Osmotic Pressure Calculator
Find the pressure that stops osmosis from concentration, ions and temperature.
Twelve pressure units, ten concentration scales, and molarity from a weighed solute.
Updated October 17, 2026
Introduction
Osmotic pressure is the pressure that has to be applied to a solution to stop solvent from crossing a semi-permeable membrane into it. Put a membrane between pure water and salty water and water drifts towards the salt side on its own; press on the salt side hard enough and the drift stops. That balancing pressure is what this calculator computes, and it is a surprisingly large number for ordinary solutions: 0.15 mol/L sodium chloride at room temperature already asks for about 7 bar, and that is close to the strength of the saline used in a laboratory or a clinic.
The calculation needs four things about the solution: how many ions each dissolved formula unit produces, how far the real solution departs from ideal behaviour, the molar concentration, and the temperature. Every one of those four is also an answer the calculator can give you. Type a pressure you measured in a lab and leave the concentration blank, and the concentration is what comes back; leave the ion count blank instead and the particle count is solved. A second relation, in the collapsed group below the main boxes, turns a weighed mass of solute, its molecular weight and the solution volume into that same molar concentration, so an experiment that starts at the balance can finish at a pressure.
It is used wherever water movement across a membrane matters: laboratory measurements of particle number, biology coursework on plant and animal cells, water treatment and reverse osmosis, and food or pharmaceutical formulation where a solution has to be matched to a target osmotic strength. The sections below cover the four inputs, a worked example, every direction the two relations solve, and the places where the ideal formula quietly stops being accurate.
12 pressure units
Pascals to millimetres of mercury, including bar, atm and psi
Any one box
Pressure, molarity, ions, coefficient or temperature as the unknown
R is exact
8.314 462 618… J/(mol·K) with no uncertainty
Two relations, one shared concentration
The van't Hoff relation and the weighing relation meet at the concentration box. That is why filling in a solute mass, its molecular weight and the volume can make the pressure appear without you typing a molarity at all: the weighing sets the concentration, and the concentration feeds the pressure.
Quick start
All of the boxes start empty. Fill the four in the upper group and the pressure follows.
Count the ions one formula unit releases
Sodium chloride gives two ions, calcium chloride three, and a sugar or a protein that dissolves intact gives one. This is the ideal count from the formula, not a measured one; if you are starting from a measured van't Hoff factor, the last worked example shows the two consistent ways to split it between this box and the coefficient.
Enter the osmotic coefficient
Set it to 1 for an ideal solution. Real electrolytes sit below 1 because oppositely charged ions pair up and stop behaving as independent particles; sodium chloride near 0.1 mol/L is commonly tabulated just under 1, which is why the example below uses 0.93.
Give the concentration — directly, or from a weighing
Type the molarity in mol/L if you have it. If you have a bottle of solution and a balance instead, open Parameters of solute and solvent, enter the mass of solute, its molecular weight and the volume of the finished solution, and the concentration box fills itself in. The concentration box is read as mol per the volume unit shown beside it, which is litres unless you change it.
Read the pressure — or type the one you measured
The pressure appears once its four inputs are present. Prefer the other direction? Type a measured pressure over it: with exactly one of the other four boxes empty, that box is what the calculator solves for, and with all four filled one of them is recalculated to keep the set consistent — check which one changed. Leave two empty and it will not guess between them.
Worked example: 0.1 mol/L sodium chloride at 25 °C
With two ions, an osmotic coefficient of 0.93 and a concentration of 0.1 mol/L, the particle concentration is the first product. The second is the gas constant times the absolute temperature, which is the pressure one mole of particles would exert per litre at 25 °C:
That is the number in the pressure box
The pressure box opens on hectopascals, so it reads 4,610.86 hPa — the same 4.61086 bar on a scale that divides a bar into a thousand parts, and 4.55057 atm if you read it as atmospheres. Treat the answer as the pressure difference across the membrane: a membrane used to hold this solution back has to tolerate it, and the mechanical strength of the membrane is a separate engineering question.
