Osmotic Pressure Calculator

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Introduction to osmotic pressure and the van 't Hoff equation

Osmotic pressure is the excess pressure that must be applied to a solution to stop pure solvent from flowing into it across a membrane that passes solvent but not solute. It is not a pressure the solution already exerts on its container; it is the pressure you would have to supply to hold osmosis at bay. IUPAC defines it as the excess pressure needed to maintain osmotic equilibrium between a solution and the pure solvent separated by a membrane permeable only to the solvent, and gives the rigorous expression in terms of solvent activity rather than concentration.

Thermodynamically, dissolving anything in a solvent lowers that solvent's chemical potential. Solvent on the pure side therefore sits at a higher chemical potential than solvent on the solution side, and it moves down the gradient. Applying hydrostatic pressure to the solution raises the solvent's chemical potential there; the osmotic pressure $Π$ is exactly the pressure at which the two chemical potentials match again and net flow stops.

Osmotic pressure is a colligative property: to a first approximation it depends on how many dissolved particles are present per unit volume, not on what those particles are. A mole of glucose, a mole of sucrose and half a mole of fully dissociated sodium chloride all produce about the same osmotic pressure in a litre of water, because all three deliver about one mole of independently moving particles. That is why an ionic solute needs a multiplier — the van 't Hoff factor — before its molarity can be compared with a molecular solute.

This calculator implements the van 't Hoff equation with three refinements that matter in practice: the temperature is always converted to kelvin before use, the gas constant is derived from the exact SI value rather than a rounded textbook figure, and an optional osmotic coefficient lets you correct the ideal particle count for the non-ideality of real electrolyte solutions. It also reports osmolarity alongside pressure, because in clinical and pharmaceutical work the particle concentration is usually the number people actually want.

Formula: from solvent activity to Π = φ i M R T

The exact statement of osmotic equilibrium relates the osmotic pressure to the activity of the solvent A:

Formula: Π = − (R ⁢ T) / V_A^* ⁢ ln ⁡ a_A

$Π = - \frac{R T}{V_{A}^{*}} \ln a_{A}$

where $V_{A}^{*}$ is the partial molar volume of the pure solvent and $a_{A}$ its activity in the solution. Expanding the logarithm for a dilute solution, in which $a_{A} \approx x_{A} = 1 - x_{B}$ , gives the limiting law that carries van 't Hoff's name:

Formula: Π = c_B ⁢ R ⁢ T

$Π = c_{B} R T$

Here $c_{B}$ is the concentration of individually moving entities — molecules, ions, colloidal particles — irrespective of their chemical nature. For a solute that dissociates, that entity concentration is the analytical molarity multiplied by the van 't Hoff factor, and the working form used by this calculator adds the osmotic coefficient $φ$ :

Formula: Π = φ ⁢ i ⁢ M ⁢ R ⁢ T

$Π = φ i M R T$

$Π$ — osmotic pressure, reported here in atm, bar, kPa, psi or mmHg.
$φ$ — osmotic coefficient, dimensionless, 1 for an ideal solution.
$i$ — van 't Hoff factor, the limiting number of particles released per formula unit.
$M$ — analytical molarity of the solute in mol/L.
$R$ — molar gas constant.
$T$ — thermodynamic temperature in kelvin, never in degrees Celsius.

The gas constant, and why the units have to agree

Since the 2019 revision of the SI, the molar gas constant is exact:

Formula: R = 8.314462618 J mol^−1 K^−1

$R = 8.314462618 J {mol}^{- 1} K^{- 1}$

Because one joule is one pascal cubic metre, and one cubic metre is a thousand litres, the same constant can be read directly as $8.314462618 kPa L {mol}^{- 1} K^{- 1}$ . That is the value this page multiplies by, so a molarity in mol/L and a temperature in kelvin yield a pressure in kilopascals with no hidden factor. The familiar atmosphere-based value follows from the exact definition 1 atm = 101 325 Pa:

Formula: R = 8.314462618 / 101.325 = 0.0820573661 L atm mol^−1 K^−1

$R = \frac{8.314462618}{101.325} = 0.0820573661 L atm {mol}^{- 1} K^{- 1}$

Mixing the two — multiplying a molarity by 8.314 and then labelling the answer "atm" — is one of the most common errors in osmotic pressure work and inflates the result by a factor of 101.325. This calculator computes internally in kilopascals and converts once, at the end, using the exact NIST conversion factors, so the two systems can never be crossed.

