Osmotic Pressure Calculator
Enter the molarity, van 't Hoff factor and temperature to get the osmotic pressure, or switch to molarity and enter a measured pressure.
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Formula
π = i × M × R × T
πis the osmotic pressureiis the van 't Hoff factor (particles per formula unit)Mis the molarity in mol/LR = 8.314462618 J/(mol K) = 0.082057366 L atm/(mol K)(CODATA 2018)Tis the absolute temperature in kelvin (°C + 273.15)
Rearranged for molarity: M = π ÷ (i R T). Conversions: 1 atm = 101,325 Pa = 760 mmHg, 1 bar = 100,000 Pa.
Worked example
0.1 M glucose (i = 1) at 25 °C, which is 298.15 K:
π = 1 × 0.1 × 0.082057366 × 298.15 =2.4465 atm- that is 247.9 kPa or 1,859.4 mmHg
Reverse: 2 atm at 20 °C (293.15 K) with i = 1 needs M = 2 ÷ (0.082057 × 293.15) = 0.0831 mol/L.
Frequently asked questions
What is the osmotic pressure formula?
The van 't Hoff equation is π = i M R T, where M is the molarity, R the gas constant (0.082057 L atm/(mol K)) and T the absolute temperature in kelvin. For 0.1 M glucose (i = 1) at 25 °C: 0.1 × 0.082057 × 298.15 = 2.4465 atm.
What van 't Hoff factor should I use?
Use the number of particles one formula unit gives in solution: 1 for glucose or sucrose, about 2 for NaCl or KCl, about 3 for CaCl2. Real solutions give slightly less than the ideal count because of ion pairing.
How big is the osmotic pressure of saline?
A 0.15 M NaCl solution (i = 2) at body temperature, 310.15 K, gives 2 × 0.15 × 0.082057 × 310.15 = 7.635 atm, which is 773.6 kPa. Real blood plasma is close to this order of magnitude.
How accurate is the van 't Hoff equation?
It is an ideal dilute-solution law, good to a few percent below roughly 0.1 M for non-electrolytes. Concentrated or strongly interacting solutions deviate, so treat the result as an estimate. It also uses molarity, not molality.