Percentage strength for phosphoric acid is read as % w/v: grams of solute in 100 mL of solution. So 1% is 1 g per 100 mL, which for this compound works out at 0.10205 mol/L, and 0.9% is 9 g per litre or 0.091843 mol/L. The calculator takes a percentage and a volume and returns the grams to weigh, with the molarity and mg/mL equivalents beside it.
The figure comes from the formula. Phosphoric acid is 3 × 1.008 (H) + 30.9738 (P) + 4 × 15.999 (O), which is 97.993762 g/mol, taking standard atomic weights, and every page here computes that sum rather than quoting it. Oxygen makes up the largest share of the mass: 4 of the 8 atoms in a formula unit are oxygen, and they account for 63.996 g of the 97.99376 g, or 65.31% by mass. The derivation table below breaks the whole molecule down element by element.
Three different percentages are in circulation and they are not interchangeable. Per cent w/v is mass in a volume, the one used here and on medical labels; per cent w/w is mass in mass, the one on drums of concentrated reagent; per cent v/v is volume in volume, used for liquids mixed into liquids. For a dilute aqueous solution w/v and w/w are within a percent of each other, but for anything concentrated the density has to come into it.
The acid in cola, a rust converter and a buffer component. Food grade is usually 75 or 85% w/w, so the percentage matters more than the molarity. At 97.99376 g/mol it is heavier than 7 of the 12 acids covered here, and that ranking matters more than it looks: lactic acid has a molar mass of 90.078 g/mol, so a gram of it contains 8.79% more formula units than a gram of phosphoric acid. Weigh by mass and you are not weighing equal amounts of substance.
One more step applies if you are starting from a concentrated bottle. Concentrated acids are labelled as a percentage by weight together with a density, not as a molarity, so getting to mol/L means multiplying density by that percentage and dividing by 97.993762 g/mol. A page like this one gives you the last of those three numbers; the first two are on the bottle, and they vary between grades.
The formula
p- The strength you want, as % w/v
V- The volume of solution, in millilitres
m- The mass of phosphoric acid to weigh out, in grams
97.993762- The molar mass of phosphoric acid in g/mol, derived from its formula
How it works, step by step
- Enter the percentage strength you want, as % w/v.
- Enter the volume of solution in millilitres.
- Grams needed is percentage × volume ÷ 100, since 1% w/v is 1 g per 100 mL.
- The molarity that strength corresponds to for phosphoric acid is shown beneath, using 97.993762 g/mol.
Worked examples
0.9% w/v phosphoric acid in 500 mL
0.9% w/v is 0.9 g per 100 mL, so 500 mL needs 4.5 g. In molar terms that solution is 0.091843 mol/L, and it is 9 mg/mL if you are dosing by volume.
5% w/v phosphoric acid in 100 mL
5% w/v is 5 g per 100 mL, so 100 mL needs 5 g. In molar terms that solution is 0.51024 mol/L, and it is 50 mg/mL if you are dosing by volume.
10% w/v phosphoric acid in 1000 mL
10% w/v is 10 g per 100 mL, so 1000 mL needs 100 g. In molar terms that solution is 1.0205 mol/L, and it is 100 mg/mL if you are dosing by volume.
How to read your score
Frequently asked questions
What is the molar mass of phosphoric acid (H3PO4)?
It is 97.993762 g/mol. That is the sum of the standard atomic weights of every atom in the formula: 3 × 1.008 (H) + 30.9738 (P) + 4 × 15.999 (O). One mole of phosphoric acid therefore weighs 97.99376 g, and a gram of it is 10.205 mmol.
What percentage of phosphoric acid is oxygen?
65.31% by mass. Each formula unit contains 4 oxygen atoms contributing 63.996 g of the 97.99376 g total, so 100 g of phosphoric acid contains 65.31 g of oxygen and a kilogram contains 653.06 g of it.
How many grams of phosphoric acid make a 1% w/v solution?
1 g in 100 mL of solution, 5 g in 500 mL, 10 g in a litre. The percentage is fixed to the volume, not to the compound, so those masses are the same whatever is being dissolved — what changes with the compound is the molarity they come to.
What molarity is a 1% w/v solution of phosphoric acid?
0.102047 mol/L, because 1% w/v is 10 g/L and 97.99376 g/L is one molar. A 0.9% solution is 0.091843 mol/L and a 5% solution is 0.51024 mol/L.
Is % w/v the same as % w/w?
No. Per cent w/v is grams per 100 mL of solution; per cent w/w is grams per 100 g of solution. They coincide only when the solution has a density of 1.00 g/mL, which dilute aqueous solutions approximately do and concentrated ones do not. Labels on concentrated reagents are usually w/w.
What is 1% w/v in mg/mL?
10 mg/mL, since 1 g in 100 mL is 1000 mg in 100 mL. For phosphoric acid that is also 102.05 mmol/L, which is the form a dose calculation usually wants.
Percentage strengths of phosphoric acid
| Element | Atoms | Atomic weight | Contribution (g/mol) | By mass |
|---|---|---|---|---|
| Oxygen (O) | 4 | 15.999 | 63.996 | 65.31% |
| Phosphorus (P) | 1 | 30.97376 | 30.97376 | 31.61% |
| Hydrogen (H) | 3 | 1.008 | 3.024 | 3.086% |
| Total — one mole of phosphoric acid | 97.993762 | 100% |
Standard atomic weights, IUPAC 2021. The contribution column is atoms × atomic weight, and the total is the molar mass this page uses: 97.993762 g/mol.
| Strength | per 100 mL | per 500 mL | per 1 L | Molarity (mol/L) |
|---|---|---|---|---|
| 0.1% w/v | 100 mg | 500 mg | 1 g | 0.010205 |
| 0.25% w/v | 250 mg | 1.25 g | 2.5 g | 0.025512 |
| 0.5% w/v | 500 mg | 2.5 g | 5 g | 0.051024 |
| 0.9% w/v | 900 mg | 4.5 g | 9 g | 0.091843 |
| 1% w/v | 1 g | 5 g | 10 g | 0.10205 |
| 2% w/v | 2 g | 10 g | 20 g | 0.20409 |
| 3% w/v | 3 g | 15 g | 30 g | 0.30614 |
| 5% w/v | 5 g | 25 g | 50 g | 0.51024 |
| 10% w/v | 10 g | 50 g | 100 g | 1.0205 |
| 20% w/v | 20 g | 100 g | 200 g | 2.0409 |
A 1% w/v solution is 1 g in 100 mL, which for this compound is 0.10205 mol/L because 10 g/L divided by 97.993762 g/mol gives that figure.
| Compound | Formula | Molar mass (g/mol) | Millimoles in 1 g |
|---|---|---|---|
| Nitric acid | HNO3 | 63.012 | 15.87 |
| Oxalic acid | C2H2O4 | 90.034 | 11.107 |
| Lactic acid | C3H6O3 | 90.078 | 11.101 |
| Phosphoric acid (this page) | H3PO4 | 97.99376 | 10.205 |
| Sulfuric acid | H2SO4 | 98.072 | 10.197 |
| Tartaric acid | C4H6O6 | 150.086 | 6.6628 |
| Ascorbic acid | C6H8O6 | 176.124 | 5.6778 |
Ordered by molar mass. The last column is 1000/M, which is the number a weighed gram actually gives you.