Percent Solution Calculator
Percent Solution Calculator
Work out the percentage strength of a solution as % w/v, % v/v or % w/w — three conventions that share a symbol and mean different things.
Percent solution
Amount ÷ volume → %5 g of solid made up to 100 mL of solution, expressed as % w/v
Formula, and which of the three you mean
% w/v = g solute per 100 mL solution · % v/v = mL solute per 100 mL solution · % w/w = g solute per 100 g solution
- amount of solute
- grams for w/v and w/w, millilitres for v/v. The units on the top and bottom of the fraction are what distinguish the three conventions
- final solution
- the FINAL volume or mass of the whole solution, not the volume of solvent added to the solute
- × 100
- expresses the fraction per hundred; it is the only part of the calculation the three conventions share
- w/v, v/v, w/w
- not interchangeable. A 5% w/v solution and a 5% v/v solution are different preparations, and a label giving only the number is incomplete
Worked example
5 g of solid made up to 100 mL of solution, expressed as % w/v
5 g ÷ 100 mL × 100 = 5.000% w/v
The same statement written as a mass concentration is 50 g/L
Dissolve the 5 g in roughly 80 mL, then make up to the 100 mL mark — do not add 100 mL of solvent to the 5 g
Between 1% and 20% → typical working range
The three conventions compared
| Convention | Reads as | Worked example | Temperature dependence |
|---|---|---|---|
| % w/v | Grams of solute in 100 mL of finished solution | 0.9% w/v NaCl = 0.9 g in 100 mL = 9 g/L = about 154 mmol/L | Yes — the volume of the solution changes as it warms |
| % v/v | Millilitres of liquid solute in 100 mL of finished solution | 70% v/v ethanol = 70 mL of absolute ethanol made up to 100 mL | Yes, and volumes of alcohol and water are not additive |
| % w/w | Grams of solute in 100 g of finished solution | 37% w/w formaldehyde stock = 37 g in 100 g of solution | No — mass does not change with temperature |
Familiar solutions, and what the percentage actually means
| Solution | Percentage | Same thing in other units |
|---|---|---|
| Sodium chloride 0.9% (normal saline) | 0.9% w/v | 9 g/L; 154 mmol/L sodium and 154 mmol/L chloride |
| Dextrose 5% | 5% w/v | 50 g/L; about 278 mmol/L glucose |
| Sodium chloride 3% (hypertonic) | 3% w/v | 30 g/L; about 513 mmol/L sodium |
| Ethanol 70% | 70% v/v | 70 mL of ethanol made up to 100 mL, not 70 g in 100 mL |
| Neutral buffered formalin 10% | 10% v/v of the stock | A 1-in-10 dilution of 37–40% w/w formaldehyde, so roughly 4% w/v formaldehyde |
Three percentages that share one symbol
A percentage strength is a fraction of a hundred, but the fraction can be built three ways and the three are not interchangeable. Weight in volume is grams of solute per 100 mL of finished solution; volume in volume is millilitres of liquid solute per 100 mL; weight in weight is grams per 100 g. A 5% w/v solution contains 5 g in 100 mL, while a 5% v/v solution contains 5 mL, and unless the solute happens to have a density of 1 g/mL those are different amounts of substance. A label or a method that gives the number without the convention has not said enough.
Weight in volume is the odd one out, because it divides a mass by a volume and so is not a true ratio at all: the units do not cancel, and the hundred is a convention rather than a dimensionless fraction. Chemists dislike it for that reason and clinical practice uses it almost everywhere, because it maps directly onto how solutions are actually made and given. Normal saline is 0.9% w/v, meaning 0.9 g of sodium chloride in 100 mL of solution — 9 g/L, or about 154 mmol/L of each ion. Reading it as anything else, such as 0.9 g in 100 g, gives a slightly but consistently wrong answer.
Whichever convention is in use, the denominator is the finished solution, not the solvent added to it. The solute occupies space of its own, so tipping 5 g of powder into 100 mL of water gives more than 100 mL of solution and a strength below the one on the label. The error is trivial at 0.1% and substantial at 20%. Dissolve the solute in perhaps 80% of the final volume, then make up to the mark in a volumetric flask, and write the method as make up to rather than add to.
Only weight in weight is temperature-independent, because mass does not expand and volume does. That is why concentrated acids, hydrogen peroxide and formaldehyde stocks are certified in w/w on the bottle while the working solutions made from them are described in w/v or v/v. It is also why volume in volume needs care with alcohols: ethanol and water contract on mixing, so 70 mL of ethanol plus 30 mL of water is less than 100 mL of solution, and 70% v/v ethanol has to be made up to the mark rather than assembled by addition.
Frequently asked questions
What is the difference between % w/v and % v/v?
Weight in volume is grams of solute per 100 mL of finished solution; volume in volume is millilitres of liquid solute per 100 mL. A 5% w/v solution and a 5% v/v solution are therefore different preparations, and a percentage quoted without its convention is incomplete.
Why is 0.9% saline described as w/v?
Because it is 0.9 g of sodium chloride in 100 mL of solution, which is 9 g/L, or about 154 mmol/L of sodium and of chloride. Weight in volume mixes a mass with a volume and is not a true ratio, but it is the near-universal clinical convention.
Do I add the solute to 100 mL or make up to 100 mL?
Make up to 100 mL. The denominator of every percentage strength is the finished solution, and the solute has a volume of its own. Dissolve in about 80% of the final volume, then bring it to the mark.
Which percentage convention is temperature-independent?
Weight in weight, because mass does not change with temperature while volume does. That is why concentrated stocks such as formaldehyde and the mineral acids are certified in w/w on the bottle.
Is 10% formalin the same as 10% formaldehyde?
No. Neutral buffered formalin 10% is a 1-in-10 dilution of a 37–40% w/w formaldehyde stock, so it contains roughly 4% formaldehyde. It is the same fixative that a protocol calling for 4% paraformaldehyde is aiming at.
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References
- Cohen ER, Cvitaš T, Frey JG, et al., eds. Quantities, Units and Symbols in Physical Chemistry (the IUPAC Green Book). 3rd ed. RSC Publishing.
- Thompson A, Taylor BN. Guide for the Use of the International System of Units (SI). NIST Special Publication 811.
- Rifai N, Horvath AR, Wittwer CT, eds. Tietz Textbook of Clinical Chemistry and Molecular Diagnostics. Elsevier — solution preparation and expression of concentration.