Temperature conversion

Formula: T /K = θ /°C + 273.15

$T / K = θ / °C + 273.15$

and, for a Fahrenheit input,

Formula: T /K = (θ /°F − 32) / 1.8 + 273.15

$T / K = \frac{(θ / °F - 32)}{1.8} + 273.15$

Using a Celsius number directly in $Π = i M R T$ is not a small error. At 25 °C the ratio 298.15 / 25 is 11.9, so the answer comes out nearly twelve times too small; at 0 °C it collapses to zero, which is obviously wrong for a solution that is very much still exerting osmotic pressure. The calculator therefore prints the kelvin value it used.

Osmolarity, osmolality and the entity count

The intermediate quantity $φ i M$ is the effective osmolarity, expressed in osmol/L or, more commonly in medicine, mOsmol/L:

Formula: osmolarity = φ ⁢ i ⁢ M, Π = osmolarity × R ⁢ T

$osmolarity = φ i M, Π = osmolarity \times R T$

Osmolality is the closely related but distinct quantity measured per kilogram of solvent rather than per litre of solution. USP General Chapter 785 defines osmolality in osmol or mOsmol per kilogram and specifies freezing point depression osmometry as the reference method, precisely because a mass-based ratio is independent of temperature and of the volume occupied by the solutes themselves. Osmolarity is calculated; osmolality is measured. For dilute aqueous fluids at room temperature the numbers differ by roughly one to two per cent, but for a concentrated or protein-rich solution the gap widens because a litre of solution contains noticeably less than a kilogram of water. IUPAC in fact discourages the term osmolarity altogether, preferring an explicit statement of the entity concentration. This page reports osmolarity, keeps the label honest, and never silently relabels it as osmolality.

How to use this osmotic pressure and osmolarity tool

Pick a solute preset, or leave it on Custom. Choosing sodium chloride, calcium chloride, glucose and so on fills in the limiting van 't Hoff factor for you. Only sodium chloride also carries a published osmotic coefficient; the others default to $φ = 1$ because this page does not invent constants it cannot cite.
Enter the molarity $M$ in mol/L. Use the analytical concentration of the solute as weighed out, not the ion concentration — the factor $i$ does that multiplication. If you know the solution only as a mass percentage, divide grams per litre by the molar mass first: 9 g/L of NaCl at 58.44 g/mol is 0.154 mol/L.
Enter the temperature and choose its unit. Degrees Celsius, kelvin and degrees Fahrenheit are all accepted. Body temperature is 37 °C; standard laboratory temperature is 25 °C.
Set the van 't Hoff factor $i$ . Use 1 for a non-electrolyte, 2 for a 1:1 salt, 3 for a 2:1 or 1:2 salt, and so on. Weak electrolytes sit between 1 and 2 depending on their degree of dissociation.
Set the osmotic coefficient $φ$ . Leave it at 1 for an ideal-solution answer, or enter a measured value to correct for non-ideality. Values below 1 mean the solution behaves as if it contains fewer free particles than stoichiometry suggests.
Choose the pressure unit and calculate. The result panel gives the pressure in your chosen unit and in every other supported unit, plus the osmolarity, the kelvin temperature actually used, and a tonicity comparison against the human plasma reference interval.

The chart below the form plots osmotic pressure against molarity at your chosen temperature and marks your operating point, so you can see immediately how sensitive the answer is to a concentration error. The buttons under the result let you copy a text summary, download a CSV of the sweep, or copy a permalink that reproduces the exact scenario for a colleague.

Worked example: 0.9 % sodium chloride infusion fluid

Normal saline is the most useful benchmark on this page because both its theoretical and its measured osmotic concentrations are published, so every step can be checked.

Problem. A 0.9 % w/v sodium chloride solution is infused at body temperature. Estimate its osmolarity and osmotic pressure, first ideally and then with the osmotic coefficient applied.

