Osmotic pressure calculator: Π = i · M · R · T
This osmotic pressure calculator uses Π = i · M · R · T from OpenStax Chemistry 2e with R = 0.08206 L·atm/(mol·K). Example: a 0.30 M glucose solution at 37 °C (310.15 K) has an osmotic pressure of 7.64 atm.
Example: Concentration as: molarity M · Molarity M 0.3 mol/L · Temperature 25 °C · van ’t Hoff factor i 1 → Osmotic pressure: Osmotic pressure 7.34 atm = 7.44 bar. Source: OpenStax Chemistry 2e, 11.4 Colligative Properties: Π = MRT, R = 0.08206 L·atm/(mol·K), Example 11.10 (0.30 M glucose, 37 °C → 7.6 atm), check-your-learning (5.0 g methanol in 0.750 L → 5.3 atm), Table 11.3 van’t Hoff factors (read 09.10.2026). Updated: .
How it is calculated
Π = i × M × R × T. The osmotic pressure of a dilute solution depends only on the molar concentration M of dissolved particles and on the absolute temperature T in kelvin. R is the gas constant, 0.08206 L·atm/(mol·K) in the units OpenStax uses. The van ’t Hoff factor i counts the particles per formula unit: 1 for glucose, 2 for NaCl if it dissociates completely.
Examples
| Solution | M | i | Temperature | Π |
|---|---|---|---|---|
| glucose | 0.30 mol/L | 1 | 37 °C | 7.64 atm |
| 5.0 g methanol in 0.750 L | 0.208 mol/L | 1 | 37 °C | 5.30 atm |
| NaCl | 0.10 mol/L | 2 | 25 °C | 4.89 atm |
| any non-electrolyte | 1.0 mol/L | 1 | 25 °C | 24.47 atm |
OpenStax gives 7.6 atm and 5.3 atm for the first two. Converted with 1 atm = 101325 Pa (NIST), 7.64 atm are 7.74 bar. The default 0.30 mol/L at 25 °C gives 7.34 atm or 7.44 bar.
Electrolytes and real solutions
For salts, multiply by i. OpenStax Table 11.3 shows that measured factors are smaller than the ideal ones – 1.9 instead of 2 for NaCl at 0.050 m – because ions attract each other. Applying a pressure greater than Π reverses osmosis; this is the principle of reverse osmosis water purification. Molarity from mass and volume is worked out by the molarity calculator; the freezing point and boiling point of a solution by the freezing point depression calculator.
Frequently asked questions
What is the formula for osmotic pressure?
Π = i · M · R · T with M in mol/L, T in kelvin and R = 0.08206 L·atm/(mol·K). 0.30 M glucose at 37 °C: 0.30 × 0.08206 × 310.15 = 7.64 atm.
How do I calculate osmotic pressure from grams?
First the molarity: 5.0 g methanol ÷ 32.04 g/mol = 0.156 mol in 0.750 L = 0.208 mol/L. At 37 °C that gives 5.30 atm.
What is i for NaCl?
Ideally 2, because NaCl splits into Na⁺ and Cl⁻. Measured values are slightly lower, 1.9 at 0.050 m.
Why must the temperature be in kelvin?
The equation is proportional to absolute temperature. The calculator adds 273.15 to the value in °C.
How do I convert atm to bar or kPa?
1 atm = 101325 Pa = 1.01325 bar = 101.325 kPa. 24.47 atm are 24.79 bar.
How exact is the result?
It is a calculated value for an ideal, dilute solution. Concentrated or ionic solutions show a lower osmotic pressure than this estimate.
Sources and legal basis
- OpenStax Chemistry 2e, 11.4 Colligative Properties: Π = MRT, R = 0.08206 L·atm/(mol·K), Example 11.10 (0.30 M glucose, 37 °C → 7.6 atm), check-your-learning (5.0 g methanol in 0.750 L → 5.3 atm), Table 11.3 van’t Hoff factors (read 09.10.2026)
- NIST SP 811, Appendix B.8 – 1 atm = 101 325 Pa, 1 bar = 10⁵ Pa (read 09.10.2026)
As of: · Editorial policy
Related tools
- Molarity calculatorMolarity calculator: mol/L from mass and volume, the mass to weigh out for a solution, molarity from mass percent and density, and simple stoichiometry.
- Freezing point depression calculator with boiling point elevationFreezing point depression calculator: ΔTf = i·Kf·m and ΔTb = i·Kb·m for water, acetic acid, benzene, chloroform or nitrobenzene – from molality or from grams.
- Molar Mass CalculatorCalculate molar mass in g/mol from any chemical formula – with brackets, hydrates like CuSO4·5H2O, mass percent by element, working steps and n = m/M.
- Ideal Gas Law Calculator: Pressure, Volume, Moles or TemperatureIdeal gas law calculator: solve PV = nRT for pressure, volume, moles or temperature – units from Pa to psi and atm, °C, K or °F, plus mass, density and steps.
- Dilution Calculator: C1V1 = C2V2, Dilution Ratios and MixingDilution calculator using C1V1 = C2V2: stock volume and diluent, final concentration, ratios like 1:50 (parts or total) and mixing two solutions.
- Online CalculatorCalculator online, free and instant: type or tap and see the answer as you go – order of operations, brackets, percent, square root, steps and a history list.
- Bar Graph MakerBar graph maker: type or paste your data, choose vertical or horizontal bars, sort them by size and save the finished chart as PNG or SVG – free, no sign-up.
- Rounding CalculatorRounding calculator: round numbers to decimal places, tens or 5 cents – half up, half to even, round down or up – with the working and a comparison.
- Square numbers and cube numbersSquare numbers as a list up to 200 with differences, plus cube, triangular and other figurate numbers. Check whether a number belongs, with root and neighbours.