Osmotic pressure calculator

Estimate the ideal osmotic pressure of water from its dissolved-species concentrations, or use a clearly defined sodium chloride (NaCl) approximation when only TDS is available. This is a screening calculation, not a reverse osmosis system design.

Calculation methodDissolved-species analysisTDS as an NaCl surrogate

In analysis mode, enter the dissolved species below; the separate TDS field is ignored. Blank species are counted as zero. In NaCl surrogate mode, only TDS and temperature are used; the species fields are ignored.

Water analysis

Dissolved species	Concentration	Unit	Brackish-water example (mg/L)	Seawater example (mg/L)
Ammonium (NH4+)		mg/L ppm g/m3 mol/L mmol/L	0.05	-
Potassium (K+)		mg/L ppm g/m3 mol/L mmol/L	3.3	390
Sodium (Na+)		mg/L ppm g/m3 mol/L mmol/L	36	10900
Magnesium (Mg2+)		mg/L ppm g/m3 mol/L mmol/L	6	1310
Calcium (Ca2+)		mg/L ppm g/m3 mol/L mmol/L	84	410
Strontium (Sr2+)		mg/L ppm g/m3 mol/L mmol/L	0.7	13
Barium (Ba2+)		mg/L ppm g/m3 mol/L mmol/L	0.07	0.05
Carbonate (CO32-)		mg/L ppm g/m3 mol/L mmol/L	-	-
Bicarbonate (HCO3-)		mg/L ppm g/m3 mol/L mmol/L	265	152
Nitrate (NO3-)		mg/L ppm g/m3 mol/L mmol/L	4.3	0.6
Chloride (Cl-)		mg/L ppm g/m3 mol/L mmol/L	45	19700
Fluoride (F-)		mg/L ppm g/m3 mol/L mmol/L	0.14	1.4
Sulfate (SO42-)		mg/L ppm g/m3 mol/L mmol/L	24	2740
Silica (SiO2)		mg/L ppm g/m3 mol/L mmol/L	9	5
Boron (B)		mg/L ppm g/m3 mol/L mmol/L	-	5

Use brackish-water example Use seawater example

The examples select analysis mode, restore concentration units to mg/L and set temperature to 12 °C for brackish water or 20 °C for seawater. They do not replace an analysis of your own water. A dash in an example means zero is entered for this demonstration.

TDS for NaCl surrogate mode (mg/L)

Water temperature

Temperature unit°C°FK

Calculate ideal osmotic pressure Clear values

Results

Sum of reported concentrations (mg/L)
Total dissolved-particle concentration (mmol/L)
Ideal osmotic pressure (bar)

What is osmotic pressure?

Osmosis is the movement of water through a semipermeable membrane towards the side with the higher dissolved-particle concentration. Osmotic pressure is the pressure needed to stop this net movement under equilibrium conditions. The number of dissolved particles matters: equal masses of different salts can produce different osmotic pressures.

Formula and units

π = RTΣc_j, where π is ideal osmotic pressure in bar, R = 0.0831446 L·bar/(mol·K), T is temperature in kelvin (°C + 273.15), and Σc_j is the sum of dissolved-particle concentrations in mol/L. The displayed particle concentration is in mmol/L. Molarity is measured per litre of solution; molality is measured per kilogram of solvent and cannot be obtained exactly from these inputs without additional density and composition information.

The analysis already lists individual ions, so each ion is counted once; no additional dissociation factor is applied. In the NaCl surrogate, complete dissociation into Na⁺ and Cl⁻ is assumed, so Σc_j = 2 × TDS/(58.44 × 1000), with TDS in mg/L. For example, 1,000 mg/L as NaCl at 25 °C gives approximately 0.848 bar in this ideal model.

How to enter the analysis

Use concentrations reported as the named species: calcium as Ca, bicarbonate as HCO₃, silica as SiO₂, and boron as B. Convert values reported as CaCO₃, nitrogen or another reporting basis before entering them. The calculation treats dissolved silica and each mole of boron as one particle; it does not calculate pH-dependent speciation. Include relevant dissolved constituents and check the ionic balance of the analysis. Missing ions, dissolved gases or unlisted organic solutes can affect the result.

The ppm option is treated as numerically equal to mg/L, an approximation for dilute aqueous solutions; g/m³ equals mg/L. The reported concentration sum covers only the entered species and their stated reporting basis, so it is not a laboratory TDS measurement. TDS alone does not identify salt composition, and the NaCl surrogate does not reproduce full seawater chemistry.

Why this is not the RO operating pressure

Reverse osmosis depends on the osmotic-pressure difference between the feed/concentrate and permeate, together with the applied hydraulic-pressure difference. Required operating pressure also depends on recovery, membrane permeability, flow, pressure losses and concentration polarization. A fixed multiple of feed osmotic pressure cannot determine a pump duty or select a membrane.

Limits of the estimate

The model assumes ideal behaviour and does not apply an osmotic coefficient or activity correction. It is most appropriate as a dilute-solution approximation. For seawater, brines or design decisions, use a suitable non-ideal model and membrane design calculation. The accepted temperature interval of 0–100 °C is a software input limit, not a validated accuracy range or a membrane operating limit.

Contact Lenntech about your water analysis and RO application.

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References: OpenStax Chemistry 2e, Colligative Properties; DuPont FilmTec RO/NF Technical Manual.

Warning: Lenntech BV cannot be held responsible for errors in the calculation, the program itself or the explanation. For questions or remarks please contact us.