Osmotic Pressure Calculator
Osmotic pressure from molarity, temperature, and van't Hoff factor.
What it does
Osmotic pressure is the pressure needed to stop solvent from crossing a semipermeable membrane into a solution. It is a colligative property, which means dissolved particle count matters more than the chemical identity of the solute.
The ideal relationship is pi = iMRT. Molarity supplies the concentration, R is the gas constant in pressure-volume units, and T is absolute temperature. The van't Hoff factor i accounts for how many particles each formula unit produces in solution.
The tool above returns the pressure in atmospheres, kilopascals, millimeters of mercury, and pounds per square inch. The default case, 0.15 M with i = 2 at 37 C, gives about 7.63 atm, a pressure close to the osmotic strength of a typical saline solution.
The formula assumes ideal dilute behavior. Strong electrolytes do not dissociate completely, ion pairing reduces the effective particle count, and concentrated solutions need activity corrections. Use the result as an estimate, not a measured colligative property.
How to use
- Enter the solute molarity in moles per liter.
- Enter the van't Hoff factor for the solute. Use 1 for a non-electrolyte such as glucose.
- Enter the temperature in Celsius.
- Read the pressure in atm first, then the converted units.
- Check that i is reasonable for the solute and concentration.
- Reduce the effective i if the solution is concentrated or strongly ion paired.
Formula
- Pi
- Osmotic pressure in atmospheres before unit conversion.
- i
- Van't Hoff factor, the effective number of particles per formula unit.
- M
- Solute molarity in moles per liter.
- R
- Ideal gas constant, 0.082057 L atm/(mol K).
- T
- Absolute temperature in kelvin.
One atm equals 101.325 kPa, 760 mmHg, and 14.6959 psi. The calculator computes the atmosphere value first and converts it, so the four outputs stay consistent.
Worked example
Example: 0.15 M, i = 2, 37 C
A saline-like solution has molarity 0.15 mol/L, van't Hoff factor 2, and temperature 37 C.
- Convert temperature: 37 + 273.15 = 310.15 K.
- Multiply i x M: 2 x 0.15 = 0.30 mol/L of particles.
- Multiply by R: 0.30 x 0.082057 = 0.0246171.
- Multiply by T: 0.0246171 x 310.15 = 7.635 atm.
- Convert: 7.635 x 101.325 = 773.62 kPa.
- Convert: 7.635 x 760 = 5,803 mmHg, and 7.635 x 14.6959 = 112.20 psi.
Reference table
| Solute | Particles | Typical i |
|---|---|---|
| Glucose | 1 molecule | 1 |
| NaCl | 2 ions | 2 |
| CaCl2 | 3 ions | 3 |
| Na3PO4 | 4 ions | 4 |
| Protein | 1 molecule | 1 |
Limits
- Assumes ideal dilute solution behavior. High molarity, ion pairing, and solute-solute interactions reduce accuracy.
- Uses the ideal van't Hoff factor you enter. Real electrolytes often have an effective i below the formula count.
- Does not account for membrane permeability, hydrostatic pressure, or the presence of multiple solutes unless you combine them into the molarity and i.
- Temperature is assumed uniform. Osmotic pressure in a living system can also depend on reflection coefficients and active transport.
Common mistakes
- Leaving temperature in Celsius instead of converting to kelvin.
- Using the number of ions in the formula as i without considering incomplete dissociation.
- Entering millimolar concentration as if it were molar.
- Adding the molarities of each ion and then multiplying by i again.
- Treating the ideal result as exact for seawater or other concentrated solutions.
Try it yourself
Quick checks. Answers sit tucked under each question.
0.10 M glucose, i = 1, at 20 C. What is the osmotic pressure?
T is 293.15 K. Pi = 1 x 0.10 x 0.082057 x 293.15 = 2.41 atm, or about 243.74 kPa.
0.10 M Na3PO4, i = 4, at 20 C. What is the pressure?
Pi = 4 x 0.10 x 0.082057 x 293.15 = 9.62 atm. The factor 4 assumes complete dissociation.
The default solution has i = 2 and gives 7.63 atm. What happens if the solute behaves as a non-electrolyte with i = 1?
The pressure halves to 3.82 atm because the particle count is halved. The other inputs stay the same.
Questions
What is osmotic pressure in simple terms?
It is the pressure required to stop water from moving across a semipermeable membrane into a solution. Higher solute particle concentration means higher osmotic pressure.
Why is the van't Hoff factor needed?
The formula counts particles, not formula units. NaCl releases two ions per formula unit in dilute solution, so i is about 2.
Is osmotic pressure the same as osmolarity?
No. Osmolarity is a concentration of particles. Osmotic pressure is the pressure those particles can generate at a given temperature.
Can osmotic pressure be negative?
The ideal formula gives a positive pressure for a positive concentration. A negative gauge reading would reflect a pressure difference, not the absolute osmotic pressure.
Why use 0.082057 for R?
That value pairs with liters, atmospheres, moles, and kelvin. Using 8.314 would give pascals instead, so the units must match.
Does temperature really change osmotic pressure?
Yes. The formula is directly proportional to absolute temperature, so warming a fixed solution raises its osmotic pressure.