Calculation method
The van't Hoff relation is the ideal-gas law applied to a dilute solution. Pressure, concentration and absolute temperature are tied together by one constant:
The one number in the equation that is an input
Everything except the gas constant is something about your solution. The gas constant is fixed by the SI: its value is 8.31446261815324 J/(mol·K) and it carries no measurement uncertainty, as the CODATA value published by NIST records. In the units of this page, with the pressure in bar and the volume in litres, the same constant is:
The two forms are the same number, because one litre-bar is exactly 100 joules. Nothing is rounded anywhere in that conversion.
Keeping the constant exact means the pressure you get back is only as uncertain as the concentration, the particle count and the temperature you supplied — not the constant.
Where the molarity comes from
When you fill in the solute group, the calculator divides a mass by a molar mass and a volume:
The three boxes are normalised to kilograms, kilograms per mole and litres before the division, so a mass in pounds, a molar weight in ounces per mole and a volume in cubic inches all land in the same mol/L. The same relation runs backwards: with a concentration and two of the three solute quantities, the third is solved for. Need the molar weight of a compound rather than of a known substance? The molar mass calculator builds it from the elements in the formula.
Every direction it solves
- Forward: four known quantities give the pressure, as in the quick-start example.
- Pressure back to concentration: — the measurement direction, where a membrane balance tells you how many dissolved particles a sample contains.
- Pressure back to the particle count: — with the coefficient set to 1 and the concentration known, this returns the measured effective particle count, slightly below the ideal number whenever the solution is not perfectly dissociated.
- Pressure back to the coefficient: — divide the measured pressure by the ideal prediction and you have the non-ideality factor at that concentration.
- Pressure back to temperature: — the temperature is in kelvin, so a result below zero is flagged rather than reported as a Celsius reading.
- Weighing relation: any one of mass, molar weight, volume or concentration from the other three.
What the units do to a number
The concentration box is the one place where the menu changes the meaning of the digits rather than just their dress. It reads mol per one of the volume units shown beside it, so 0.1 in mol/L and 0.0001 in mol/cm³ describe the same solution — a factor of a thousand apart. That is one of the most common ways to be out by three orders of magnitude in this calculation. The pressure menu has no such trap: 4.61086 bar, 4,610.86 hPa and 4.55057 atm are three ways of writing one pressure, and the temperature menu always converts to kelvin before the multiplication.
Worked examples
Three short cases, each one chosen because it exercises a different direction of the two relations. The results are the values this calculator returns for those inputs.
A membrane measurement becomes a molarity
A sample at 25 °C is measured to hold 25 bar of osmotic pressure — 25,000 on the default hectopascal scale — and the solute is known to stay intact in solution, so and . With pressure, ion count, coefficient and temperature filled in and the concentration left empty, the concentration is the answer:
That 1.008489 is the molarity of dissolved particles, which is exactly what a colligative measurement can see. For a small molecule it is the molarity of the substance; for a polymer or a protein it is a number-average quantity, and mixing it with a weighed mass concentration is how osmometry estimates a number-average molar mass.
From a weighing to a pressure
9 g of glucose is dissolved and made up to 0.5 L of solution. Glucose does not dissociate, so and an ideal solution is a fair starting point, . The weighing first becomes a concentration:
and the pressure follows from that concentration at 25 °C:
That is 2,478.96 hPa in the pressure box. Notice how much pressure a modest amount of sugar generates: a tenth of a mole per litre is enough to hold back nearly two and a half bar of water pressure.
The same particle count, written two ways
A reference table may quote one combined van't Hoff factor instead of an ion count and a coefficient. The 0.93 coefficient used above, with two ions, is the same statement as a single factor of 1.86 — the two notations multiply to the same number:
At 0.1 mol/L and 25 °C, either pair returns the pressure from the quick start:
4,610.86 hPa, the same number from both notations. Enter 1.86 in the coefficient box while leaving the ion count at 2 and the product becomes 3.72 — twice the intended particle count, so the pressure doubles to 9,221.72 hPa.
Tips and pitfalls
The product of the two particle boxes is the count that matters
Only multiplies the concentration, so treat it as one number. If a table gives you one combined factor, such as 1.86 for sodium chloride, either leave the ion count at 1 and put 1.86 in the coefficient, or keep the count at 2 and put 0.93 in the coefficient. A coefficient slightly above 1 is legitimate as well — some non-electrolytes give a little more effective pressure than the ideal prediction — so the calculator does not cap it. The ceiling here is physical sense, not an error message.
