{
  "id": "water-potential",
  "version": "1ec728b61da0",
  "status": "published",
  "name": "Water Potential Calculator",
  "question": "What is the water potential?",
  "summary": "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.",
  "category": "biology",
  "subcategory": "lab",
  "url": "https://www.acalculator.org/biology/water-potential-calculator",
  "markdown": "https://www.acalculator.org/biology/water-potential-calculator.md",
  "kind": "function",
  "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."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "src": {
        "title": "Solute potential from",
        "description": "Work out Ψs from the concentration, or type Ψs.",
        "type": "string",
        "enum": [
          "conc",
          "typed"
        ]
      },
      "i": {
        "title": "van ’t Hoff factor i",
        "description": "Particles each formula unit gives in water: 1 for sucrose or glucose, 2 for NaCl, 3 for CaCl₂.",
        "type": "number",
        "minimum": 1,
        "maximum": 10
      },
      "c": {
        "title": "Molar concentration C (mol/L)",
        "description": "The solute concentration in moles per liter.",
        "type": "number",
        "minimum": 0,
        "maximum": 20
      },
      "t": {
        "title": "Temperature",
        "description": "The temperature of the solution.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "temperature",
        "minimum": 1,
        "maximum": 1000
      },
      "ps": {
        "title": "Solute potential Ψs",
        "description": "The solute (osmotic) potential: 0 for pure water, negative with solutes.",
        "type": "number",
        "minimum": -10000,
        "maximum": 0
      },
      "pp": {
        "title": "Pressure potential Ψp",
        "description": "The turgor pressure of the cell, positive in a turgid cell; 0 in an open beaker.",
        "type": "number",
        "minimum": -10000,
        "maximum": 10000
      },
      "pg": {
        "title": "Gravity potential Ψg",
        "description": "Optional: the effect of height; leave empty to count it as 0.",
        "type": "number",
        "minimum": -10000,
        "maximum": 10000
      },
      "pm": {
        "title": "Matric potential Ψm",
        "description": "Optional: water bound to surfaces such as a dry seed’s; 0 or negative.",
        "type": "number",
        "minimum": -10000,
        "maximum": 0
      },
      "u": {
        "title": "Potentials in",
        "description": "The unit of the typed potentials and of the answer: megapascals or bars (1 MPa = 10 bar).",
        "type": "string",
        "enum": [
          "MPa",
          "bar"
        ]
      }
    }
  },
  "outputs": {
    "result": {
      "label": "Answer",
      "description": "The water potential in the chosen unit, with the other unit.",
      "format": "text"
    },
    "psiMPa": {
      "label": "Water potential Ψ (MPa)",
      "description": "Ψs + Ψp + Ψg + Ψm in megapascals.",
      "format": "number"
    },
    "psiBar": {
      "label": "Water potential Ψ (bar)",
      "description": "Ψs + Ψp + Ψg + Ψm in bars.",
      "format": "number"
    },
    "psiSMPa": {
      "label": "Solute potential Ψs (MPa)",
      "description": "−iCRT, or as typed, in megapascals.",
      "format": "number"
    },
    "psiSBar": {
      "label": "Solute potential Ψs (bar)",
      "description": "−iCRT, or as typed, in bars.",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "src": "conc",
      "i": 1,
      "c": 0.3,
      "t": "20 °C",
      "ps": -0.7,
      "pp": 0.5,
      "u": "MPa"
    },
    "outputs": {
      "result": "Ψ = −0.231215 MPa (−2.31215 bar)",
      "psiMPa": -0.2312154149534867,
      "psiBar": -2.3121541495348668,
      "psiSMPa": -0.7312154149534867,
      "psiSBar": -7.312154149534867
    },
    "text": "Ψ = −0.231215 MPa (−2.31215 bar)."
  },
  "examples": [
    {
      "given": {
        "src": "conc",
        "i": 1,
        "c": 1,
        "t": 295.15,
        "pp": 0,
        "u": "bar"
      },
      "expect": {
        "psiSBar": -24.54013641747929,
        "psiMPa": -2.454013641747929,
        "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; hand calculation in content.mdx; Python 3"
    },
    {
      "given": {
        "src": "conc",
        "i": 2,
        "c": 0.15,
        "t": 298.15,
        "pp": 0.3,
        "u": "MPa"
      },
      "expect": {
        "psiSMPa": -0.7436871088807165,
        "psiMPa": -0.44368710888071655
      },
      "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; hand calculation in content.mdx; Python 3"
    },
    {
      "given": {
        "src": "typed",
        "ps": -0.7,
        "pp": 0.6,
        "u": "MPa"
      },
      "expect": {
        "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; hand calculation in content.mdx"
    },
    {
      "given": {
        "src": "conc",
        "i": 1,
        "c": 0,
        "t": 293.15,
        "pp": 0,
        "u": "MPa"
      },
      "expect": {
        "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; hand calculation in content.mdx"
    }
  ],
  "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)"
  ],
  "related": [
    "vpd",
    "serial-dilution",
    "hardy-weinberg",
    "centrifuge"
  ],
  "changelog": []
}