Percent Concentration Converter (% w/w, % w/v, % v/v, mg/mL)

% w/w, % w/v, % v/v, mg/mL, ppm and molarity, joined by the one number that separates them: the solution’s density. Concentrated hydrochloric acid is 37% w/w and 44.03% w/v — and 50 mL of ethanol plus 50 mL of water makes 96.5 mL, not 100.

Last updated 24 Sep 2026

Percent strength, four ways, through the density

Any percent + density → all of them

What is your number?USP General Notices 8.140 defines the first three. Note that % w/v is grams per 100 millilitres, so it is not a percentage of anything at all.

How much?In the unit above. The default is concentrated hydrochloric acid as it is supplied: 37% w/w.

Density of the SOLUTION, g/mLTHIS IS THE NUMBER THE CONVERSION CANNOT BE DONE WITHOUT. It is on the bottle. Concentrated hydrochloric acid is 1.19; concentrated sulfuric 1.84; 50% sodium hydroxide 1.52; dilute aqueous anything, 1.00.

Molar mass of the solute, g/molOptional — leave at 0 to skip the molarity rows. 36.46 for HCl, 58.44 for NaCl, 342.30 for sucrose, 98.08 for H2SO4.

Density of the PURE LIQUID solute, g/mLOptional, and only meaningful when the solute is a liquid. Leave at 0 to skip the % v/v and alcohol rows. Ethanol at 20 °C is 0.78934; glycerol 1.261; acetone 0.7845.

A scale drawing, not a circuit, and the two columns are drawn to one scale BY VOLUME. The right-hand column is 100 mL of your solution; the left-hand one is 100 g of the same solution, and its height is 100 divided by the density, so it is shorter than 100 mL whenever the solution is denser than water and taller when it is lighter. The horizontal line is the 100 mL mark carried across, so the difference in height IS the difference between the two percentages. Both columns hold the same solution at the same strength; the numbers beneath them are the grams of solute in each, and those two numbers are the % w/w and the % w/v. They are equal only when the two columns are the same height, which happens at a density of exactly 1.000 g/mL and nowhere else.

44.0300% w/vExample

concentrated hydrochloric acid as supplied: 37% w/w at a density of 1.19 g/mL

One multiplication, and it is the density

% w/v = % w/w × ρ · mg/mL = 10 × % w/v · ppm = 10 000 × % w/w · mol/L = 10 × % w/v ÷ M · % v/v = % w/w × ρ ÷ ρ_solute

ρ: density of the SOLUTION in g/mL, off the bottle. This is the quantity the conversion cannot be done without
ρ_solute: density of the pure liquid solute in g/mL. Only volume per cent needs it
M: molar mass of the solute in g/mol. Only the molarity rows need it
% w/v: grams of solute per 100 mL of solution. Not a percentage of anything

Worked example

concentrated hydrochloric acid as supplied: 37% w/w at a density of 1.19 g/mL
A litre of this acid weighs 1.19 × 1000 = 1,190 g, of which 37% is HCl: 440.3 g
That is 44.030 g per 100 mL, so 44.03% w/v — seven percentage points above the 37% on the label, and the difference is entirely the density
Which is also 440 mg/mL and 440 g/L, since those are the same number
Divide by the molar mass, 36.46 g/mol: 12.076 mol/L — which is why every lab calls this bottle “12 molar”. The 37 and the 12 are the same acid
And in ppm by mass it is 370,000, exactly 37% × 10 000. Going the other way, through % w/v and assuming water, would give 440,300 ppm — 19% too high

