Osmotic Pressure Calculator

Background.

This calculator applies van 't Hoff's law, Π = i·c·R·T, in three directions: predicting the osmotic pressure of a solution, recovering a concentration and molar mass from a pressure you measured, and recovering the van 't Hoff factor itself. Results come back in kilopascals, bar and atmospheres, because osmotic pressures are quoted in all three and the conversions between them are a common source of factor-of-a-hundred errors.

Osmotic pressure is defined by IUPAC (Gold Book, term O04344) as the excess pressure required to maintain osmotic equilibrium between a solution and the pure solvent separated by a membrane permeable only to the solvent. It is a pressure you would have to apply to the solution to stop solvent flowing into it — not a pressure the solution exerts on its container, which is the usual first misconception.

The numbers are larger than most people expect. A 0.1000 mol/L sucrose solution at 25 °C — 34.23 grams per litre, a weak syrup — has an osmotic pressure of 247.90 kPa, which is 2.479 bar or 2.447 atmospheres. That is roughly two and a half times atmospheric pressure, from a solution you could drink. The reason reverse osmosis is energetically expensive is written into that number.

Here is the check that shows the units are right, and it is also the historical point of the law. Take 1 mol/L of an ideal solute at 0 °C: Π = 2271.10 kPa = 22.414 atm. That figure, 22.414, is the molar volume of an ideal gas at 0 °C and 1 atmosphere in litres per mole. Van 't Hoff's 1887 insight was exactly this — that a dissolved solute behaves, as far as osmotic pressure goes, like a gas occupying the volume of the solution.

The part that needs stating above the answer rather than in a footnote is the van 't Hoff factor. It is routinely taught as a particle count — 1 for sucrose, 2 for NaCl, 3 for CaCl₂ — and for a real solution that is wrong, sometimes badly. NIST's critically evaluated osmotic coefficients for sodium chloride (Hamer and Wu, Journal of Physical and Chemical Reference Data 1, 1047, 1972, Table 16) give i = 2φ = 1.976 at 0.001 mol/kg, 1.866 at 0.1, 1.842 at 0.5, and 2.540 at 6 mol/kg. So the ideal value of 2 is about 7 % too high at 0.1 molal — and about 21 % too LOW at 6 molal, because the osmotic coefficient climbs back through 1 near 1.5 molal. The error does not just grow with concentration, it changes sign. Treat i on this page as the practical, experimentally determined factor, and use a measured value when you have one.

Two further limits. A pressure measurement determines only the product i × c, never the two separately, so recovering a molar mass from osmometry requires you to know that the solute does not dissociate — which is exactly why the technique is used for polymers and proteins and not for salts. And van 't Hoff's law is a limiting law, exact only as concentration approaches zero; its accuracy at working concentrations is what the osmotic coefficient measures.

One convention note. The quantity i × c is often called osmolarity and quoted in osmol/L. The IUPAC Gold Book entry for osmotic pressure explicitly discourages both that unit and that term, so this page reports it as a total dissolved particle concentration in mol/L. And unlike the sibling freezing-point-depression and boiling-point-elevation calculators, which use molality, this law is written in molarity — moles per litre of solution. The two differ by about 0.4 % for a 0.1 mol/L aqueous solution and by a great deal more in concentrated or non-aqueous ones.

What is osmotic pressure calculator?

Osmosis is the net movement of solvent through a semipermeable membrane from the side where the solvent's chemical potential is higher — the dilute side — to the side where it is lower. Osmotic pressure is the pressure that must be applied to the concentrated side to stop that flow. Formally, and this is the IUPAC definition (Gold Book term O04344), it is the excess pressure required to maintain osmotic equilibrium between a solution and the pure solvent across a membrane permeable only to the solvent.

It is a colligative property, which means it depends on how many solute particles are present and not on what they are. A mole of glucose, a mole of urea and a mole of a synthetic polymer all exert the same osmotic pressure at the same molar concentration and temperature. That indifference to chemical identity is what makes osmometry useful for measuring molar mass: dissolve a known mass, measure the pressure, and the number of particles follows regardless of what the substance is.

Van 't Hoff showed in 1887 that a dilute solution obeys Π = i·c·R·T, formally identical to the ideal gas law with the molar concentration in place of n/V. The analogy is not a coincidence but it is also not an assertion that solute particles behave like a gas in any mechanical sense; both arise from the same statistical counting of particles in a volume. Van 't Hoff received the first Nobel Prize in Chemistry in 1901, partly for this work.

The factor i is where the law meets reality. For a substance that does not dissociate, i is 1. For an electrolyte the ideal value is the number of ions per formula unit — 2 for NaCl, 3 for CaCl₂ — but real electrolyte solutions deviate, because ions interact electrostatically and are not independent particles. The measured deviation is expressed as the osmotic coefficient φ, with i = νφ for a salt releasing ν ions. NIST's evaluated tables show φ falling below 1 in dilute solution, reaching a minimum, and then climbing above 1 in concentrated solution.

