Osmotic Pressure Calculator (Π = iMRT, or molar mass from a measured Π)

Understanding the osmotic pressure calculator — concept and principle

This calculator finds the osmotic pressure of a dilute solution from the solute mass, molar mass, solution volume, temperature and van 't Hoff factor, or works backwards from a measured osmotic pressure to the molar mass of the solute. It is used in chemistry, biology and medicine, and for finding molar masses of large molecules such as proteins.

Dissolved particles behave like a gas: concentration × R × T gives a pressure of over 7 atmospheres.

How it is calculated

Π = i M R T

M = (solute mass ÷ molar mass) ÷ volume (L)

R = 0.082057 L·atm/(mol·K); T = °C + 273.15

Molar mass from a measurement: M = Π ÷ (i R T); molar mass = grams ÷ (M × litres)

Results are also shown in kPa, bar and mmHg; osmolarity = i × M.

The principle

When a solution and pure solvent are separated by a membrane that lets only solvent through, solvent flows into the solution to dilute it. The pressure that must be applied to the solution to stop that flow is the osmotic pressure. For dilute solutions it behaves like the pressure of an ideal gas made of the solute particles: proportional to their concentration and to absolute temperature. The van 't Hoff factor counts how many particles each formula unit produces.

Worked example

Default inputs: 54.05 g of glucose (180.16 g/mol) in 1.000 L, 37 °C, i = 1.

n = 54.05 ÷ 180.16 = 0.300 mol, so M = 0.3 mol/L; osmolarity 0.3 osmol/L.
T = 37 + 273.15 = 310.15 K.
Π = 1 × 0.3 × 0.082057 × 310.15 = 7.635 atm.
In other units: 773.6 kPa, 7.736 bar, 5,803 mmHg.

Each point is the calculator re-run with only “Molar mass of the solute (g/mol)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Molar mass of the solute (g/mol)	Osmotic pressure Π (atm)
45	30.54
90.1	15.27
135	10.18
180	7.635
225	6.108
270	5.09
360	3.818

How to read the result

Osmotic pressures are large even for modest concentrations: a 0.3 M solution at body temperature produces over 7 atmospheres. Blood plasma has an osmolarity close to this, which is why intravenous fluids must be made to a matching concentration. Because Π is so sensitive, measuring it is a good way to find the molar mass of proteins and polymers.

Common mistakes

Using °C instead of kelvin.
Forgetting the van 't Hoff factor for salts (i ≈ 2 for NaCl).
Using molality instead of molarity at high concentrations.
Applying the ideal formula to concentrated solutions.

Keep in mind: The equation assumes ideal dilute solutions. Medical fluid preparation must follow pharmaceutical standards, not this estimate.

Frequently asked questions

Why is osmotic pressure so large?

Π scales like a gas pressure; 1 mol/L of particles at room temperature gives about 24 atm.

What is the van 't Hoff factor?

The number of particles produced per formula unit in solution.

How is osmotic pressure used to find molar mass?

Measure Π, compute M = Π/(iRT), then divide the grams by moles.

What is osmolarity?

The concentration of dissolved particles, i × M.

Sources: OpenStax, Chemistry: Atoms First 2e, section 11.4 "Colligative Properties"

Checked 9 Nov 2026. OpenStax, Chemistry: Atoms First 2e, §11.4 “Colligative Properties” (Π = MRT, van ’t Hoff factor; Example 11.10, 0.30 M glucose at 37 °C ≈ 7.6 atm; Example 11.12, molar mass from Π); R = 8.314462618 J/(mol·K) ÷ 101.325 = 0.082057 L·atm/(mol·K).

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