Convert the mass percentage to molarity. 0.9 % w/v means 0.9 g per 100 mL, that is 9 g/L. With a molar mass of 58.44 g/mol:
Formula: M = (9 g/L) / (58.44 g/mol) = 0.1540 mol/L

$M = \frac{9 g/L}{58.44 g/mol} = 0.1540 mol/L$
Apply the van 't Hoff factor. Sodium chloride dissociates into Na⁺ and Cl⁻, so $i = 2$ :
Formula: i ⁢ M = 2 × 0.1540 = 0.3080 osmol/L = 308 mOsmol/L

$i M = 2 \times 0.1540 = 0.3080 osmol/L = 308 mOsmol/L$

This is the familiar 308 mOsmol/L printed on saline bags.
Convert the temperature.
Formula: T = 37 + 273.15 = 310.15 K

$T = 37 + 273.15 = 310.15 K$
Compute the ideal osmotic pressure.
Formula: Π = 0.3080 × 0.0820573661 × 310.15 = 7.84 atm

$Π = 0.3080 \times 0.0820573661 \times 310.15 = 7.84 atm$

In SI units the same product is $0.3080 \times 8.314462618 \times 310.15 = 794 kPa$ , or 7.94 bar.
Apply the osmotic coefficient. A commonly used clinical value for sodium chloride is $φ = 0.926$ :
Formula: φ ⁢ i ⁢ M = 0.926 × 0.3080 = 0.2852 osmol/L = 285 mOsmol/L

$φ i M = 0.926 \times 0.3080 = 0.2852 osmol/L = 285 mOsmol/L$

Formula: Π = 0.2852 × 0.0820573661 × 310.15 = 7.26 atm = 735 kPa

$Π = 0.2852 \times 0.0820573661 \times 310.15 = 7.26 atm = 735 kPa$
Check against reality. The corrected figure of about 285 mOsmol/L is within a couple of units of the measured 286 mOsmol per kilogram of water reported for 0.9 % saline, and it lands inside the 275–295 mOsmol/kg plasma reference interval, which is exactly why the fluid is described as isotonic. The uncorrected 308 mOsmol/L sits above that interval and would misleadingly label normal saline as mildly hypertonic. That six-per-cent difference is the whole practical value of the osmotic coefficient.

Entering M = 0.154, T = 37 °C, i = 2 and φ = 0.926 into the form reproduces these numbers, and the chart marks the operating point on the pressure-versus-molarity line.

Reading the result: tonicity, direction of flow and sensitivity

The number the calculator returns is the pressure that would exactly oppose solvent entry across a perfectly semipermeable membrane. Four readings of it are useful.

Direction of flow. Solvent moves from the lower osmotic pressure toward the higher one. Of two solutions separated by a solvent-permeable membrane, the one with the larger $Π$ draws water in.
Tonicity against plasma. Human serum osmolality has a commonly quoted reference interval of 275 to 295 mOsmol/kg. A calculated osmolarity below that band is hypotonic and will tend to swell cells; above it is hypertonic and will tend to shrink them. Tonicity is not identical to osmolarity, though — it counts only the solutes that cannot cross the cell membrane. Urea contributes to osmolarity but crosses membranes readily, so a urea solution can be iso-osmolar yet functionally hypotonic.
Sensitivity. Because $Π$ is strictly proportional to both $M$ and $T$ , a one per cent concentration error is a one per cent pressure error. A temperature error is far more forgiving: moving from 25 °C to 37 °C changes the absolute temperature by only four per cent, so it changes the pressure by four per cent. The result panel prints both derivatives so you can see this directly.
Magnitude. Osmotic pressures are surprisingly large. Plasma at 290 mOsmol/L works out near 7.4 atm at 37 °C, and seawater at roughly 1.1 osmol/L reaches about 27 bar at 25 °C. Those numbers explain why reverse osmosis needs high-pressure pumps, and why a red blood cell placed in pure water bursts.

Where osmotic pressure calculations are actually used

Clinical and pharmaceutical practice

Parenteral fluids. Intravenous solutions are formulated close to plasma osmolality so that infusion does not shift water into or out of red cells. USP General Chapter 785 exists specifically to govern how the osmolality of such preparations is measured and labelled.
Ophthalmic and nasal preparations. Eye drops far from isotonic sting and can damage the corneal epithelium, so tonicity adjustment with sodium chloride or a sugar is routine.
The osmolar gap. Clinicians compare a measured osmolality against one calculated from sodium, glucose and urea. A large gap points to an unmeasured osmotically active substance such as methanol or ethylene glycol, which is why the osmolarity-versus-osmolality distinction is not academic.