Four things written as “%”, and what each one means

USP General Notices 8.130 settles which one a bare “percent” means, and the answer depends on what is dissolved in what: weight in weight for mixtures of solids and semisolids, weight in volume for solids or suspensions in liquids, volume in volume for liquids in liquids, and weight in volume again for gases in liquids. So “5% cream” and “5% saline” and “5% vinegar” are three different kinds of number, and nothing on the label says so.
Written	Means	USP’s words	Coincides with the others when
% w/w	g of solute per 100 g of solution	“the number of g of a solute in 100 g of solution”	always the same as itself; equals % w/v only at 1.000 g/mL
% w/v	g of solute per 100 mL of solution	“the number of g of a solute in 100 mL of solution”	the density is exactly 1.000 g/mL
% v/v	mL of liquid solute per 100 mL of solution	“the number of mL of a solute in 100 mL of solution”	never, for ethanol — volumes do not add
mg/mL	milligrams of solute per millilitre of solution	not a percentage at all	always: 1% w/v = 10 mg/mL exactly, by arithmetic
ppm	mg of solute per kg of solution — a MASS ratio	not in the General Notices	the density is 1.000 g/mL, when 1% w/v = 10 000 ppm

What 1% w/w becomes at each solution density

The fourth column never moves, because ppm by mass and % w/w are the same ratio in different units — 1% w/w is 10 000 ppm exactly, always. The fifth column is what you get by going through % w/v and assuming water, and the last column is how wrong that is. For dilute aqueous solutions it is a fraction of a per cent and nobody cares; for concentrated hydrochloric acid at 1.19 g/mL it is -16.0%, and for concentrated sulfuric at 1.84 it is -45.7%. The familiar rule “1% w/v = 10 mg/mL = 10 000 ppm” is two identities and one approximation, and the page keeps them apart.
Density (g/mL)	% w/v	mg/mL	ppm by mass	ppm if you assume density 1.000	Error in that assumption (%)
0.800	0.8000	8.000	10,000	12,500.0	25.00
0.900	0.9000	9.000	10,000	11,111.1	11.11
1.000	1.0000	10.000	10,000	10,000.0	0.00
1.050	1.0500	10.500	10,000	9,523.8	-4.76
1.100	1.1000	11.000	10,000	9,090.9	-9.09
1.190	1.1900	11.900	10,000	8,403.4	-15.97
1.400	1.4000	14.000	10,000	7,142.9	-28.57
1.840	1.8400	18.400	10,000	5,434.8	-45.65

Ethanol in water at 20 °C: mass per cent, volume per cent and the contraction between them

Densities from Perry’s handbook. The third column is computed, not quoted: % v/v = % w/w × ρ(solution) ÷ ρ(ethanol), which is exact. The last column is the interesting one — it is how much less the mixture measures than the two pure liquids did separately, and it peaks in the middle of the range at about 3.6%. That is why an ethanol solution’s strength is defined against the total volume AFTER mixing, and why alcohol strength tables exist at all: you cannot get from a recipe to a strength by adding volumes. The US proof column is exactly twice the ABV, which 27 CFR 30.11 makes a definition rather than an approximation.
% w/w (ABW)	Solution density (g/mL)	% v/v (ABV)	US proof	How much the volumes shrank (%)
0	0.99823	0.000	0.00	—
10	0.98187	12.439	24.88	0.964
20	0.96864	24.543	49.09	2.172
30	0.95382	36.251	72.50	3.137
40	0.93518	47.390	94.78	3.601
50	0.91384	57.886	115.77	3.659
60	0.89113	67.737	135.47	3.446
70	0.86766	76.946	153.89	3.022
80	0.84344	85.483	170.97	2.382
90	0.81797	93.264	186.53	1.459
95	0.80424	96.793	193.59	0.822
100	0.78934	100.000	200.00	-0.000

