Reverse Osmosis Calculator (osmotic pressure, recovery, flux)

Understanding the reverse osmosis calculator — concept and principle

Reverse osmosis (RO) pushes water through a semi-permeable membrane against its natural osmotic flow, leaving dissolved salts behind. The calculator estimates the feed osmotic pressure from total dissolved solids (treated as sodium chloride), the recovery, the osmotic pressure of the concentrate leaving the system and the average membrane flux.

Salt stays behind and concentrates along the membrane, so the osmotic pressure rises toward the outlet.

How it is calculated

Osmotic pressure π = i × M × R × T, with i = 2 for NaCl, M = TDS ÷ 58,440 (mol/L when TDS is in mg/L), R = 0.0831446 L·bar/(mol·K) and T in kelvin.
Recovery r = Q_p ÷ Q_f × 100.
Concentrate osmotic pressure = π_feed ÷ (1 − r), assuming the membrane rejects all salt.
Flux = Q_p × 1,000 ÷ A, in litres per square metre per hour (LMH).

The principle

Water moves spontaneously from a dilute solution to a concentrated one across a membrane that blocks salt; the pressure that would stop this flow is the osmotic pressure. Van 't Hoff showed that for dilute solutions it behaves like an ideal gas pressure of the dissolved particles, so it rises with the number of ions per litre and with absolute temperature. NaCl splits into two ions, hence i = 2. To produce permeate, the applied pressure must exceed the osmotic pressure. As water leaves, the salt in the remaining stream becomes more concentrated by a factor 1/(1 − r), and so does its osmotic pressure.

Worked example

Inputs: TDS 35,000 mg/L, 25 °C, feed 100 m³/h, permeate 45 m³/h, area 2,500 m².
M = 35,000 ÷ 58,440 = 0.5989 mol/L; T = 298.15 K.
π = 2 × 0.5989 × 0.0831446 × 298.15 = 29.69 bar.
Recovery = 45 ÷ 100 = 45%; concentrate π = 29.69 ÷ 0.55 = 53.99 bar.
Flux = 45 × 1,000 ÷ 2,500 = 18 LMH.

Each point is the calculator re-run with only “Feed TDS (mg/L as NaCl)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Feed TDS (mg/L as NaCl)	Feed osmotic pressure (bar)
8,750	7.423294722
17,500	14.84658944
26,250	22.26988417
35,000	29.69317889
43,750	37.11647361
52,500	44.53976833
70,000	59.38635778

How to read the result

The feed pressure at the tail of the system must exceed the concentrate osmotic pressure plus a net driving pressure, so higher recovery quickly raises energy use and scaling risk. The ideal van 't Hoff value slightly overstates real seawater, which is about 27 bar, because ions do not behave ideally at this strength. Compare flux with the membrane manufacturer's guideline for your water type.

Common mistakes

Using TDS in g/L or ppm by weight without checking that it means mg per litre.
Treating the average flux as the flux of every element; lead elements run higher than tail elements.

Keep in mind: This is an ideal estimate: it ignores salt passage, concentration polarisation, pressure losses, fouling and non-NaCl ions. Plant design needs projection software, water analysis and qualified engineers.

Frequently asked questions

Why does seawater RO need such high pressure?

Because the concentrate at the end of the vessel can approach 50–60 bar of osmotic pressure at typical recoveries, and the pump must exceed that.

Can recovery simply be raised to save water?

Only up to the limits set by osmotic pressure and by scaling of sparingly soluble salts, which precipitate as the concentrate thickens.

Sources: J. H. van 't Hoff, Zeitschrift für physikalische Chemie 1 (1887) 481 · AWWA Manual M46, Reverse Osmosis and Nanofiltration, American Water Works Association · J. C. Crittenden et al., MWH's Water Treatment: Principles and Design, Wiley

Checked 8 Nov 2026. Standard textbook formulas in SI units, computed in your browser. For learning and estimates — real designs must follow your local codes and be checked by a qualified engineer.

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