Membrane engineering and food science

Reverse osmosis. The applied pressure must exceed the feed osmotic pressure everywhere in the module. The van 't Hoff estimate gives the thermodynamic floor; real designs add margin for concentration polarisation and for the rising salinity of the brine.
Forward osmosis and pressure-retarded osmosis. Both are driven by an engineered osmotic pressure difference, so the draw solution is selected on exactly the quantity this calculator returns.
Osmotic dehydration and preservation. Curing, brining and sugar-infusion all rely on a hypertonic external solution to draw water out of tissue and out of microbial cells.

Comparison: ideal van 't Hoff behaviour versus real solutions

Aspect	Ideal van 't Hoff model	Real solution behaviour
Valid concentration range	Exact only in the limit of infinite dilution; usually within a few per cent below about 0.1 osmol/L	Deviations of ten per cent or more become routine above about 1 osmol/L
Particle count	Integer $i$ from the dissociation stoichiometry (1, 2, 3, …)	Effective count reduced by ion pairing and long-range electrostatics; captured by $φ < 1$
Driving variable	Molar concentration used directly	Solvent activity $a_{A}$ , requiring activity coefficients or a Pitzer model
Concentration basis	Osmolarity, per litre of solution, temperature dependent	Osmolality, per kilogram of solvent, temperature independent and directly measurable
Higher-order terms	Linear in concentration only	Virial expansion $Π = c R T (1 + B c + \dots)$ needed for polymers and proteins
0.9 % NaCl at 37 °C	308 mOsmol/L, 7.84 atm	285 mOsmol/L with $φ = 0.926$ , 7.26 atm
Best use	Teaching, screening estimates, order-of-magnitude membrane sizing	Formulation, concentrated brines, quality control against measured osmolality

Reference van 't Hoff factors

Solute	Dissociation	Limiting $i$	Note
Glucose, sucrose, urea, glycerol	None	1	Molecular solutes; $φ$ stays very close to 1 well past 0.5 mol/L
NaCl, KCl	Two ions	2	Strong 1:1 electrolytes; $φ \approx 0.93$ for NaCl at physiological concentration
CaCl₂, MgCl₂, Na₂SO₄	Three ions	3	Higher charge means stronger ion pairing, so $φ$ falls faster with concentration
Acetic acid in water	Partial	Between 1 and 2	Weak electrolyte; $i = 1 + α$ where $α$ is the degree of dissociation
Albumin and other proteins	Effectively none	≈ 1	Very low molarity but non-negligible virial terms; measured colloid osmotic pressure of plasma averages about 25 mmHg

Limitations, assumptions and the failure modes to watch for

It is a limiting law. The assumptions built into $Π = c R T$ are that solute particles do not interact and occupy no volume. Both fail progressively as concentration rises, always in the direction of overstating the pressure for a strong electrolyte.
The van 't Hoff factor is not a measured constant. Quoting $i = 2$ for sodium chloride describes stoichiometry, not behaviour. The measured particle activity is always lower; if you need accuracy, put the correction in $φ$ and cite where the value came from.
Osmolarity is calculated, osmolality is measured. This page returns osmolarity. If you need a number to compare against an osmometer reading, remember the osmometer reports osmolality, and the two are not interchangeable for concentrated, lipaemic or protein-rich samples.
Tonicity is a biological question, not a thermodynamic one. Only impermeant solutes contribute to tonicity. The calculator cannot know whether your membrane rejects a given solute, so treat the tonicity band as a screening aid, not a verdict.
Temperature range. The equation itself is general, but aqueous solution work below 273.15 K or above 373.15 K at ordinary pressure runs into freezing and boiling. The calculator flags temperatures outside that window rather than silently returning a number.
Mixtures. For a solution containing several solutes, the osmotic pressures add. Compute the entity concentration of each component and sum them; a single $i$ cannot represent a mixed electrolyte.
Not a design or dosing tool. Results here are educational and first-pass. Clinical fluid decisions, pharmacopoeial release testing and desalination plant design require measured data and the applicable standard, not a limiting-law estimate.