Proof: one definition still in force, one abolished in 1980

The American definition is clean: proof is twice the ABV, full stop, and the only subtlety is that it is stated at 60 °F while the OIML and European ABV is defined at 20 °C, so the two are not measuring the same liquid at the same temperature. The British system is messier than it is usually made to sound. The 57.15% everyone quotes comes from the 1816 specific-gravity definition. The Order that abolished proof gives an equivalence of 2.595 litres of alcohol per proof gallon, and with the imperial gallon at 4.54609 litres that is 57.0820% — a different number. The same Order’s other conversions are rounded to whole per cent and imply anything from 55.9% to 57.5%, so there is no single exact British figure to recover. This page offers both and labels them.
System	Definition	100° proof is	40% ABV is	Status
United States	“The ethyl alcohol content of a liquid at 60 degrees Fahrenheit, stated as twice the percent of ethyl alcohol by volume” (27 CFR 30.11)	50.00% ABV	80° proof	Current. Exact by definition, with no table and no rounding
United Kingdom, traditional	A spirit at proof weighs 12/13 of an equal volume of water at 51 °F — a specific gravity of 0.923077, or 923 kg/m³	57.15% ABV	69.99° proof	Abolished 1 January 1980 by SI 1979/241
United Kingdom, as the abolishing Order computes it	“One gallon of spirits at proof shall be taken to be equivalent to 2.595 litres of alcohol” (SI 1979/241, art. 2(7))	57.08% ABV	70.07° proof	Historical. 0.12% away from the traditional figure
The “× 1.75” rule of thumb	proof = 1.75 × ABV	57.14% ABV	70° proof	A rounding of the traditional figure, accurate to 0.012%

Four numbers, one percent sign, and a density in between

“10%” on a bottle is four different numbers, and which one it is depends on what is dissolved in what. Per cent weight in weight is grams of solute per 100 grams of solution. Per cent weight in volume is grams of solute per 100 millilitres of solution — which means it is not a percentage of anything at all, since grams and millilitres are different quantities. Per cent volume in volume is millilitres per 100 millilitres. And mg/mL is a fourth thing that is routinely written as a percentage by moving a decimal point. USP General Notices 8.140 defines the first three and 8.130 says which one a bare “percent” means: weight in weight for solids and semisolids, weight in volume for solids dissolved in liquids, volume in volume for liquids in liquids.

The bridge between % w/w and % w/v is the solution’s density, and that is the whole reason this page exists. % w/v = % w/w × ρ, with ρ in g/mL. They are equal when and only when the density is exactly 1.000 g/mL, which is water and almost nothing else. Concentrated hydrochloric acid, the default here, is supplied at 37% w/w and has a density of 1.19 g/mL — so it is 44.03% w/v, 440 mg/mL and 12.08 mol/L. That last figure is the check worth making: every laboratory calls concentrated hydrochloric acid “12 molar”, and 37 × 1.19 × 10 ÷ 36.46 comes out at 12.076. The 37 and the 12 are the same bottle, and the 1.19 is what connects them.

1% w/v is 10 mg/mL exactly, and 10 000 ppm only if the solution is water-like. The first is pure arithmetic: one gram in 100 mL is 0.01 g/mL is 10 mg/mL, and nothing can make it otherwise. The second is an approximation, because ppm is a ratio of masses. 1% w/w IS 10 000 ppm exactly, always. Going via % w/v you have to divide by the density, and for concentrated hydrochloric acid that is a 16% error. The page prints the correct ppm and the water-assumption ppm side by side, with the gap between them, so you can see whether it matters for your solution.

Volumes do not add, and this is the best fact on the page. Mix 50.0 mL of absolute ethanol with 50.0 mL of water at 20 °C and you do not get 100 mL. You get about 96.5 mL. The arithmetic, from Perry’s density table: 50 mL of ethanol at 0.78934 g/mL is 39.467 g, 50 mL of water at 0.99823 is 49.911 g, so the mixture weighs 89.379 g and is 44.16% ethanol by mass. A 44.16% w/w ethanol solution has a density of 0.92652 g/mL, so 89.379 g of it occupies 96.467 mL. The volume has shrunk by 3.53 mL, which is 3.5 per cent, because ethanol and water molecules hydrogen-bond and pack more closely together than either does alone. Merck’s independent table, which maps mass per cent to volume per cent directly, gives 96.6 mL — the same answer to a tenth of a millilitre from a different source. And the consequence is the one people trip over: that mixture is 51.83% ABV, not 50%, because ABV is measured against the total volume AFTER mixing. This is why alcohol strength tables exist. You cannot dilute a spirit by adding volumes and predict the result arithmetically.

