The percent concentration tells you how much of a substance is in every 100 parts of a solution. 25 g of salt dissolved in 225 g of water makes 250 g of solution, so the concentration is 25 ÷ 250 × 100 = 10% by mass. The calculator works out the three forms used in class, the lab and on labels, and the reverse: how much solute to weigh and how much water to add for the strength you want.
Three ways to write a percent
| Form | Formula | Unit | Typical use |
|---|---|---|---|
| Mass percent (w/w) | solute (g) ÷ solution (g) × 100 | g per 100 g | chemistry exercises, alloys, concentrated acids |
| Mass/volume (w/v) | solute (g) ÷ solution (mL) × 100 | g per 100 mL | medicine, biology labs |
| Volume percent (v/v) | liquid (mL) ÷ solution (mL) × 100 | mL per 100 mL | alcohol, disinfectants |
For dilute water solutions the three are close, because 1 mL of water weighs very nearly 1 g. For strong solutions they drift apart, and a label will say which one it means.
Worked examples
| You have | Calculation | Concentration |
|---|---|---|
| 10 g of sugar in 90 g of water | 10 ÷ 100 × 100 | 10% w/w |
| 10 g of sugar in 100 g of water | 10 ÷ 110 × 100 | 9.09% w/w |
| 50 g of salt in 200 g of water | 50 ÷ 250 × 100 | 20% w/w |
| 9 g of salt made up to 1,000 mL | 9 ÷ 1,000 × 100 | 0.9% w/v |
| 40 mL of ethanol made up to 100 mL | 40 ÷ 100 × 100 | 40% v/v |
The second line is the classic trap: adding 10 g to 100 g of water gives 9.09%, not 10%.
Making a solution
To make a given mass of solution at a given strength, weigh the solute first: solute = total × % ÷ 100, then the solvent is the rest. 1,000 g of a 0.9% solution needs 9 g of salt and 991 g of water. For w/v or v/v, dissolve or measure the solute, then top up with water to the final volume in a measuring cylinder or a volumetric flask, rather than adding the full volume of water.
To weaken a solution you already have, use the dilution calculator (C₁V₁ = C₂V₂). Both run on your device and work offline.
Frequently asked questions
How do I calculate mass percent?
Divide the mass of the solute by the mass of the whole solution (solute plus solvent) and multiply by 100. 25 g of salt in 225 g of water: 25 ÷ 250 × 100 = 10%.
What is the difference between w/w, w/v and v/v?
w/w is grams per 100 g of solution; w/v is grams per 100 mL of solution; v/v is milliliters per 100 mL of solution. Saline at 0.9% is w/v (0.9 g in every 100 mL); a 40% spirit is v/v.
How much salt do I need for 1 kg of a 5% solution?
5% of 1,000 g = 50 g of salt, dissolved in 950 g of water. Choose 'Make a solution' in the calculator.
Why is 25 g in 225 g of water not 11.1%?
Because the percentage is of the whole solution, 250 g, not of the water alone. Dividing by the solvent is a frequent slip in exercises.
How do I turn a percent into ppm?
Multiply by 10,000. A 0.05% solution is 500 parts per million (by mass when it is a mass percent).
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