Osmotic pressure is unusually large compared with the other colligative properties, and that is why it is measurable where they are not. A solution dilute enough to depress a freezing point by an unmeasurable few thousandths of a degree may still develop several kilopascals of osmotic pressure. For a polymer of molar mass 100,000 g/mol at 10 g/L, the freezing-point depression is around 0.0002 °C — hopeless — while the osmotic pressure is around 0.25 kPa, which a differential manometer reads comfortably.

How to use this calculator.

1. 01Choose the direction. Predicting a pressure is the forward calculation; the two inverse modes are for when you have measured a pressure and want either the concentration and molar mass, or the van 't Hoff factor.
2. 02Enter the concentration as MOLARITY — moles per litre of solution. If you have molality, they differ by under half a per cent in dilute aqueous solution but diverge in concentrated ones.
3. 03Set the van 't Hoff factor. Use 1 for anything that does not dissociate: sugars, urea, glycerol, polymers, proteins. For a salt, prefer a measured value at your concentration over the formula-unit count, which is systematically wrong.
4. 04Set the temperature in °C. The calculation converts to kelvin, and the pressure is proportional to absolute temperature — 25 °C and 37 °C differ by 4.0 %.
5. 05Enter the mass concentration in g/L if you want the molar mass output. It is used for nothing else.
6. 06For osmometry, choose the concentration mode, enter your measured pressure and the mass concentration you prepared, leave i at 1, and read the molar mass.
7. 07For measuring a van 't Hoff factor, choose that mode and supply both the measured pressure and a concentration you know independently. Remember that only the product i × c is determined by the pressure, so you must know one of them from elsewhere.
8. 08Check your units on the pressure input. It is in kPa; multiply a bar reading by 100 and an atmosphere reading by 101.325.

The formula.

THE LAW. Π = i·c·R·T, where Π is the osmotic pressure, i the van 't Hoff factor, c the molar concentration in mol per litre of solution, R the molar gas constant and T the absolute temperature. Rearranged, c = Π/(i·R·T) and i = Π/(c·R·T). The molar mass follows from M = (mass concentration)/c. All three modes are exact closed forms; nothing is iterated.

THE CONSTANT. R = 8.314462618… J mol⁻¹ K⁻¹, exact since the 2019 SI redefinition fixed R = N_A·k (CODATA 2022). Numerically the same value serves as 8.314462618 kPa·L·mol⁻¹·K⁻¹, which is the form used here so that concentrations in mol/L and temperatures in K give pressures directly in kPa.

WORKED. 0.1000 mol/L sucrose at 25 °C with i = 1. T = 298.15 K, so R·T = 2478.95703 kPa·L/mol and Π = 1 × 0.1000 × 2478.95703 = 247.895703 kPa. Dividing by the exact definitions 1 bar ≡ 100 kPa and 1 atm ≡ 101.325 kPa gives 2.478957 bar and 2.446540 atm. With 34.2297 g/L of sucrose dissolved, M = 34.2297/0.1000 = 342.297 g/mol, which is C₁₂H₂₂O₁₁ using the CIAAW conventional atomic weights C 12.011, H 1.008 and O 15.999.

THE UNIT CHECK WORTH REMEMBERING. Put c = 1 mol/L, i = 1 and T = 0 °C: Π = 8.314462618 × 273.15 = 2271.0955 kPa = 22.414 atm. That number is the molar volume of an ideal gas at 0 °C and 1 atm in litres per mole. Recovering it confirms the gas constant is being used in kPa·L·mol⁻¹·K⁻¹ with no stray factor, and it is precisely the analogy van 't Hoff drew in 1887.

THE VAN 'T HOFF FACTOR IS MEASURED, NOT COUNTED. For a salt releasing ν ions, i = νφ where φ is the osmotic coefficient. NIST's evaluated values for NaCl at 25 °C (Hamer and Wu 1972, Table 16) give φ = 0.988 at 0.001 mol/kg, 0.968 at 0.010, 0.933 at 0.100, 0.921 at 0.500, 0.936 at 1.000, 0.984 at 2.000 and 1.270 at 6.000. So i runs 1.976, 1.936, 1.866, 1.842, 1.872, 1.968 and 2.540. The ideal i = 2 is 7.2 % too high at 0.1 molal and 21 % too low at 6 molal — the error reverses sign around 1.5 molal, where φ passes through 1. Those coefficients are tabulated on a molality basis while this law uses molarity; the two differ by about 0.4 % for a 0.1 mol/L aqueous solution, well below the non-ideality they describe.