Proof, and why there are three British answers. American proof is exactly twice the alcohol by volume — 27 CFR 30.11 defines it that way, at 60 °F, so an 80 proof bottle is 40% ABV with no table involved. British proof was a different definition entirely: a spirit was at proof when it weighed twelve thirteenths of an equal volume of water at 51 °F, a specific gravity of 0.9231 or about 923 kg/m³, which corresponds to the 57.15% ABV usually quoted. It was abolished on 1 January 1980. The instrument that abolished it, SI 1979/241, contains the only precise equivalence in British law — one gallon of spirits at proof is 2.595 litres of alcohol — and that works out at 57.08%, not 57.15%. The same Order’s other conversions are rounded to whole percentages and imply anything between 55.9% and 57.5%. So the honest position is that the British figure is historical, that it is about 57.1% ABV, and that the fourth significant figure depends on which document you read.

What this page does not do. It will give you a molarity if you type a molar mass, because the arithmetic is one division — but it does not do dilutions, serial dilutions or the laboratory molarity case. The laboratory utilities section owns C1V1 = C2V2, serial dilution and molarity from a mass, and a second answer maintained in two places is worse than one answer in one place. For parts per million in a gas, where ppm means a ratio of VOLUMES and needs a molar mass, see the gas concentration converter. For calcium and magnesium expressed four ways see the water hardness converter. For the logarithmic side of solution chemistry see the pH and hydrogen ion converter, which makes the same kind of argument about temperature. And for the density itself — including why a specific gravity needs two temperatures stated, not one — see the density and specific gravity converter.

Frequently asked questions

Is 10% w/v the same as 10% w/w?

Only if the solution’s density is exactly 1.000 g/mL. % w/v = % w/w × density, so a 10% w/w solution at 1.19 g/mL is 11.9% w/v, and a 10% w/w solution at 0.90 g/mL is 9.0% w/v. For dilute aqueous solutions the two are within a fraction of a per cent and the distinction is academic; for anything concentrated, or any organic solvent, it is not.

What is % w/v actually a percentage of?

Nothing. It is grams of solute per 100 millilitres of solution — a mass over a volume, wearing a percent sign because 1 g per 100 mL happens to look like 1%. USP defines it that way and it is universal in pharmacy and in the lab, but it is a concentration in disguised units: 1% w/v is 10 g/L, which is 10 mg/mL.

Is 1% w/v really 10 000 ppm?

Only for a solution whose density is 1.000 g/mL. ppm is a ratio of masses, so it maps exactly onto % w/w: 1% w/w is 10 000 ppm, always, for everything. Getting there from % w/v means dividing by the density, which for concentrated hydrochloric acid at 1.19 g/mL makes 1% w/v 8,403 ppm rather than 10 000. The page prints both.

Why doesn’t 50 mL of ethanol plus 50 mL of water make 100 mL?

Because volumes are not additive. At 20 °C the mixture comes to about 96.5 mL — a contraction of roughly 3.5 mL, or 3.5 per cent — because ethanol and water molecules hydrogen-bond to each other and pack more tightly than either liquid does on its own. The result is 51.8% ABV, not 50%. This is computed here from Perry’s density table and cross-checked against Merck’s, which agree to a tenth of a millilitre.

How do I convert ABV to ABW?

% w/w = % v/v × ρ(pure solute) ÷ ρ(solution). Both densities are needed and that is exact — no table required. For ethanol at 20 °C the pure density is 0.78934 g/mL, so a 40% ABV spirit whose solution density is 0.948 g/mL is 33.31% w/w. Enter the ABV, the solution density and 0.78934 as the pure solute density and this page will do it. Without the solution density there is no conversion, which is why the official alcoholometric tables exist.

Is US proof exactly twice the ABV?

Yes, by regulation. 27 CFR 30.11 defines proof as “the ethyl alcohol content of a liquid at 60 degrees Fahrenheit, stated as twice the percent of ethyl alcohol by volume”. So 80 proof is 40% and 151 proof is 75.5%, exactly. The only fine print is the temperature: American proof is stated at 60 °F and the European ABV at 20 °C, so a strength figure does not transfer between them without a small temperature correction.

