Water Potential Calculator
Water potential (Ψ) drives water movement across plant cell membranes. Enter your solute concentration and temperature to compute osmotic potential via the van't Hoff equation, add pressure and gravitational components, and get total water potential instantly. Switch between MPa, kPa, bar, and atm units. Determine which direction water will flow between two systems.
Formula
Worked example
A sucrose solution (C = 0.5 mol/L, i = 1) at 25°C: T = 298.15 K, Ψs = -1 × 0.5 × 0.0083145 × 298.15 = -1.2395 MPa. With turgor pressure Ψp = 0.3 MPa and all other components zero: Ψ = -1.2395 + 0.3 = -0.9395 MPa.
What is water potential?
Water potential (Ψ, psi) measures the free energy of water per unit volume relative to pure water at the same temperature and pressure. Pure water is defined as Ψ = 0. Any dissolved solutes or tension lower Ψ below zero, while hydrostatic pressure can push it above zero. Water always moves from regions of higher (less negative) water potential to regions of lower (more negative) water potential - the process called osmosis. This principle governs how plants absorb water from soil, transport it through xylem, and lose it through stomata.
Components of water potential
Total water potential is the algebraic sum of its components. The osmotic (solute) potential (Ψs) arises from dissolved solutes and is always negative or zero - the more concentrated the solution, the more negative Ψs. The pressure potential (Ψp) represents hydrostatic or turgor pressure; it is positive in turgid cells and negative in water-stressed xylem. The gravitational potential (Ψg) is significant in tall trees where water must be raised tens of metres, contributing about -0.0098 MPa per metre of height. The matric potential (Ψm) accounts for water binding to soil particles or cell-wall matrices and is always negative or zero. In most introductory biology courses, only Ψs and Ψp are used, giving Ψ = Ψs + Ψp.
The van't Hoff equation for osmotic potential
Osmotic potential is calculated from the van't Hoff equation: Ψs = -iCRT, where i is the ionization constant (the number of particles one formula unit produces in solution: 1 for sucrose, 2 for NaCl, 3 for CaCl2), C is the molar concentration in mol/L, R is the gas constant (0.0083145 L·MPa/(mol·K)), and T is the absolute temperature in Kelvin. A 0.5 mol/L sucrose solution at 25°C gives Ψs = -1 × 0.5 × 0.0083145 × 298.15 = -1.24 MPa. For NaCl at the same concentration, Ψs doubles because each NaCl dissociates into two ions.
Water potential and plant stress
Plant physiologists use water potential as a measure of water stress. At field capacity (soil Ψ around -0.03 MPa), plants can absorb water freely. As soil dries, its water potential drops. Once soil Ψ falls below the permanent wilting point (about -1.5 MPa), most crop plants cannot extract sufficient water and wilt permanently. Halophytes and xerophytes tolerate much lower potentials by accumulating compatible solutes (organic osmolytes) that lower their own Ψs, maintaining the inward gradient needed for water uptake even from salty or dry soils.
Typical water potentials in plant cells and tissues
| Tissue or condition | Ψ (MPa) | Interpretation |
|---|---|---|
| Pure water | 0.00 | Reference state |
| Well-watered plant leaf | -0.2 to -0.6 | Adequate hydration |
| Mild water stress (wilting onset) | -0.6 to -1.0 | Stomata begin closing |
| Significant drought stress | -1.0 to -1.5 | Growth reduction |
| Severe drought / permanent wilting | below -1.5 | Cell turgor lost |
| Soil at field capacity | -0.01 to -0.05 | Good soil water availability |
| Soil at permanent wilting point | about -1.5 | Plants cannot extract water |
| Halophyte in saline soil | -3.0 to -6.0 | Extreme osmotic stress |
Approximate values in MPa. More negative = greater water deficit. Pure water = 0 MPa.
Frequently asked questions
Why is water potential usually negative?
Water potential is measured relative to pure water (Ψ = 0). Dissolving solutes reduces the free energy of water molecules, making Ψs negative. Unless an external positive pressure is applied that exceeds the osmotic component, total water potential stays below zero in biological solutions. The only common positive contribution is turgor pressure (Ψp) in turgid plant cells.
What is the ionization constant (i) and why does it matter?
The ionization constant (van't Hoff factor, i) accounts for how many particles a solute produces when dissolved. Sucrose and glucose do not dissociate, so i = 1. NaCl dissociates into Na+ and Cl-, giving i = 2. CaCl2 gives Ca2+, Cl-, and Cl-, so i = 3. Because Ψs = -iCRT, a 0.5 mol/L NaCl solution has twice the osmotic effect of a 0.5 mol/L sucrose solution at the same temperature.
What is the difference between osmotic potential and water potential?
Osmotic potential (Ψs) is just one component of total water potential. It reflects the effect of solutes alone. Water potential (Ψ) is the sum of osmotic potential, pressure potential, gravitational potential, and matric potential. In a simple beaker of solution with no applied pressure, Ψ equals Ψs. Inside a plant cell, turgor pressure (Ψp) adds a positive term, making Ψ less negative than Ψs alone.
Which direction does water move between two systems?
Water always moves from the system with higher (less negative) water potential to the system with lower (more negative) water potential. For example, if a plant cell has Ψ = -0.8 MPa and the surrounding soil solution has Ψ = -0.3 MPa, water moves from soil into the cell because soil has higher potential. The "Compare two systems" section of this calculator works this out automatically.
What are typical water potential values for plant cells?
Well-hydrated leaf cells usually have Ψ between -0.2 and -0.6 MPa. Mild stress begins around -0.6 to -1.0 MPa, where stomata start closing. Below -1.5 MPa most crop plants reach the permanent wilting point. Xerophytes can tolerate -3.0 MPa or lower. Soil at field capacity is around -0.03 MPa, and pure water is 0 MPa by definition.