Check the volume basis before typing a concentration
The concentration box means mol per one unit of the volume shown beside it. Switching that unit rewrites the number you see, not the solution: 0.1 mol/L becomes 0.0001 when read per cubic centimetre. If your stock is described as grams per litre, mass percent or a dilution ratio, convert it first — the concentration calculator handles those forms.
Use the finished solution volume, not the solvent added
The volume box is the volume the solution ends up occupying, the one your volumetric flask is filled to. For dilute aqueous work the two are nearly the same; for a concentrated brine or a solution made by adding a large volume of liquid solute, using the solvent volume inflates the concentration and the pressure with it.
Take temperature seriously, and measure at the one you care about
Pressure is proportional to absolute temperature, so the change from 25 °C to 35 °C moves the result by about 3.4% — small but not negligible when you are comparing a measurement with a prediction. Celsius and Fahrenheit entries are converted to kelvin before the multiplication; a value below absolute zero is rejected.
What a red number, or an empty one, is telling you
An empty box is not an error — it usually means the direction you are trying to solve still has two unknowns. A red number is a value the calculator did compute but will not vouch for: a pressure below zero, or one so far past any real membrane process that the input scale is probably wrong. The number stays visible so you can see how far out it landed, with a short explanation on the field itself.
Questions
Is osmotic pressure the pressure inside a cell?
No. It is the pressure that would have to be applied from outside to stop water crossing a membrane into the solution. In a plant cell, water entering the vacuole pushes the membrane against the wall, and the wall pushes back; the balance you observe as turgor is the wall pressure, not the osmotic pressure itself. The two are equal only when the cell has reached equilibrium, and the calculator gives you only the osmotic side of that balance.
Should I enter osmolarity or osmolality?
The concentration box counts moles per litre of finished solution, which is the osmolarity basis, and the quantity that multiplies in the pressure is the osmolarity itself, . A laboratory osmometer usually reports osmolality instead — milliosmoles per kilogram of solvent. In dilute aqueous solutions the two are nearly the same number; in concentrated ones they diverge, and if that difference matters you need the solution's density to convert before using this calculator.
Why did the concentration change when I filled in the solute mass?
Because the concentration box is shared by both relations. Entering mass, molecular weight and volume determines the molarity, so the calculator writes that value into the shared box and then uses it for the pressure. It is one consistent solution, not two copies of the same number: the quantities you supply set the state, and the value that keeps the set consistent is derived from them. When every box is filled, the entry you just typed is honoured and one of the others is recalculated — so check which box changed.
Can I use it for seawater, a body fluid or a concentrated brine?
You can calculate an estimate, but read the result as an estimate. The van't Hoff relation is a dilute-solution approximation, and the further the solution is from ideal the more the answer depends on the osmotic coefficient you supply. For seawater, brines, blood or a formulation, take that coefficient (or a directly measured osmotic pressure) from data at the actual concentration and temperature, rather than assuming 1. For a value that will drive a process decision, use measured data or the relevant standard.
How far to trust it
- The relation is a dilute-solution approximation. It treats the solution as ideal apart from the single coefficient you enter. Near 0.1 mol/L that is a reasonable working assumption; in concentrated brines the true osmotic pressure can depart from the ideal prediction by a large fraction, and no formula on this page can recover that without measured coefficients.
- The particle count and the coefficient are inputs, not predictions. The calculator cannot know how far your particular salt dissociates or how your particular protein behaves in your particular buffer. It will apply whatever you give it.
- Volumes and temperatures must describe the same state. The volume is the finished solution, and the temperature is the one at which the pressure is defined. A solution measured warm and calculated cold will not agree with itself.
- Not for clinical dosing, membrane design or compliance work. Intravenous fluids, dialysis baths, cell-culture media and membrane systems are specified from measured osmolality or osmotic pressure and from their own standards. Use this calculator to understand the physics and to check a calculation, then confirm against measured data or a qualified specification before acting on it.
If your result looks wrong, the order to check is: the concentration unit basis, then the product of the two particle boxes, then the solution volume, and only then the temperature. Those four account for most disagreements in practice, and each of them is visible in the numbers on screen.
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