Osmotic Pressure Calculator — van't Hoff Equation π = iMRT
Enter the molar concentration of your solute, its van't Hoff factor i (1 for non-electrolytes, 2 for NaCl, etc.) and the solution temperature to calculate the osmotic pressure in atm, kPa, mmHg and bar.
Solute type (van't Hoff factor i)
mol/L
°C
Pressure needed to stop osmotic flow across a semipermeable membrane
- 1
Temperature in Kelvin
25 + 273.15 = 298.15 - 2
i × M × R
1 × 0.1 × 0.082057 = 0.008206 - 3
Osmotic pressure π = i × M × R × T
0.008206 × 298.15 = 2.4465π = iMRT; result in atm using R = 0.082057 L·atm/(mol·K).
How does this calculator work?
Osmotic pressure is π = i × M × R × T, where i is the van't Hoff factor, M is molarity (mol/L), R = 0.08206 L·atm/(mol·K) and T is temperature in Kelvin. A 0.1 M glucose solution at 25 °C gives π ≈ 2.45 atm; 0.1 M NaCl gives ≈ 4.89 atm because i = 2.
Formula
How this is calculated
Osmosis is the net flow of solvent through a semipermeable membrane from a region of lower solute concentration to higher concentration. The osmotic pressure π is the external pressure needed to exactly stop this flow. The van't Hoff equation π = iMRT treats a dilute solution like an ideal gas: the product of the particle count factor i, the molar concentration M (mol/L), the gas constant R (0.08206 L·atm/mol·K) and the absolute temperature T (Kelvin) gives π in atmospheres.
The van't Hoff factor i accounts for dissociation of electrolytes in water. A non-electrolyte such as glucose stays as one particle (i = 1). A strong 1:1 electrolyte such as NaCl dissociates completely into Na⁺ and Cl⁻ (i = 2 ideally). Real solutions deviate from ideal values because of ion pairing — actual i values are slightly less than the integer; the presets use ideal values as a conservative approximation.
Osmotic pressure can be surprisingly large: a 1 M NaCl solution at 25 °C has π ≈ 49 atm (≈ 4.9 MPa), far above the pressure of a car tyre. This is why desalination by reverse osmosis requires high-pressure pumps. The equation is accurate for dilute solutions (M < ~0.5 mol/L); at higher concentrations activity coefficients deviate significantly from 1.
Frequently asked questions
i is the number of particles (ions and molecules) produced per formula unit when the solute dissolves. For glucose (non-electrolyte) i = 1. For NaCl (strong electrolyte) i ≈ 2 because it splits into Na⁺ + Cl⁻. For CaCl₂ i ≈ 3 (Ca²⁺ + 2 Cl⁻). Real values are slightly lower due to ion–ion interactions.
The formula uses molarity M in mol per litre (mol/L), not molality. Enter how many moles of solute are dissolved in each litre of solution. If you have a mass fraction or weight percent, you will need to convert first using the molar mass of your solute.
Temperature appears explicitly in the van't Hoff equation (T in Kelvin). Higher temperature increases osmotic pressure proportionally — a 10 °C rise from 25 °C to 35 °C increases π by about 3.4%. Body temperature (37 °C) is used in clinical osmolarity calculations for blood and IV fluids.
Also known as
TG we-Calculate Editorial Team. (2026). Osmotic Pressure Calculator — van't Hoff Equation π = iMRT [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/osmotic-pressure-calculator
TG we-Calculate Editorial Team. "Osmotic Pressure Calculator — van't Hoff Equation π = iMRT." TG we-Calculate. 2026. https://we-calculate.com/calculator/osmotic-pressure-calculator.
TG we-Calculate Editorial Team, "Osmotic Pressure Calculator — van't Hoff Equation π = iMRT," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/osmotic-pressure-calculator
@misc{wecalculate_osmotic_pressure_calculator, title = {Osmotic Pressure Calculator — van't Hoff Equation π = iMRT}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/osmotic-pressure-calculator}}, year = {2026}, note = {TG we-Calculate} }
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