrated acids and bases almost always use this |
| % (v/v) | mL of solute per 100 mL of solution | Liquid-in-liquid: ethanol, glycerol, Triton |
The difference between w/v and w/w comes down to solution density:
% (w/v) = % (w/w) × solution density (g/mL)
Concentrated HCl is labeled 37% (w/w); density 1.18 g/mL gives 43.7% (w/v). Confusing the two produces an 18% concentration error — not obvious enough to trigger suspicion.
One unit conversion requires no prerequisites:
1% (w/v) = 10 g/L = 10 mg/mL (holds for any solute)
Molecular weight is only needed when converting to mol/L.
Checking the math: concentrated HCl should be 12 M
37% (w/w) × 1.18 g/mL = 437 g/L ÷ 36.46 g/mol = 12.0 mol/L — the textbook value. 70% (v/v) ethanol: 0.789 g/mL × 700 mL/L ÷ 46.07 g/mol = 12.0 mol/L, also equal to 0.7 × 17.1 M. Both independent reference values agree, confirming the conversion chain is correct.
ppm is not always mg/L
ppm is strictly a mass ratio: mg solute per kg solution.
mg/L = ppm × solution density (kg/L)
For dilute aqueous solutions (density ≈ 1 kg/L), 1 ppm ≈ 1 mg/L — sufficient for water samples and buffers. For concentrated brines, organic solvents, or gases it is not valid. This tool uses the strict definition; density defaults to 1.00.
Ethanol cannot be prepared by “adding water to make up the total”
“70 mL absolute ethanol + 30 mL water” does not give 100 mL. Hydrogen bonding causes volume contraction on mixing — the classic example is 50 mL water + 50 mL ethanol yielding only ~97 mL.
The correct procedure is always bring to volume: measure 70 mL absolute ethanol, then add water to the 100 mL mark. The “70 + 30” approach gives a smaller volume and higher concentration, with a ratio-dependent offset.
Glycerol, isopropanol, and acetic acid have the same problem. This tool reports “how much to take and what volume to bring it to” — not “how much solvent to add” — because the latter is wrong for these solvents. The two approaches are equivalent only when solute volume is negligible.
X× stock solutions
“10×” is a dilution factor, not a concentration unit: take 1 part stock and bring to a final volume of 10 parts (1 part stock + 9 parts solvent). Adding 10 parts solvent gives an 11-fold dilution. All components — buffer salts included — are diluted by the same factor.
Related tools
For concentration–volume–mass interconversions given molecular weight, see Molarity Calculator; for stock dilutions and serial dilutions, see Dilution Calculator; for preparing buffers at a target pH, see Buffer pH Calculator; for nucleic acid OD260 and ng/pmol conversions, see Nucleic Acid Concentration Calculator.
FAQ
What is the difference between % (w/v) and % (w/w)?
The denominator. % (w/v) is g of solute per 100 **mL of solution**; % (w/w) is g of solute per 100 **g of solution**. They differ by solution density: % (w/v) = % (w/w) × density (g/mL). Biology labs default to w/v; reagent bottle labels (37% HCl, 25% ammonia) are almost always w/w. HCl density 1.18 makes 37% (w/w) equal to 43.7% (w/v) — mixing them up gives an 18% error.
What is 0.9% saline in mM?
154 mM. 0.9% (w/v) = 9 g/L; NaCl molar mass 58.44; 9 ÷ 58.44 = 0.154 mol/L. If your result is not near 154 mM, you most likely entered 0.9% as w/w, or used the wrong molar mass.
How many g/L is 1%? Does it depend on the solute?
No. **1% (w/v) is always 10 g/L = 10 mg/mL**, regardless of the solute — by definition it is g per 100 mL. Molecular weight is only needed to go further to mol/L. 1% (w/w) does require density.
Is ppm the same as mg/L?
Approximately, for dilute aqueous solutions — but strictly, no. ppm is a **mass ratio**: mg solute per kg solution. To get mg/L, multiply by solution density (kg/L). Near density 1, 1 ppm ≈ 1 mg/L, which is adequate for water samples and buffers. Not valid for concentrated brines, organic solvents, or gases.
To make 70% ethanol, is it 70 mL ethanol plus 30 mL water?
No. Ethanol and water contract on mixing — 50 mL + 50 mL gives only ~97 mL. The correct method is **bring to volume**: measure 70 mL absolute ethanol, then add water to the 100 mL mark. The "70 + 30" shortcut gives a smaller volume and higher concentration, with a ratio-dependent offset. Glycerol, isopropanol, and acetic acid behave the same way, so this tool reports "how much to take and what volume to bring to" — not "how much solvent to add."
To dilute a 10× stock, do I add 10 parts or 9 parts of solvent?
Take 1 part stock and **bring to a final volume of 10 parts** — meaning 1 part stock + 9 parts solvent. Adding 10 parts solvent gives an 11-fold dilution, ~9% too dilute. Also, **all** components — buffer salts, EDTA, detergents — are diluted by the same factor; diluting a stock cannot adjust one component independently.
Why doesn't the mol/L result match my reagent's datasheet?
Check three things: (1) is the label % given as w/w or w/v? Concentrated acids and bases are typically w/w and require solution density; (2) is the molar mass for the anhydrous form or a hydrate? CuSO₄ is 159.6, CuSO₄·5H₂O is 249.7 — a 56% difference; (3) for % (v/v) of a liquid reagent, enter **solute** density, not solution density. Any one of these errors produces a result that looks plausible but is wrong.
Related tools
OD₆₀₀ to Cell Concentration Calculator (Dilution Correction / Plate Reader Path-Length / Inoculum Back-Calculation)
Convert OD₆₀₀ readings to cells/mL and total cell count, with dilution back-calculation, path-length correction, and linear-range checking.
Gel Band Size Estimation (DNA bp / Protein kDa, Semi-log Standard Curve)
Fit a semi-log curve to marker migration distances and estimate unknown band sizes; flags linear-interpolation overestimation and out-of-range extrapolation.
Cell Split Ratio & Regrowth Time Calculator — Back-Calculate the Right 1:N Ratio from Doubling Time
Calculate regrowth time after a 1:N cell split, or back-calculate the ratio needed. Diluting twice as much buys only one extra doubling, not twice the time.
Buy me a coffee