Water Potential Calculator (ψ = ψs + ψp)
Calculate the total water potential (ψ) of a plant cell or solution from its solute concentration, ionization coefficient, temperature and pressure potential. Water moves from higher (less negative) to lower water potential.
mol/L
°C
MPa
ψ = ψs + ψp • Water flows from higher (less negative) to lower ψ
- 1
Absolute temperature (T)
25 + 273.15 = 298.15 - 2
Solute potential (ψs = −i × C × R × T)
−1 × 0.1 × 8.314×10⁻³ × 298.15 = -0.2479R = 8.314×10⁻³ L·MPa/(mol·K); result is always ≤ 0. - 3
Total water potential (ψ = ψs + ψp)
-0.2479 + 0 = -0.2479
How does this calculator work?
Water potential ψ = ψs + ψp, where solute potential ψs = −iCRT (R = 0.008314 L·MPa/mol·K, T in kelvin, i = van 't Hoff factor, C = molarity) and ψp is turgor/pressure potential in MPa. Water moves from higher to lower ψ. Plant cells typically operate between −0.5 and −2 MPa.
Formula
How this is calculated
Water potential (ψ) is the free energy per unit volume of water in a system, measured in megapascals (MPa). It governs osmosis: water flows spontaneously from regions of higher (less negative) water potential to regions of lower (more negative) water potential, just as heat flows from hot to cold.
The total water potential has two main components. The solute potential (ψs, also called osmotic potential) is always zero or negative and is computed using the van 't Hoff equation: ψs = −iCRT. Here i is the dimensionless van 't Hoff factor (the number of particles one formula unit of solute produces in solution: 1 for non-electrolytes such as sucrose, 2 for fully dissociated NaCl, 3 for CaCl₂ yielding Ca²⁺ + 2 Cl⁻). C is the molar concentration in mol/L, R is the gas constant expressed as 8.314 × 10⁻³ L·MPa/(mol·K), and T is the absolute temperature in kelvin (°C + 273.15).
The pressure potential (ψp) accounts for turgor pressure in a turgid plant cell (positive, from the cell wall resisting expansion) or tension in the xylem (negative). For a flaccid or open solution ψp = 0. Summing ψs and ψp gives the total water potential, which determines whether a cell gains or loses water to its surroundings. Note that this model omits the gravitational and matric components relevant to soil-water physics; for cell-level osmosis problems these terms are negligible.
Frequently asked questions
Leaf cells typically range from −0.5 to −2.0 MPa, low enough to draw water up from roots. Roots sitting in soil near 0 MPa experience a large gradient driving water inward. Wilted plants have more negative leaf water potentials than turgid ones.
It counts the effective number of solute particles per formula unit in solution. Non-electrolytes (sucrose, glucose) give i = 1. Strong binary electrolytes like NaCl give i ≈ 2; CaCl₂ ≈ 3. For weak electrolytes or high-concentration solutions, i lies between 1 and the theoretical maximum due to ionic interactions.
Water potential is defined relative to pure water at the same temperature and pressure, which is set to zero by convention. Adding solutes lowers ψ below zero; applying pressure raises it. A cell at ψ = 0 is in equilibrium with pure water and will neither gain nor lose water by osmosis.
Also known as
TG we-Calculate Editorial Team. (2026). Water Potential Calculator (ψ = ψs + ψp) [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/water-potential-calculator
TG we-Calculate Editorial Team. "Water Potential Calculator (ψ = ψs + ψp)." TG we-Calculate. 2026. https://we-calculate.com/calculator/water-potential-calculator.
TG we-Calculate Editorial Team, "Water Potential Calculator (ψ = ψs + ψp)," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/water-potential-calculator
@misc{wecalculate_water_potential_calculator, title = {Water Potential Calculator (ψ = ψs + ψp)}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/water-potential-calculator}}, year = {2026}, note = {TG we-Calculate} }
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