What's the difference between % (w/v), % (w/w), and % (v/v)?

All three are ratios of solute to solution multiplied by 100. % (w/v) = grams of solute per 100 mL of solution — the biology-lab default (e.g. 0.9 % NaCl saline). % (w/w) = grams of solute per 100 g of solution — used on concentrated-reagent bottles (37 % HCl). % (v/v) = mL of solute per 100 mL of solution — used for miscible liquids like 70 % ethanol disinfectant.

How do I convert % (w/w) to % (w/v)?

You need the density of the solution. The relation is % (w/v) = % (w/w) × ρ_solution, where ρ is in g/mL. For 37 % (w/w) HCl with ρ ≈ 1.19 g/mL, the equivalent is 37 × 1.19 = 44 % (w/v). Enter a density in the density field to see the cross-conversion under your result.

How do I prepare 0.9 % NaCl saline?

Weigh 0.9 g of NaCl into a 100 mL volumetric flask, add ~80 mL of water and swirl to dissolve, then fill to the 100 mL mark. This gives 0.9 % (w/v) NaCl — isotonic with human plasma (~154 mM Na⁺). For 1 L, scale to 9.0 g of NaCl.

Which percent convention should I use?

Follow the source: use the same convention as the protocol you're reproducing. In practice, biochem uses % (w/v) for salt, protein, and agarose stocks; industrial and inorganic chemistry uses % (w/w) for acids and bases; and food, pharmacy, and cleaning products use % (v/v) for ethanol and other miscible liquids. Never mix conventions in the same calculation.

Percent Solution Calculator — % w/v, w/w, v/v

Percent-solution concentrations are the most common shorthand in wet chemistry — every bottle of “37 % HCl”, every “0.9 % saline” recipe, every “70 % ethanol” spray bottle is a percent-solution calculation in disguise. This calculator handles all three conventions in one place: % (w/v), % (w/w), and % (v/v).

Percent Solution Calculator

Choose the percent convention, enter any two of the three quantities, and pick which to solve for.

Equations used

One definition per convention:

% (w/v) = 100 \cdot \frac{m _{solute} [ g ]}{V _{solution} [ mL ]}

% (w/w) = 100 \cdot \frac{m _{solute}}{m _{solution}}

% (v/v) = 100 \cdot \frac{V _{solute}}{V _{solution}}

The three conventions

Each definition is a ratio of solute to solution (not to solvent), multiplied by 100:

% (w/v) = 100 · (g solute) / (mL solution)
% (w/w) = 100 · (g solute) / (g solution)
% (v/v) = 100 · (mL solute) / (mL solution)

Only % (w/v) mixes units — grams of solute per milliliters of solution — so its numerical value depends on the specific choice of “g / 100 mL”. The other two are true dimensionless ratios (g/g, mL/mL) and are temperature-invariant.

Converting between conventions

When you need to translate a % (w/w) label to % (w/v) (or vice versa), you need the density of the solution in g/mL. The relation follows straight from the definitions:

% (w/v) = % (w/w) · ρ_solution (with ρ in g/mL).

Worked example

Prepare 100 mL of 0.9 % (w/v) NaCl — physiological saline — for a cell-biology assay.

Worked example — 0.9 % (w/v) NaCl saline

% (target): 0.9 % (w/v)
V (solution): 100 mL
MW (NaCl): 58.44 g/mol (PubChem CID 5234) — informational; not used in a % calc

Formula
$m = \frac{% \cdot V}{100}$
Substitute
$m = \frac{0.9 \cdot 100}{100}$
Note
Weigh 0.9 g of NaCl into a 100 mL volumetric flask, add ~80 mL of water and swirl to dissolve, then top up to the 100 mL mark. The result is 0.9 % (w/v) NaCl, which is isotonic with human plasma (~154 mM Na⁺). Note: percent-solution recipes do not need a molecular weight — that's only needed if you want to convert to molarity.
Result
$m = 0.9 g NaCl$

Common ranges

Application	Typical concentration
Physiological saline	0.9 % (w/v) NaCl ≈ 154 mM
Agarose gel (DNA electrophoresis)	0.7–2 % (w/v)
Concentrated HCl bottle	37 % (w/w) ≈ 44 % (w/v) ≈ 12 M
Concentrated H₂SO₄ bottle	96 % (w/w) ≈ 176 % (w/v) ≈ 18 M
Disinfectant ethanol	70 % (v/v)
Absolute ethanol	≥ 99.5 % (v/v)

Common pitfalls

Solution ≠ solvent. All three conventions divide by the total mass or volume of the final solution, not by the mass or volume of the solvent. Use a volumetric flask (for w/v and v/v) or weigh the whole flask + contents (for w/w); do not just add “100 mL of water” to the solute.
% (w/v) hides its units. “0.9 %” of a saline solution and “0.9 %” of alcohol in blood are different physical quantities. Always write “0.9 % (w/v)” or “0.9 % (v/v)” so the reader knows which ratio you mean.
Cross-conversion needs density. You cannot translate between % (w/w) and % (w/v) without the solution’s density. For concentrated reagents (HCl, H₂SO₄, NH₃, HNO₃) the bottle or the supplier’s spec sheet lists it; for dilute aqueous solutions, ρ ≈ 1.00 g/mL is close enough.
v/v volumes are not perfectly additive. Mixing 70 mL ethanol with 30 mL water gives slightly less than 100 mL of solution due to hydrogen bonding. The nominal “70 % (v/v)” convention treats them as additive; for high-precision work, prepare by mass and convert.

