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Short answer
A mass percent solution states how much of a solution’s total mass is the dissolved substance. The formula is mass percent = (mass of solute / mass of solution) x 100, where the mass of the solution is solute plus solvent. A solution made from 10 g of sodium chloride and 90 g of water is a 10 % mass percent solution, because the solution weighs 100 g.
Definition and scope
Mass percent is a mass fraction written as a percentage. The IUPAC Green Book (Quantities, Units and Symbols in Physical Chemistry, 3rd edition) defines the mass fraction w of a component B as wB = mB / Σmi: the mass of that component divided by the summed mass of all components. It is a dimensionless quantity with SI unit 1, and the percent sign stands for the number 10-2. A mass fraction of 0.10 and a mass percent of 10 % are therefore the same statement.
Labs and reagent labels usually write this as “% w/w” (weight per weight). This guide uses “mass percent” and “w/w” interchangeably for that reading. It does not cover weight per volume (w/v) or volume per volume (v/v); the w/v case is worked through in molarity and solution calculations for the lab.
Mass percent solution formula
Because the mass of the solution is the sum of everything in it, the formula can be written two equivalent ways.
- Mass percent = (mass of solute / mass of solution) x 100
- Mass percent = (mass of solute / (mass of solute + mass of solvent)) x 100
The denominator is the finished solution, not the solvent alone. Dividing by the solvent mass instead is a slip to avoid, because it gives a larger number than the true mass percent.
How to calculate a percent solution
The following worked examples are illustrations of the arithmetic, not data from a source.
Finding the mass percent of a solution you have
25 g of solute is dissolved in water and the finished solution weighs 250 g. Mass percent = (25 g / 250 g) x 100 = 10 %. The solvent mass is 225 g, so using the solvent alone as the denominator would wrongly give about 11.1 %.
Finding how much solute a target percent needs
Rearrange the formula: mass of solute = mass percent / 100 x mass of solution. For a 5 % solution with a total mass of 200 g, the solute is 0.05 x 200 g = 10 g, and the solvent is the remaining 190 g. The quantities are weighed on a balance; no volume measurement is involved. See analytical balance calibration and weighing technique for the weighing side.
Why the answer does not depend on density
Mass is conserved when components are combined, so the solution mass is the sum of the parts. A mass percent therefore stays the same at any temperature, whereas a figure expressed per volume of solution can change as the volume of a liquid changes. That is a consequence of the definition, not a claim about any particular reagent.
Reading a label: w/w, w/v and the notation problem
Two sources ask writers to stop attaching “(m/m)” to the percent sign. NIST SP 811, section 7.10.2, says the symbol % represents simply a number, so it is not meaningful to attach information to it, and that forms such as “% (m/m)” and “% (V/V)” should be avoided. The IUPAC Green Book section 3.10.2 gives the same advice: qualifying labels may be added to the symbol for a physical quantity, but never to units, and its example is a mass fraction w = 0.5 %, but not 0.5 % (m/m). NIST also warns in section 7.4 against attaching letters or symbols to a unit to say what quantity it measures.
Written forms and what the two sources say about them:
| Written form | What NIST SP 811 and the IUPAC Green Book say |
|---|---|
| “10 % w/w” or “10 % (m/m)” | Labelling the percent sign should be avoided (NIST 7.10.2; IUPAC 3.10.2) |
| “The mass fraction is 10 %” | Preferred form: the quantity is named in words, the symbol carries only the number (NIST 7.10.2) |
| wB = 0.10 | Preferred form: the quantity symbol carries the label, the value is a plain number (NIST 7.10.2; IUPAC) |
| “2.6 x 10-6” with no quantity named | Ambiguous and should be avoided; state which fraction is meant (IUPAC 3.10.1) |
Reagent labels and protocols often use “% w/w”, so you will meet it. Read it as the mass of solute per 100 units of total solution mass. A “% w/v” figure instead refers to mass of solute per 100 mL of solution, which is a different quantity; a label does not convert from one to the other without the solution’s density.
Checklist before you use a percent figure
- Is the basis stated: mass of solution, volume of solution, or volume of the components? IUPAC says percent symbols are used for several kinds of fraction and should be used only where the meaning of the quantity is carefully defined.
- Is the denominator the whole solution, not just the solvent?
- If the protocol needs a volume (for example a pipetting step), does it also give a density? A mass percent cannot be turned into a volume without one.
- For records and reports, can the figure be written as a mass fraction, 0.10, or in g/kg (100 g/kg), as NIST and IUPAC prefer?
Related concepts
- Mass fraction. The same quantity without the factor of 100 (IUPAC wB).
- g/kg. NIST section 7.10.2 highly recommends forms such as wB = 3 g/kg for a mass fraction. By arithmetic, 10 % equals 100 g/kg.
- Dilute aqueous solutions. The Green Book prefers mass concentration (for example mg per dm3) to “ppm” for a mass fraction, and notes that for dilute aqueous solutions the density is about 1.0 g per cm3, so the numerical value in mg per dm3 is approximately the mass fraction expressed in parts per million.
- Volume-based percent. Disinfectant alcohols are an example where concentration is given by volume; see what isopropyl alcohol is.
Where it matters for labs, clinics and supply decisions
When a reagent, stock solution or cleaning agent is described as a percent, the staff using it need to know which percent. Two practical consequences follow from the definitions above. First, a solution prepared by weighing is defined by the recorded masses of solute and total solution. Second, a procedure that mixes a percent by mass with a percent by volume needs the density to reconcile them. For precision of the weighing and measuring steps, see accuracy vs precision in measurement.
Common misunderstandings
- “10 % means 10 g in 100 mL.” That describes weight per volume. A 10 % mass percent solution has 10 g of solute in 100 g of solution.
- “Add 10 g to 100 g of water.” That gives 110 g of solution and a mass percent of about 9.1 %, not 10 %.
- “The percent sign tells you the type.” It does not; NIST and IUPAC both say it is simply a number, which is why they ask for the quantity to be named in words or symbol.
- “A percent can be reported without context.” IUPAC calls statements such as “the concentration of nickel was 2.6 x 10-6” ambiguous.
Frequently asked questions
What is the mass percent solution formula?
Mass percent = (mass of solute / mass of solution) x 100, with the mass of solution equal to solute plus solvent.
How do I calculate a percent solution?
For a w/w percent, weigh the solute (target percent / 100 x total mass), then add solvent until the total reaches the target mass. For example, 5 % of 200 g is 10 g solute plus 190 g solvent.
Is mass percent the same as w/v?
No. Mass percent is solute mass per 100 units of solution mass; w/v is solute mass per 100 mL of solution. Converting needs the solution density.
Should I write “% w/w” in a report?
NIST SP 811 and the IUPAC Green Book ask that the percent symbol not carry such labels; write “the mass fraction is 10 %”, w = 0.10, or 100 g/kg instead.
Sources
- NIST, Guide for the Use of the International System of Units (SI), NIST SP 811, Chapter 7 “Rules and style conventions for expressing values of quantities”, sections 7.4 and 7.10.2: https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-7-rules-and-style-conventions-expressing-values (date checked 2026-10-29).
- IUPAC, Quantities, Units and Symbols in Physical Chemistry (Green Book), 3rd edition, 2nd printing 2012, mass fraction table and sections 3.10.1 and 3.10.2: https://iupac.org/wp-content/uploads/2019/05/IUPAC-GB3-2012-2ndPrinting-PDFsearchable.pdf (date checked 2026-10-29).
The worked examples and the arithmetic conversions (such as 10 % = 100 g/kg) are illustrations derived from the definitions above.
