What this calculator does
Mass percent is the solute mass divided by the total solution mass. Five grams of solute in 95 grams of solvent gives 100 grams of solution and a mass percent of exactly 5%.
The denominator is the total, not the solvent, and that is the usual error. Five grams in 100 grams of solvent is 4.76%, not 5%. The difference is small at low concentrations and grows quickly: 50 grams in 95 grams of solvent is 34.5%, not 52.6%.
The formula
The solute mass is divided by the sum of solute and solvent masses, then multiplied by 100. Parts per million and parts per billion are the same ratio on different scales, with 1% equal to 10,000 ppm. Because everything is a mass ratio, the result does not change with temperature, unlike any volume-based measure.
| Term | Meaning |
|---|---|
| Mass percent | Solute mass over total solution mass, as a percentage. Also written % w/w. |
| ppm | Parts per million by mass. 1% is 10,000 ppm. |
| % w/v | A different measure: mass of solute per volume of solution, which is not the same thing. |
| Total solution mass | Solute plus solvent, which is the denominator. |
The inputs explained
| Field | What to enter |
|---|---|
| Mass of solute (g) | Mass of solute. |
| Mass of solvent (g) | Mass of solvent. The calculator adds the two to get the total solution mass. |
When to use it
Preparing a solution by weight
Weighing both components is more accurate than measuring volume and avoids temperature effects entirely.
Reading a product label
Concentrations on chemical and food labels are frequently given as mass percent.
Converting to ppm
Trace concentrations are quoted in ppm or ppb, which are the same ratio expressed on a different scale.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does the solute mass affect the percentage?
A range of solute masses in the same quantity of solvent.
| Mass of solute | Mass percent | Total solution mass | Concentration in ppm |
|---|---|---|---|
| 1 g | 1.04% | 96.00 g | 10,417 ppm |
| 5 g | 5.00% | 100.00 g | 50,000 ppm |
| 20 g | 17.4% | 115.00 g | 173,913 ppm |
| 50 g | 34.5% | 145.00 g | 344,828 ppm |
Questions
Is mass percent the solute over the solvent or over the total?
Over the total, meaning solute plus solvent. This is the single most common error. Five grams in 95 grams of solvent is 5%, because the solution weighs 100 grams. Five grams in 100 grams of solvent is 4.76%.
What is the difference between % w/w and % w/v?
Mass over mass against mass over volume. A 5% w/w solution has 5 g of solute per 100 g of solution; a 5% w/v solution has 5 g per 100 mL. They coincide only when the solution density is exactly 1 g/mL, which for dilute aqueous solutions is roughly true and otherwise is not.
How do I convert mass percent to ppm?
Multiply by 10,000. One percent is 10,000 ppm, and 1 ppm is 0.0001%. For dilute aqueous solutions, 1 ppm is also approximately 1 mg/L, since a litre of dilute solution weighs close to a kilogram.
Does mass percent change with temperature?
No, and that is its advantage over molarity. Both masses are temperature-independent, so the ratio is fixed. Molarity uses volume, which expands when heated, so a solution prepared at 20 °C is slightly less concentrated at 40 °C.
For a concentration in moles per litre, see the molarity calculator. For converting ppm to molarity, see the ppm to molarity calculator.