Practice problems

Attempt each on paper, then expand the worked solution to check your arithmetic and sig-figs.

Problem 1 Easy How much NaCl do you weigh to prepare 500 mL of 0.9 % (w/v) saline?

Answer: 4.5 g NaCl

Solve for solute mass (% w/v)

%: 0.9 % (w/v)
V (solution): 500 mL

Formula
$m = \frac{% \cdot V}{100}$
Substitute
$m = \frac{0.9 \cdot 500}{100}$
Result
$m = 4.5 g NaCl$

Problem 2 Easy You dissolve 5.00 g of sucrose in enough water to make 250 mL of solution. What is the concentration in % (w/v)?

Answer: 2.00 % (w/v)

Solve for percent (% w/v)

m (solute): 5.00 g
V (solution): 250 mL

Formula
$% = 100 \cdot \frac{m}{V}$
Substitute
$% = 100 \cdot \frac{5.00}{250}$
Result
$% = 2.00 % (w/v)$

Problem 3 Intermediate How much 100 % ethanol and water do you mix to make 500 mL of 70 % (v/v) disinfectant?

Answer: 350 mL of 100 % ethanol, top up to 500 mL with water

Solve for solute volume (% v/v)

%: 70 % (v/v)
V (solution): 500 mL

Formula
$V_{solute} = \frac{% \cdot V _{soln}}{100}$
Substitute
$V_{solute} = \frac{70 \cdot 500}{100}$
Note
Measure 350 mL of absolute ethanol into a 500 mL cylinder, then top up to the 500 mL mark with water. Volumes of miscible liquids are slightly non-additive, but for lab disinfectant work the mL-to-mL algebra is close enough.
Result
$V_{solute} = 350 mL$

Problem 4 Intermediate A bottle of concentrated HCl is labeled 37.0 % (w/w) with ρ = 1.19 g/mL. What is the concentration in % (w/v)?

Answer: 44.0 % (w/v)

Cross-conversion (% w/w → % w/v)

%: 37.0 % (w/w)
ρ (solution): 1.19 g/mL

Formula
$% (w/v) = % (w/w) \cdot ρ_{soln}$
Substitute
$% (w/v) = 37.0 \cdot 1.19$
Note
% (w/w) times solution density in g/mL gives % (w/v). Enter 37.0 in the percent field and 1.19 in the density field with mode set to w/w; the cross-conversion appears under the result.
Result
$% (w/v) = 44.0 %$

Frequently asked questions

What's the difference between % (w/v), % (w/w), and % (v/v)?: All three are ratios of solute to solution multiplied by 100. % (w/v) = grams of solute per 100 mL of solution — the biology-lab default (e.g. 0.9 % NaCl saline). % (w/w) = grams of solute per 100 g of solution — used on concentrated-reagent bottles (37 % HCl). % (v/v) = mL of solute per 100 mL of solution — used for miscible liquids like 70 % ethanol disinfectant.
How do I convert % (w/w) to % (w/v)?: You need the density of the solution. The relation is % (w/v) = % (w/w) × ρ_solution, where ρ is in g/mL. For 37 % (w/w) HCl with ρ ≈ 1.19 g/mL, the equivalent is 37 × 1.19 = 44 % (w/v). Enter a density in the density field to see the cross-conversion under your result.
How do I prepare 0.9 % NaCl saline?: Weigh 0.9 g of NaCl into a 100 mL volumetric flask, add ~80 mL of water and swirl to dissolve, then fill to the 100 mL mark. This gives 0.9 % (w/v) NaCl — isotonic with human plasma (~154 mM Na⁺). For 1 L, scale to 9.0 g of NaCl.
Which percent convention should I use?: Follow the source: use the same convention as the protocol you're reproducing. In practice, biochem uses % (w/v) for salt, protein, and agarose stocks; industrial and inorganic chemistry uses % (w/w) for acids and bases; and food, pharmacy, and cleaning products use % (v/v) for ethanol and other miscible liquids. Never mix conventions in the same calculation.

Sources

Harris, Quantitative Chemical Analysis, 10th ed. (2020), §1-4
IUPAC Gold Book — mass concentration (M03713)
IUPAC Gold Book — volume fraction (V06643)
PubChem CID 5234 — Sodium chloride
PubChem CID 313 — Hydrochloric acid

Last updated: 2026-09-18.