Osmotic Pressure Calculator

π = iMRT. This compares calculated iM with an illustrative 280–320 mOsm/L reference band only. Tonicity also depends on the membrane and solute permeability. Urea can cross red-cell membranes, so equal osmolarity does not establish isotonicity. This calculation cannot predict cell shape or determine whether a solution is suitable for infusion.

What is Osmotic Pressure?

Osmosis is the net movement of solvent (usually water) across a semipermeable membrane from a region of low solute concentration to a region of high solute concentration. Osmotic pressure is the external pressure that would have to be applied to the more concentrated side to stop that flow completely. Because it depends only on the number of dissolved particles and not on what they are, osmotic pressure is a colligative property, like freezing point depression and boiling point elevation.

Osmotic Pressure Formula (van't Hoff Equation)

For a dilute solution, osmotic pressure follows an equation that looks just like the ideal gas law:

where:

• π = osmotic pressure (atm)
• i = van't Hoff factor — the number of particles each formula unit produces in solution
• M = molarity of the solution (mol/L)
• R = ideal gas constant = 0.08206 L·atm/(mol·K)
• T = absolute temperature in kelvin (K) — add 273.15 to a Celsius value

The product i × M is the osmolarity of the solution (osmol/L), which is what really drives osmosis. Multiply by 1000 to express it in mOsm/L, the unit most often used in biology and medicine.

Worked Example: Isotonic Saline

Normal saline used for IV drips is 0.9% NaCl, which is about 0.15 mol/L. Sodium chloride dissociates into Na⁺ and Cl⁻, so i ≈ 2. At body temperature (37 °C = 310.15 K):

This compares calculated iM with an illustrative 280–320 mOsm/L reference band only. Tonicity also depends on the membrane and solute permeability. Urea can cross red-cell membranes, so equal osmolarity does not establish isotonicity. This calculation cannot predict cell shape or determine whether a solution is suitable for infusion.

Understanding the van't Hoff Factor (i)

These are ideal values that assume complete dissociation. In real solutions, ion pairing makes the measured factor slightly lower (for example, NaCl is closer to 1.9 in practice). You can type a measured value into the van't Hoff factor box to override the default.

Osmolarity comparison

This compares calculated iM with an illustrative 280–320 mOsm/L reference band only. Tonicity also depends on the membrane and solute permeability. Urea can cross red-cell membranes, so equal osmolarity does not establish isotonicity. This calculation cannot predict cell shape or determine whether a solution is suitable for infusion.

Where Osmotic Pressure Matters

How to Use This Calculator

1. Enter the concentration: Type the molarity directly, or switch to mass mode and enter the solute mass, molar mass and solution volume.
2. Set the van't Hoff factor: Pick the solute type to load its ideal i, or enter a measured value.
3. Enter the temperature: Choose °C, K or °F — the tool converts to kelvin for you.
4. Click Calculate: The osmotic pressure is shown in atm, kPa, mmHg, bar and psi.
5. π = iMRT; Osmolarity comparison.

Frequently Asked Questions

What is osmotic pressure?

Osmotic pressure is the pressure that must be applied to a solution to stop pure solvent from flowing into it across a semipermeable membrane. It is a colligative property, meaning it depends on the number of dissolved particles rather than their identity. The more particles dissolved, the higher the osmotic pressure.

What is the formula for osmotic pressure?

The van't Hoff equation is π = i × M × R × T, where π is the osmotic pressure, i is the van't Hoff factor (number of particles per formula unit), M is the molarity in mol/L, R is the gas constant 0.08206 L·atm/(mol·K), and T is the absolute temperature in kelvin.

What is the van't Hoff factor?

The van't Hoff factor i is the number of dissolved particles produced by one formula unit of solute. Non-electrolytes such as glucose or urea do not dissociate, so i is 1. NaCl splits into two ions, so i is about 2. CaCl₂ splits into three, so i is about 3. Real solutions fall slightly below these ideal values because of ion pairing.

Why must temperature be in kelvin?

Osmotic pressure is directly proportional to absolute temperature. Only the kelvin scale starts at absolute zero, so it is the only scale that gives a correct proportional relationship. Using Celsius or Fahrenheit directly would give a wrong answer. To convert, add 273.15 to a Celsius temperature.

What does isotonic, hypotonic and hypertonic mean?

They describe what a solution does to a cell. In an isotonic solution the cell neither gains nor loses water; in a hypotonic solution it takes in water and swells; in a hypertonic solution it loses water and shrinks. This calculator only compares the calculated iM with an illustrative 280–320 mOsm/L band. Tonicity also depends on the membrane and on whether solutes can cross it: urea crosses red-cell membranes, so equal osmolarity does not make a solution isotonic. The result cannot predict cell shape or show whether a solution is suitable for infusion.

What is the osmotic pressure of blood?

Blood plasma has an osmolality of roughly 280–300 mOsm/kg. With the van't Hoff equation at body temperature (37 °C), about 0.29–0.30 osmol/L corresponds to an osmotic pressure of roughly 7.4–7.6 atm. Treat this as an approximation, because body fluids are not ideal solutions.

Related Calculators

• Freezing Point Depression Calculator
• Boiling Point Elevation Calculator
• Molarity Calculator
• Ideal Gas Law Calculator

Additional Resources

• Osmotic Pressure - Wikipedia
• Tonicity - Wikipedia