# What is the water potential?

Finds the water potential Ψ of a plant cell or solution as the sum of the solute, pressure, gravity and matric potentials, with the solute potential from Ψs = −iCRT, in megapascals and bars.

- Page: https://www.acalculator.org/biology/water-potential-calculator
- JSON spec: https://www.acalculator.org/biology/water-potential-calculator.json
- Version: 1ec728b61da0

## Default answer

Example with the default inputs (Solute potential from Concentration, van ’t Hoff factor i 1, Molar concentration C (mol/L) 0.3, Temperature 20 °C, Pressure potential Ψp 0.5, Potentials in MPa): Ψ = −0.231215 MPa (−2.31215 bar).

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| src | Solute potential from | Work out Ψs from the concentration, or type Ψs. |
| i | van ’t Hoff factor i | Particles each formula unit gives in water: 1 for sucrose or glucose, 2 for NaCl, 3 for CaCl₂. |
| c | Molar concentration C (mol/L) | The solute concentration in moles per liter. |
| t | Temperature | The temperature of the solution. |
| ps | Solute potential Ψs | The solute (osmotic) potential: 0 for pure water, negative with solutes. |
| pp | Pressure potential Ψp | The turgor pressure of the cell, positive in a turgid cell; 0 in an open beaker. |
| pg | Gravity potential Ψg | Optional: the effect of height; leave empty to count it as 0. |
| pm | Matric potential Ψm | Optional: water bound to surfaces such as a dry seed’s; 0 or negative. |
| u | Potentials in | The unit of the typed potentials and of the answer: megapascals or bars (1 MPa = 10 bar). |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| result | Answer | The water potential in the chosen unit, with the other unit. |
| psiMPa | Water potential Ψ (MPa) | Ψs + Ψp + Ψg + Ψm in megapascals. |
| psiBar | Water potential Ψ (bar) | Ψs + Ψp + Ψg + Ψm in bars. |
| psiSMPa | Solute potential Ψs (MPa) | −iCRT, or as typed, in megapascals. |
| psiSBar | Solute potential Ψs (bar) | −iCRT, or as typed, in bars. |

## Method

Ψ = Ψs + Ψp + Ψg + Ψm; Ψs = −i × C × R × T with R = 0.00831446261815324 L·MPa/(mol·K) and T in kelvins; 1 MPa = 10 bar.

## Assumptions

- An ideal dilute solution: Ψs = −iCRT, with i the particles per formula unit (a whole number for full ionization).
- Pure water at atmospheric pressure, at the reference height, is 0 MPa; water moves from higher to lower water potential.

## Worked examples

1. src = conc, i = 1, c = 1, t = 295.15, pp = 0, u = bar gives psiSBar = −24.5401, psiMPa = −2.45401, result = Ψ = −24.5401 bar (−2.45401 MPa). Source: OpenStax, Biology 2e, §30.5 Transport of Water and Solutes in Plants (Ψ = Ψs + Ψp + Ψg + Ψm; Ψs = −MiRT; pure water 0 MPa), https://openstax.org/books/biology-2e/pages/30-5-transport-of-water-and-solutes-in-plants; NIST, CODATA value: molar gas constant R = 8.314 462 618… J/(mol·K), exact, https://physics.nist.gov/cgi-bin/cuu/Value?r.
2. src = conc, i = 2, c = 0.15, t = 298.15, pp = 0.3, u = MPa gives psiSMPa = −0.743687, psiMPa = −0.443687. Source: OpenStax, Biology 2e, §30.5 Transport of Water and Solutes in Plants (Ψ = Ψs + Ψp + Ψg + Ψm; Ψs = −MiRT; pure water 0 MPa), https://openstax.org/books/biology-2e/pages/30-5-transport-of-water-and-solutes-in-plants; NIST, CODATA value: molar gas constant R = 8.314 462 618… J/(mol·K), exact, https://physics.nist.gov/cgi-bin/cuu/Value?r.
3. src = typed, ps = -0.7, pp = 0.6, u = MPa gives psiMPa = −0.1, psiBar = −1, result = Ψ = −0.1 MPa (−1 bar). Source: OpenStax, Biology 2e, §30.5 Transport of Water and Solutes in Plants (Ψ = Ψs + Ψp + Ψg + Ψm; Ψs = −MiRT; pure water 0 MPa), https://openstax.org/books/biology-2e/pages/30-5-transport-of-water-and-solutes-in-plants.
4. src = conc, i = 1, c = 0, t = 293.15, pp = 0, u = MPa gives psiMPa = 0, result = Ψ = 0 MPa (0 bar). Source: OpenStax, Biology 2e, §30.5 Transport of Water and Solutes in Plants (Ψ = Ψs + Ψp + Ψg + Ψm; Ψs = −MiRT; pure water 0 MPa), https://openstax.org/books/biology-2e/pages/30-5-transport-of-water-and-solutes-in-plants: pure water’s potential is 0 MPa by definition.

## FAQ

### How do I calculate water potential?

Add its parts: Ψ = Ψs + Ψp (+ Ψg + Ψm when gravity or dry surfaces matter). A cell with a solute potential of −0.7 MPa and a turgor pressure of 0.6 MPa has Ψ = −0.7 + 0.6 = −0.1 MPa.

### How do I calculate solute potential?

Use Ψs = −iCRT: i is the van ’t Hoff factor, the particles per formula unit (1 for sucrose, 2 for NaCl), C the molar concentration, R the gas constant (0.00831446 L·MPa/(mol·K), or 0.0831446 L·bar/(mol·K)) and T the temperature in kelvins. 1.0 M sucrose at 22 °C: −1 × 1.0 × 0.0831446 × 295.15 = −24.54 bar.

### Why is my answer slightly different from my AP Biology worksheet?

AP materials round R to 0.0831 L·bar/(mol·K) and add 273 for kelvins: −1 × 1.0 × 0.0831 × 295 = −24.51 bar, which they write as −24.5 bar. The page uses R = 0.0831446 and adds 273.15, giving −24.54 bar.

### Which way does water move?

From higher (less negative) to lower (more negative) water potential. Pure water is 0 MPa, so water moves from pure water into a cell whose water potential is below 0, until the pressure potential rises enough to balance it.

### Can solute potential be positive?

No. It is 0 in pure water and negative once anything is dissolved. Pressure potential can be positive (a turgid cell) or negative (tension in the xylem), so the total can be either sign.

### What units is water potential in?

Units of pressure: biologists use megapascals (MPa), and AP Biology often uses bars. 1 MPa = 10 bar. The solute potential of cell cytoplasm is typically −0.5 to −1.0 MPa, and turgor pressure 0.6 to 0.8 MPa (OpenStax).

## Sources

- OpenStax, Biology 2e, §30.5 Transport of Water and Solutes in Plants: Ψsystem = Ψs + Ψp + Ψg + Ψm, Ψs = −MiRT, pure water at 0 MPa, solute potential negative in a cell, pressure potential positive or negative, gravity and matric potentials negative to zero, solute potential of cell cytoplasm −0.5 to −1.0 MPa and turgor 0.6 to 0.8 MPa. https://openstax.org/books/biology-2e/pages/30-5-transport-of-water-and-solutes-in-plants (retrieved 2026-10-19)
- NIST, CODATA value: molar gas constant R = 8.314 462 618… J/(mol·K), exact (N_A × k). https://physics.nist.gov/cgi-bin/cuu/Value?r (retrieved 2026-10-19)