Water Potential Calculator

Calculate water potential (Ψ = Ψs + Ψp) and solute potential (Ψs = -iCRT) in bars from solute concentration, temperature, and pressure potential.

Quick Facts

Formula
Ψ = Ψs + Ψp, with Ψs = -iCRT and R = 0.0831 L·bar/mol·K
Temperature is converted to Kelvin (K = °C + 273). Results are in bars.

Your Results

Calculated
Water potential (Ψ)
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Ψ = Ψs + Ψp, in bars
Solute potential (Ψs)
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Ψs = -iCRT, in bars
Pressure potential (Ψp)
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As entered, in bars

Ready

Enter concentration, temperature, and pressure potential, then calculate.

About water potential

Water potential (symbol Ψ, the Greek letter psi) measures the potential energy of water per unit volume relative to pure water at atmospheric pressure. It predicts the direction water will move: water always flows from a region of higher (less negative) water potential to a region of lower (more negative) water potential. Because it is expressed as an energy per volume, water potential is reported in pressure units — most commonly bars or megapascals (1 MPa = 10 bars). Pure water at standard atmospheric pressure has a water potential of exactly 0.

The formula

In plant physiology, water potential is the sum of two components:

Ψ = Ψs + Ψp

  • Ψs — solute potential (also called osmotic potential). Dissolved solutes lower the free energy of water, so Ψs is always negative or zero.
  • Ψp — pressure potential. Physical pressure such as the turgor pressure exerted by a cell wall. It is usually positive inside a living cell and can be negative (tension) in the xylem.

Solute potential is calculated with the van't Hoff-style relation used throughout introductory biology:

Ψs = −iCRT

  • i — ionization (dissociation) constant: the number of particles a solute breaks into. For sucrose i = 1.0; for NaCl i = 2.0; for CaCl₂ i ≈ 3.0.
  • C — molar concentration of the solute in mol/L.
  • R — the pressure constant, 0.0831 liter·bar / (mol·K).
  • T — temperature in Kelvin, found by adding 273 to the Celsius temperature.

The leading minus sign guarantees that adding any solute produces a negative solute potential, which is why solutions always have a lower water potential than pure water.

Why it matters

Water potential explains osmosis without hand-waving. A plant cell placed in distilled water (Ψ = 0) has negative internal water potential from its dissolved solutes, so water moves in until the rising turgor pressure raises Ψp enough to bring the cell's total Ψ up to 0. A cell placed in a strong sugar or salt solution loses water, plasmolyzes, and wilts because the surrounding solution is more negative than the cell interior. The same principle governs how roots pull water from soil and how water climbs a tree.

Common reference points

  • Pure water, open to the atmosphere: Ψ = 0 bars.
  • 0.15 mol/L NaCl (roughly the salinity of physiological saline) at 25 °C: Ψs = −(2)(0.15)(0.0831)(298) ≈ −7.43 bars.
  • 1.0 mol/L sucrose at 20 °C: Ψs = −(1)(1.0)(0.0831)(293) ≈ −24.35 bars.
  • Well-watered soil: about −0.1 to −0.3 bars; permanent wilting point for most crops: about −15 bars.

Frequently Asked Questions

What is the formula for water potential?
Water potential is Ψ = Ψs + Ψp (solute potential plus pressure potential). Solute potential is found separately with Ψs = −iCRT, where i is the ionization constant, C is molar concentration in mol/L, R is 0.0831 L·bar/mol·K, and T is temperature in Kelvin (°C + 273). Results are in bars.
Why is solute potential always negative?
Dissolving a solute lowers the free energy of water. The minus sign in Ψs = −iCRT means any positive concentration gives a negative value, so a solution always has lower water potential than pure water. This is what drives water to move into a solution by osmosis.
What value of R should I use, and in what units?
Use R = 0.0831 liter·bar per mole·kelvin. Paired with concentration in mol/L and temperature in kelvin, this gives solute potential directly in bars — the convention used in AP Biology and most introductory plant physiology. If you need megapascals instead, divide the result by 10 (1 MPa = 10 bars).
What is the ionization constant (i) for common solutes?
The ionization constant counts how many particles a solute dissociates into in water. Sucrose and glucose stay as single molecules, so i = 1.0. Sodium chloride (NaCl) splits into Na⁺ and Cl⁻, so i = 2.0. Calcium chloride (CaCl₂) yields three ions, so i ≈ 3.0. Ionic compounds therefore lower water potential more than an equal molar concentration of sugar.
How does pressure potential (Ψp) fit in?
Pressure potential is the physical pressure component. In a turgid plant cell it is positive because the cell wall pushes back on the swelling protoplast; in xylem under transpirational pull it is negative (tension). At the moment of incipient plasmolysis, or for an open solution in a beaker, Ψp = 0, so the water potential equals the solute potential alone.