Osmotic pressure questions answered

Does this calculator use Celsius or kelvin in the van 't Hoff equation?

The van 't Hoff equation requires an absolute temperature, so every calculation is carried out in kelvin. You may type the temperature in degrees Celsius, in kelvin or in degrees Fahrenheit, and the calculator converts it before multiplying by the gas constant. Feeding 25 straight into the equation instead of 298.15 would understate the osmotic pressure by a factor of about twelve, so the converted kelvin value is always shown in the result breakdown for you to check.

What is the difference between osmolarity and osmolality?

Osmolarity counts osmotically active particles per litre of solution and is reported in osmol/L, while osmolality counts them per kilogram of solvent and is reported in osmol/kg. Osmolality is a ratio of amount to mass, so it does not change when the solution is warmed or cooled, whereas osmolarity does because the volume expands. For dilute aqueous solutions near room temperature the two agree to within roughly two per cent, and this calculator works in osmolarity because the van 't Hoff equation is written in terms of molar concentration.

Which van 't Hoff factor should I use for NaCl, CaCl2 and glucose?

Use i = 2 for sodium chloride because each formula unit releases one sodium ion and one chloride ion, i = 3 for calcium chloride because it releases one calcium ion and two chloride ions, and i = 1 for glucose because it dissolves as intact neutral molecules. Those are limiting values that assume complete dissociation into non-interacting particles. At any real concentration the effective particle count is lower, and the osmotic coefficient field is the correct place to apply that correction rather than shaving the integer factor.

What is the osmotic coefficient and when does it matter?

The osmotic coefficient is a dimensionless factor that scales the ideal particle concentration down to the value that actually reproduces the measured osmotic pressure. It approaches 1 at infinite dilution and falls as electrostatic attraction and ion pairing reduce the thermodynamic independence of the ions. A commonly used clinical value for sodium chloride is 0.926, which is why 0.9 per cent saline has a theoretical osmolarity of 308 mOsmol/L yet behaves in the body like about 286 mOsmol per kilogram of water.

Why is the osmotic pressure of blood plasma calculated as several atmospheres?

A plasma osmolality of 275 to 295 mOsmol/kg corresponds to an osmotic pressure near 7 atmospheres at body temperature. That figure is the pressure that would be required to hold back pure water across an ideal membrane impermeable to every solute. Capillary walls are nothing like that membrane, because sodium, chloride, urea and glucose cross them freely, so the pressure that actually governs fluid exchange between plasma and interstitium is the far smaller colloid osmotic pressure of roughly 25 mmHg generated by plasma proteins.

How accurate is the van 't Hoff equation at high concentration?

The van 't Hoff equation is a limiting law valid as the solution approaches infinite dilution, so its accuracy degrades as concentration rises. Below about 0.1 mol/L of dissolved particles it is usually within a few per cent for a strong electrolyte, and by 1 mol/L the ideal form can overstate the true osmotic pressure by ten per cent or more. Beyond that range you should either supply a measured osmotic coefficient or move to a full activity model such as the Pitzer equations.

Can I use this calculator to size a reverse osmosis system?

You can use it for a first estimate of the thermodynamic floor. Standard seawater carries roughly 1.1 osmol of dissolved ions per litre, which the van 't Hoff equation turns into about 27 bar at 25 degrees Celsius, and no membrane can produce fresh water below that applied pressure. Real plants run well above it because concentration polarisation at the membrane surface, rising brine concentration along the module and hydraulic losses all add to the requirement, so treat the calculated value as a lower bound and not as a design pressure.

Sources and provenance of the constants

Every constant on this page is taken from the primary document named below, not from secondary summaries. Values that could not be traced to a citable source are left at their ideal defaults rather than guessed.

