Water Potential Calculator
Enter solute potential Ψs and pressure potential Ψp to compute total water potential Ψ and determine osmotic water-flow direction, for plant physiology and osmosis study.
Input Data
Results
At a glance:Water potential (Ψ) measures the free energy of water molecules in a system, determining the direction of osmotic flow — water always moves from higher to lower water potential. Pure water at standard state (atmospheric pressure, no solutes) is defined as 0. Water potential has two components: solute potential Ψs (lowered by solutes, always ≤ 0) and pressure potential Ψp (positive for turgor, negative for tension). A plant cell's water potential is Ψ = Ψs + Ψp, commonly in megapascals (MPa).
Formula
Water potential: Ψ = Ψs + Ψp.
Ψs (solute potential) is 0 or negative; Ψp (pressure potential) is positive for turgor, negative for tension.
van't Hoff: Ψs = −i·C·R·T (i ionization, C molarity, R = 0.00831, T absolute K).
$$\Psi = \Psi_s + \Psi_p$$$$\Psi_s = -iCRT$$$$\Psi_{water} = 0 \text{ MPa}$$How to Use
- Enter solute potential Ψs (more concentrated is more negative; pure water 0).
- Enter pressure potential Ψp (positive turgor, negative xylem tension, 0 in open container).
- The right panel shows total Ψ; compare two systems' Ψ to judge osmotic flow direction.
Water potential of common states (approx., MPa)
| System / state | Solute Ψs | Pressure Ψp | Water Ψ |
|---|---|---|---|
| Pure water (open) | 0 | 0 | 0 |
| Turgid cell | −0.7 | 0.4 | −0.3 |
| Wilting cell | −0.7 | 0 | −0.7 |
| 0.15 M sucrose (open) | −0.37 | 0 | −0.37 |
| Transpiring xylem (tension) | −0.8 | −0.6 | −1.4 |
Water flows from high Ψ to low Ψ. Values are room-temperature approximations, varying with solute concentration, temperature, and cell turgor.
Case Studies
Decide if a cell gains or loses water
A cell Ψs = −0.7 MPa, Ψp = 0.4 MPa, so Ψ = −0.7 + 0.4 = −0.3 MPa.
If the outside solution water potential is −0.5 MPa (lower than the cell), water flows from cell (−0.3) to outside (−0.5).
The cell thus loses water and turgor drops; if outside Ψ is higher than −0.3, the cell gains water and swells.
Estimate solute potential from sucrose concentration
0.15 M sucrose at 25°C (298 K), i = 1: Ψs = −1 × 0.15 × 0.00831 × 298 ≈ −0.37 MPa.
In an open beaker with no extra pressure, Ψp = 0, so solution Ψ ≈ −0.37 MPa.
Immersing a potato strip in this solution predicts water gain or loss by comparing its tissue Ψ with −0.37.
FAQ
Why is water potential usually negative?
Because pure water at standard state is defined as 0, and solutes lower water's free energy, making solute potential Ψs always negative; unless positive turgor offsets it, total Ψ is usually negative. The more negative the water potential, the stronger the system's tendency to take up water.
Which way does water flow?
Water always flows by osmosis from the higher (less negative) water-potential side to the lower (more negative) side until both equalize. So comparing the two systems' Ψ values predicts the osmotic direction — not by concentration, but by water potential.
When is pressure potential Ψp negative?
In xylem vessels under transpirational pull, the water column is under tension (negative pressure), so Ψp is negative, making xylem water potential very low to pull water from roots to leaves. By contrast, the positive turgor from a living cell taking up water is positive Ψp.
How to compute solute potential Ψs?
Commonly by the van't Hoff equation Ψs = −iCRT: i is the ionization factor (sucrose = 1, NaCl ≈ 2), C is molarity (mol/L), R = 0.00831 L·MPa·mol⁻¹·K⁻¹, T is absolute temperature (K = °C + 273). Enter the result in the Ψs field of this calculator.
What are the units of water potential?
SI unit is pascal (Pa), but plant physiology commonly uses megapascal (MPa, 1 MPa = 10⁶ Pa) for convenience; older literature uses bar (1 bar ≈ 0.1 MPa) or atmosphere. This calculator uses MPa throughout; ensure Ψs and Ψp share the same unit.
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.