Solve Π = iMRT to find the osmotic pressure of a solution — the pressure needed to stop osmosis across a semipermeable membrane. Enter molar concentration, van't Hoff factor, and temperature directly, solve for a missing value, or compare how different solutes scale the result.
Inputs
Molarity of the solution, in moles per liter (mol/L).
Number of particles the solute dissociates into (1 for nonelectrolytes like glucose, 2 for NaCl, 3 for CaCl₂).
Absolute temperature in kelvin (K). Osmotic pressure requires Kelvin, not Celsius or Fahrenheit.
Result
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Enter molar concentration, van't Hoff factor, and temperature to compute osmotic pressure.
Osmotic pressure (kPa)—
Solve for a missing value
Target osmotic pressure in atmospheres (atm).
Molarity of the solution, in moles per liter.
Always required — the van't Hoff factor is never the value being solved for.
Absolute temperature in kelvin (K).
Result
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Enter the known values to solve for the missing one.
Inputs
Molarity of the solution, in moles per liter.
Absolute temperature in kelvin (K).
Pick a preset below or enter a custom value.
Common solutes (sets i)
Result
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Enter molar concentration, temperature, and a van't Hoff factor to compare osmotic pressures.
i = 1 (nonelectrolyte)—
i = 2 (e.g. NaCl)—
i = 3 (e.g. CaCl₂)—
i = 4—
3 min read3 steps7 terms3 examples6 FAQsΠ = iMRT
Osmotic pressure is one of the four classic colligative properties, alongside vapor pressure lowering, boiling point elevation, and freezing point depression.
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Walk-through
How to Use This Calculator
3 steps▸
1
Enter molar concentration, van't Hoff factor, and temperature
On the Osmotic Pressure tab, enter the solution's molarity (mol/L), its van't Hoff factor i (1 for a nonelectrolyte like glucose, 2 for NaCl, 3 for CaCl₂), and the absolute temperature in kelvin. The calculator updates instantly as you type.
2
Read the osmotic pressure
The result card shows Π in both atmospheres (atm) and kilopascals (kPa) — the pressure that would need to be applied to the solution to stop net osmotic flow across a semipermeable membrane.
3
Solve for a missing value or compare solutes
Switch to the Solve tab to find molarity or temperature from a known osmotic pressure, or use the van't Hoff tab to see how switching between common solutes (glucose, NaCl, CaCl₂) changes the pressure at the same concentration and temperature.
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Reference
Formula & Methodology
1 formula▸
Van't Hoff equation for osmotic pressure
Π = iMRT
Π is the osmotic pressure (atm), i is the van't Hoff factor (number of particles the solute dissociates into in solution), M is the molar concentration (mol/L), R is the ideal gas constant (0.08206 L·atm/(mol·K)), and T is the absolute temperature (K). Multiply Π in atm by 101.325 to convert to kilopascals (kPa).
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Glossary
Key Terms Explained
7 terms▸
Osmotic pressure (Π) ↗The minimum pressure that must be applied to a solution to prevent the inward flow of pure solvent across a semipermeable membrane. Measured in atmospheres (atm) or kilopascals (kPa).
Osmosis ↗The net movement of solvent molecules across a semipermeable membrane from a region of lower solute concentration to a region of higher solute concentration.
Van't Hoff factor (i) ↗The number of discrete particles a formula unit of solute produces in solution. Nonelectrolytes like glucose have i = 1; strong electrolytes like NaCl (i = 2) and CaCl₂ (i = 3) dissociate into multiple ions.
Molar concentration (M) ↗The number of moles of solute dissolved per liter of solution, expressed in mol/L.
Semipermeable membrane ↗A barrier that allows solvent molecules to pass through but blocks solute particles, enabling osmosis to occur across it.
Colligative property ↗A physical property of a solution — such as osmotic pressure, freezing point depression, or boiling point elevation — that depends on the concentration of dissolved particles rather than their chemical identity.
Tonicity ↗A comparative measure of the osmotic pressure of two solutions across a membrane, describing whether a solution is hypotonic, isotonic, or hypertonic relative to another (e.g. a cell's interior).
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Scenarios
Real-World Examples
3 worked examples▸
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Nonelectrolyte solution
0.1 M glucose at room temperature
Molar concentration 0.1 mol/LVan't Hoff factor 1Temperature 298 K
Π = 1 × 0.1 × 0.08206 × 298 ≈ 2.45 atm (≈ 248 kPa). Because glucose doesn't dissociate, i = 1, so the osmotic pressure depends only on molarity and temperature.