WHAT A PRESSURE MEASUREMENT CAN AND CANNOT TELL YOU. Π depends on i and c only through their product, so no single pressure measurement can separate them. Doubling the concentration and doubling the van 't Hoff factor give exactly the same pressure. Osmometry for molar mass therefore works only when you know independently that the solute does not dissociate — which is why it is a polymer and protein technique.

CONVENTIONS. Π in kPa, bar and atm; c in mol per litre of solution; mass concentration in g/L; T entered in °C and converted to K; i and the osmotic coefficient dimensionless; M in g/mol. There is no STP or SATP reference state, because this is a solution property rather than a gas property; what must be specified is the temperature, and that both sides of the membrane are at it. The regime is ideal-dilute with a membrane permeable to solvent only; a leaky membrane has a reflection coefficient below one and gives a lower observed pressure.

ROUNDING STAGE. Nothing is rounded at an intermediate step. Rounding happens only when a result is returned, at ten decimal places, falling back to twelve significant digits where ten decimal places would collapse a genuinely non-zero value — as it would for a nanomolar solution, whose pressure is a few micropascals.

INVALID DOMAIN. A concentration, van 't Hoff factor, measured pressure or mass concentration of zero or less raises an error naming the field. A temperature at or below −273.15 °C is rejected rather than being allowed to return a zero or negative pressure; −273.14 °C is accepted and returns a tiny positive value.

A worked example.

Frequently asked questions.

References& sources.

1. [1]IUPAC, Compendium of Chemical Terminology (the Gold Book), entry "osmotic pressure", term identifier O04344, doi:10.1351/goldbook.O04344, source documents the IUPAC Green Book 2nd and 3rd editions: "the excess pressure required to maintain osmotic equilibrium between a solution and the pure solvent separated by a membrane permeable only to the solvent"; for ideal dilute solutions it equals the product of the molar concentration of solutes, the gas constant and the absolute temperature. The same entry states that expressing the amount in "osmol", and the term "osmolarity", are DISCOURAGED — which is why the i×c output on this page is reported as a particle concentration in mol/L. Independent, open access; entry identifier and definition confirmed 2026-07-29 through the public index (the Gold Book server refuses automated fetches).
2. [2]SECOND, INDEPENDENT AUTHORITY (BUILD-BRIEF §9.1). Hamer, W. J.; Wu, Y.-C. "Osmotic Coefficients and Mean Activity Coefficients of Uni-univalent Electrolytes in Water at 25 °C." Journal of Physical and Chemical Reference Data 1(4), 1047 (1972). NIST Standard Reference Data; critically evaluated data for 79 electrolytes. Table 16 (NaCl) gives the osmotic coefficient φ = 0.988 at 0.001 mol/kg, 0.968 at 0.010, 0.933 at 0.100, 0.921 at 0.500, 0.936 at 1.000, 0.984 at 2.000 and 1.270 at 6.000 — so the practical van 't Hoff factor i = 2φ is 1.976, 1.936, 1.866, 1.842, 1.872, 1.968 and 2.540 respectively, and the ideal value of 2 errs in BOTH directions across that range. Coefficients are tabulated on the molality basis while van 't Hoff's law uses molarity; the difference is about 0.4 % for a 0.1 mol/L aqueous solution. Open access, NIST-hosted; retrieved 2026-07-29.
3. [3]CODATA 2022 recommended value of the molar gas constant R = 8.314462618… J mol⁻¹ K⁻¹, listed as exact (no standard uncertainty) because R = N_A·k is fixed by the 2019 SI redefinition. Used here in the numerically identical form 8.314462618 kPa·L·mol⁻¹·K⁻¹. NIST Reference on Constants, Units and Uncertainty; retrieved 2026-07-29.
4. [4]Commission on Isotopic Abundances and Atomic Weights (CIAAW), IUPAC — Standard Atomic Weights, 2021 table incorporating the 2024 revisions. Carbon, hydrogen and oxygen are published as INTERVALS (C = [12.0096, 12.0116], H = [1.00784, 1.00811], O = [15.99903, 15.99977]) because their isotopic composition varies naturally; the single-valued conventional atomic weights C 12.011, H 1.008 and O 15.999 are the ones used here, giving M(C₁₂H₂₂O₁₁) = 342.297 g/mol for the sucrose default. Open access; retrieved 2026-07-29.
5. [5]van 't Hoff, J. H. "Die Rolle des osmotischen Druckes in der Analogie zwischen Lösungen und Gasen." Zeitschrift für physikalische Chemie 1, 481–508 (1887) — the original statement of the law and of the gas analogy that makes 1 mol/L at 0 °C come out at 22.414 atm. PRINT / BIBLIOGRAPHIC: the 1887 volume has no machine-readable public copy and is cited as such rather than linked as though it were live.