NIST, The NIST Reference on Constants, Units, and Uncertainty — molar gas constant R: R = 8.314 462 618 J mol⁻¹ K⁻¹, exact since the 2019 revision of the SI. physics.nist.gov/cgi-bin/cuu/Value?r
NIST Special Publication 811, Guide for the Use of the International System of Units (SI), Appendix B.9: 1 atm = 1.013 25 × 10⁵ Pa (exact), 1 bar = 10⁵ Pa (exact), 1 psi = 6.894 757 × 10³ Pa, 1 mmHg (conventional) = 1.333 224 × 10² Pa. nist.gov, SP 811 Appendix B.9
IUPAC, Compendium of Chemical Terminology (the Gold Book), entry "osmotic pressure, Π" (O04344): the activity-based definition, the ideal dilute limit Π = c_BRT over individually moving entities, and the note that the term osmolarity is discouraged. doi.org/10.1351/goldbook.O04344
United States Pharmacopeia, General Chapter ⟨785⟩ Osmolality and Osmolarity: osmolality expressed in Osmol or mOsmol per kilogram of solvent, determined by freezing point depression osmometry. doi.usp.org, USP–NF ⟨785⟩
NCBI Bookshelf / StatPearls, Serum Osmolality: plasma osmolality reference interval commonly given as 275 to 295 mOsmol/kg. ncbi.nlm.nih.gov/books/NBK567764
NCBI Bookshelf / StatPearls, Physiology, Blood Plasma: plasma colloid oncotic pressure averages approximately 25 mmHg, of which albumin supplies 70–80 %. ncbi.nlm.nih.gov/books/NBK531504
Peer-reviewed clinical physiology review, Osmolality (mOsmol/kg H₂O) versus osmolarity (mOsmol/L): applied physiology to improve patient safety, PubMed Central: osmotic coefficient 0.926 for sodium chloride, theoretical 308 mOsmol/L versus effective 286 mOsmol/kg H₂O for 0.9 % saline. pmc.ncbi.nlm.nih.gov/articles/PMC12690852
P. Atkins and J. de Paula, Physical Chemistry, Oxford University Press: derivation of the van 't Hoff equation from the equality of solvent chemical potentials, and the osmotic virial expansion used for macromolecular solutions.

The osmotic coefficient defaults to 1 for every preset except sodium chloride, because this page will not present an uncited constant as if it were sourced. If your work needs φ for another salt, take it from a tabulated compilation of activity and osmotic coefficients and enter it manually.

Solute preset Fills in the limiting van 't Hoff factor. Only NaCl carries a published osmotic coefficient.

Molarity M (mol/L) Analytical concentration of the solute as weighed out, greater than 0 and at most 100 mol/L.

Temperature Converted to kelvin before use. Body temperature is 37 °C, standard laboratory temperature 25 °C.

Temperature unit Pick the unit your temperature figure is written in.

van 't Hoff factor i Particles released per formula unit: 1 for glucose, 2 for NaCl, 3 for CaCl₂.

Osmotic coefficient φ Leave at 1 for the ideal answer, or enter a measured value between 0 and 2.

Report pressure in Conversions use the exact NIST SP 811 factors.

Enter solution parameters to compute osmotic pressure and osmolarity.

Run a calculation to plot osmotic pressure against molarity at your chosen temperature. The solid line uses your osmotic coefficient; a dashed line shows the ideal φ = 1 curve whenever the two differ.

Arcade Mini-Game: Osmotic Pressure Calculator Calibration Run

Use this quick arcade run to practise separating the quantities the van 't Hoff equation actually needs from the classic mistakes that corrupt an osmotic pressure calculation.

Score: 0 Timer: 30s Best: 0

Start the game, then use your pointer or arrow keys to catch useful inputs and avoid bad assumptions.

Osmotic Pressure Calculator

Introduction to osmotic pressure and the van 't Hoff equation

Formula: from solvent activity to Π = φ i M R T

The gas constant, and why the units have to agree

Temperature conversion

Osmolarity, osmolality and the entity count

How to use this osmotic pressure and osmolarity tool

Worked example: 0.9 % sodium chloride infusion fluid

Reading the result: tonicity, direction of flow and sensitivity

Where osmotic pressure calculations are actually used

Clinical and pharmaceutical practice

Membrane engineering and food science

Comparison: ideal van 't Hoff behaviour versus real solutions

Reference van 't Hoff factors

Limitations, assumptions and the failure modes to watch for

Osmotic pressure questions answered

Sources and provenance of the constants

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