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Strong electrolyte solution
0.1 M NaCl at room temperature
Molar concentration 0.1 mol/LVan't Hoff factor 2Temperature 298 K
Π = 2 × 0.1 × 0.08206 × 298 ≈ 4.89 atm — roughly double the glucose example, because NaCl dissociates into Na⁺ and Cl⁻ ions (i = 2), doubling the effective particle concentration.
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Solving backward
Find the concentration behind a measured pressure
Osmotic pressure 5 atmVan't Hoff factor 1Temperature 310 K
Using the Solve tab with M = Π ÷ (iRT), a measured Π of 5 atm at body temperature (310 K) with i = 1 corresponds to roughly 0.196 mol/L — useful for back-calculating a solution's concentration from a lab-measured pressure.
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Reference
Cite This Calculator
APA & MLA▸
Use either format to cite this calculator in a paper, report, or resource list.
Osmotic pressure is one of the four classic colligative properties, alongside vapor pressure lowering, boiling point elevation, and freezing point depression. It tells you how strongly a solution 'pulls' solvent across a semipermeable membrane — a concept central to cell biology, IV fluid formulation, and reverse osmosis water treatment.
How the van't Hoff equation works
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The relationship Π = iMRT mirrors the ideal gas law (PV = nRT) — in fact, van't Hoff originally noticed that dilute solutions behave analogously to ideal gases. The van't Hoff factor i accounts for solutes that dissociate: a nonelectrolyte like glucose or sucrose stays as one particle per formula unit (i = 1), while ionic compounds split into multiple particles — NaCl into Na⁺ and Cl⁻ (i = 2), CaCl₂ into Ca²⁺ and two Cl⁻ (i = 3). Real solutions deviate slightly from the ideal i due to ion pairing at higher concentrations, but the formula is an excellent approximation for the dilute solutions typical of lab and biological work.
Inputs and what they mean
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Molar concentration (M) must be in moles of solute per liter of solution — not per liter of solvent (that's molality, used for freezing point depression and boiling point elevation instead). Temperature must be entered as an absolute temperature in kelvin, since the equation derives directly from the ideal gas law and using Celsius would introduce a sign error. The van't Hoff factor is a property of the specific solute, not something to be solved for — pick i = 1 for molecular solutes and look up the ionic count for salts and acids.
Limits and edge cases
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This calculator assumes ideal, dilute-solution behavior. At high concentrations, ion pairing reduces the effective van't Hoff factor below its theoretical value (e.g. real NaCl solutions behave closer to i ≈ 1.9 rather than exactly 2 at higher molarities), so lab measurements may diverge slightly from the ideal prediction. The formula also assumes the membrane is perfectly semipermeable — real membranes can have some solute leakage. For biological and medical calculations (e.g. IV fluid tonicity), always cross-check against clinical reference values rather than relying solely on the ideal formula.
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Questions
Frequently Asked Questions
6 questions▸
What is the formula for osmotic pressure?+
Osmotic pressure follows the van't Hoff equation, Π = iMRT, where Π is the osmotic pressure, i is the van't Hoff factor, M is molar concentration, R is the ideal gas constant (0.08206 L·atm/(mol·K)), and T is the absolute temperature in kelvin.
What does the van't Hoff factor mean?+
The van't Hoff factor (i) is the number of particles a solute produces when it dissolves. Nonelectrolytes like glucose or sucrose have i = 1 because they stay intact in solution. Strong electrolytes dissociate into ions: NaCl has i = 2 (Na⁺ + Cl⁻), and CaCl₂ has i = 3 (Ca²⁺ + 2 Cl⁻).
What units does this calculator use for osmotic pressure?+
The result is shown in atmospheres (atm), the natural unit given R = 0.08206 L·atm/(mol·K), and also converted to kilopascals (kPa) using 1 atm = 101.325 kPa.
Why does the formula use R = 0.08206?+
That is the ideal gas constant expressed in L·atm/(mol·K), matching the units of molarity (mol/L), pressure in atmospheres, and temperature in kelvin used throughout this calculator.
Why must temperature be in Kelvin?+
The van't Hoff equation is derived from the ideal gas law, which requires an absolute temperature scale. Using Celsius or Fahrenheit directly would produce an incorrect (or even negative) pressure, so this calculator always expects kelvin.
How does osmotic pressure relate to reverse osmosis?+
Reverse osmosis works by applying a pressure greater than a solution's natural osmotic pressure, forcing solvent to flow backward through a semipermeable membrane against its natural direction — separating pure solvent (e.g. drinking water) from the concentrated solute (e.g. salt).
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