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Osmotic Pressure Calculator (van 't Hoff)

Calculate osmotic pressure from concentration and temperature with the van 't Hoff equation, or find the van 't Hoff factor, molarity or temperature. Includes osmolarity.

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    van 't Hoff Law of Osmotic Pressure formula

    π = i M R T
    SymbolQuantitySI unitMeaning
    πOsmotic pressurePaOsmotic pressure
    ivan 't Hoff factor—van 't Hoff factor — particles produced per formula unit
    MMolar concentrationmol/m³Molar concentration of solute
    TTemperatureKAbsolute temperature

    What is van 't Hoff Law of Osmotic Pressure?

    van 't Hoff Law of Osmotic Pressure: The osmotic pressure of a dilute solution equals the pressure the solute particles would exert as an ideal gas occupying the same volume. — Jacobus van 't Hoff, 1887

    Osmosis is the diffusion of solvent through a semipermeable membrane toward the more concentrated solution. The osmotic pressure π is the pressure needed to stop that flow. For dilute solutions it follows the van 't Hoff equation, which has the same form as the ideal gas law.

    The van 't Hoff factor i counts dissolved particles: about 1 for glucose, about 2 for NaCl and about 3 for CaCl₂ (real values are slightly lower because of ion pairing). Osmotic pressure is central to reverse osmosis desalination, IV fluid design, plant turgor and molar-mass determination of polymers.

    How to use this calculator

    1. Choose the quantity you want to find in the Calculate menu. It is highlighted as the result field.
    2. Enter the known values. Scientific notation such as 1.6e-11 is accepted.
    3. Select a unit for each value. Units are converted to SI automatically.
    4. The answer updates as you type. Open Show calculation steps to see the working, or use Copy result to share a link with your inputs.

    Worked example

    Normal saline is 0.9% NaCl ≈ 0.154 mol/L, with i ≈ 2. What is its osmotic pressure at body temperature (37 °C)?

    1. T = 310.15 K, M = 154 mol/m³.
    2. π = 2 × 154 × 8.314 × 310.15 = 7.94 × 10⁵ Pa = 7.84 atm.

    Frequently asked questions

    Why is osmotic pressure so large?

    Even modest concentrations correspond to many particles. A 1 mol/L ideal solute at 25 °C produces about 24.5 atm, the same as 1 mol of ideal gas squeezed into 1 L.

    How is osmotic pressure related to diffusion?

    Osmosis is net diffusion of solvent molecules down their own chemical-potential gradient. The membrane blocks the solute, so only the solvent moves.