What was UK proof, and is it still used?

It was abolished on 1 January 1980 by SI 1979/241, which replaced it with percentage alcohol by volume at 20 °C. A spirit at 100° British proof was about 57.15% ABV, from an 1816 definition based on specific gravity — twelve thirteenths that of water at 51 °F. The abolishing Order’s own arithmetic gives 57.08% instead, and its other conversions are rounded to whole per cent. Treat it as history with a fourth digit that depends on the source.

Does this page do dilutions or molarity from a mass?

It will give you a molarity if you type a molar mass, since that is one division. It does not do C1V1 = C2V2, serial dilutions or the full laboratory molarity case — the laboratory utilities section owns those, and duplicating them here would mean two answers to maintain.

Related calculators

References

United States Pharmacopeia. General Notices, 8.130 (Percent) and 8.140 (Percentage Concentrations). The definitive statement of the three percentages: w/w is “the number of g of a solute in 100 g of solution”, w/v “the number of g of a solute in 100 mL of solution”, v/v “the number of mL of a solute in 100 mL of solution”. And 8.130 settles which one an unqualified “percent” means: w/w for mixtures of solids and semisolids, w/v for solutions or suspensions of solids in liquids, v/v for solutions of liquids in liquids, and w/v again for solutions of gases in liquids.
Perry’s Chemical Engineers’ Handbook, 7th edition, density of ethanol-water mixtures at 20 °C, served in tenth-of-a-per-cent steps by handymath.com’s ethanol-water calculator, which names Perry’s as its source. Its end points are the accepted ones — 0.78934 g/mL for absolute ethanol and 0.99823 for water — which is why it was preferred to the Merck table below. Used to compute the volume contraction on mixing.
Merck, Tabellen für das Labor, ethanol-water density and mass-per-cent / volume-per-cent table at 20 °C, reproduced at wissen.science-and-fun.de. The independent cross-check on the contraction figure. Its mass-to-volume mapping agrees with Perry’s to 0.08 percentage points at 44% w/w, although its absolute densities run 0.18% high because it uses 0.79074 g/mL for pure ethanol.
27 CFR 30.11 (TTB Gauging Manual), Meaning of terms. “Proof. The ethyl alcohol content of a liquid at 60 degrees Fahrenheit, stated as twice the percent of ethyl alcohol by volume.” The same section defines proof spirits as the liquid containing half its volume of ethyl alcohol “of a specific gravity of seven thousand nine hundred and thirty-nine ten-thousandths (0.7939) in vacuum at 60 degrees Fahrenheit referred to water at 60 degrees Fahrenheit as unity”. That 0.7939 is recovered here from independent data — ethanol at 15.56 °C over Kell’s water at the same temperature gives 0.79391.
The Alcoholic Liquors (Amendment of Enactments Relating to Strength and to Units of Measurement) Order 1979, SI 1979/241, in operation 1 January 1980. Fetched from legislation.gov.uk. This is the instrument that abolished proof in the United Kingdom and replaced it with percentage alcohol by volume at 20 °C. Its article 2(7) gives the only precise equivalence in the document: “one gallon of spirits at proof shall be taken to be equivalent to 2.595 litres of alcohol”, which makes 100° proof 57.08% ABV rather than the 57.15% usually quoted. Its other conversions are rounded to whole per cent and imply anything from 55.9% to 57.5%.
Kell, G.S. Density, thermal expansivity, and compressibility of liquid water from 0 °C to 150 °C. Journal of Chemical and Engineering Data 20 (1975) 97-105. The rational fit for the density of liquid water at 1 atm reproduced in every handbook since; it supplies the density the IAPWS ionization equation needs. It puts water’s maximum density at 999.972 kg/m³ near 3.98 °C and gives 958.36 kg/m³ at 100 °C, both of which agree with the published values to about one part in 10⁵.