{
  "id": "pressure",
  "version": "1e44f11b38f9",
  "status": "published",
  "name": "Pressure Calculator",
  "question": "What is the pressure?",
  "summary": "Computes pressure from force and area (P = F ÷ A), or the force from the pressure and area, or the area from the force and pressure, in pascals, kPa, bar, psi and atmospheres.",
  "category": "physics",
  "subcategory": "mechanics",
  "url": "https://www.acalculator.org/physics/pressure-calculator",
  "markdown": "https://www.acalculator.org/physics/pressure-calculator.md",
  "kind": "function",
  "method": "P = F ÷ A; F = P × A; A = F ÷ P.",
  "assumptions": [
    "The force presses straight onto the surface (perpendicular to it) and is spread evenly over the area.",
    "Exact unit sizes: 1 lbf = 4.4482216152605 N; 1 in² = 0.00064516 m²; 1 psi = 6,894.757293168361… Pa; 1 bar = 100,000 Pa; 1 atm = 101,325 Pa; 1 mmHg = 133.322387415 Pa."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "find": {
        "title": "Find",
        "description": "Which of pressure, force and area to work out from the other two.",
        "type": "string",
        "enum": [
          "pressure",
          "force",
          "area"
        ]
      },
      "F": {
        "title": "Force",
        "description": "The force pressing straight onto the surface.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "force",
        "minimum": 1e-9,
        "maximum": 1000000000000000
      },
      "A": {
        "title": "Area",
        "description": "The area the force is spread over.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "area",
        "minimum": 1e-12,
        "maximum": 1000000000000
      },
      "P": {
        "title": "Pressure",
        "description": "The pressure on the surface.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "pressure",
        "minimum": 1e-9,
        "maximum": 1000000000000000
      }
    }
  },
  "outputs": {
    "result": {
      "label": "Answer",
      "description": "The value worked out, to 6 significant figures, in its main units.",
      "format": "text"
    },
    "pa": {
      "label": "Pressure (Pa)",
      "description": "The pressure in pascals (N/m²).",
      "format": "number"
    },
    "kpa": {
      "label": "Pressure (kPa)",
      "description": "The pressure in kilopascals.",
      "format": "number"
    },
    "psi": {
      "label": "Pressure (psi)",
      "description": "The pressure in pounds-force per square inch.",
      "format": "number"
    },
    "bar": {
      "label": "Pressure (bar)",
      "description": "The pressure in bar (100,000 Pa).",
      "format": "number"
    },
    "atm": {
      "label": "Pressure (atm)",
      "description": "The pressure in standard atmospheres (101,325 Pa).",
      "format": "number"
    },
    "newtons": {
      "label": "Force (N)",
      "description": "The force in newtons.",
      "format": "number"
    },
    "lbf": {
      "label": "Force (lbf)",
      "description": "The force in pounds-force.",
      "format": "number"
    },
    "m2": {
      "label": "Area (m²)",
      "description": "The area in square meters.",
      "format": "number"
    },
    "in2": {
      "label": "Area (in²)",
      "description": "The area in square inches.",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "find": "pressure",
      "F": "500 N",
      "A": "0.25 m²",
      "P": "2000 Pa"
    },
    "outputs": {
      "result": "P = 2000 Pa (0.290075 psi)",
      "pa": 2000,
      "kpa": 2,
      "psi": 0.29007547546041845,
      "bar": 0.02,
      "atm": 0.019738465334320256,
      "newtons": 500,
      "lbf": 112.40447154985524,
      "m2": 0.25,
      "in2": 387.50077500155
    },
    "text": "The answer is P = 2000 Pa (0.290075 psi)."
  },
  "examples": [
    {
      "given": {
        "find": "pressure",
        "F": 500,
        "A": 0.25
      },
      "expect": {
        "pa": 2000,
        "kpa": 2,
        "result": "P = 2000 Pa (0.290075 psi)"
      },
      "source": "OpenStax, University Physics Volume 1, §14.1 Fluids, Density, and Pressure (p = F ÷ A), https://openstax.org/books/university-physics-volume-1/pages/14-1-fluids-density-and-pressure; hand calculation in content.mdx: P = 500 ÷ 0.25 = 2,000 Pa"
    },
    {
      "given": {
        "find": "pressure",
        "F": 4.4482216152605,
        "A": 0.00064516
      },
      "expect": {
        "psi": 1,
        "pa": 6894.757293168361
      },
      "source": "NIST SP 811, Appendix B.8 (1 lbf = 4.4482216152605 N; 1 in = 0.0254 m; 1 atm = 101,325 Pa; 1 bar = 100,000 Pa), https://www.nist.gov/pml/special-publication-811; hand calculation in content.mdx: 4.4482216152605 N ÷ 0.00064516 m² = 6,894.76 Pa = 1 psi"
    },
    {
      "given": {
        "find": "force",
        "P": 101325,
        "A": 1
      },
      "expect": {
        "newtons": 101325,
        "atm": 1
      },
      "source": "OpenStax, University Physics Volume 1, §14.1 Fluids, Density, and Pressure (p = F ÷ A), https://openstax.org/books/university-physics-volume-1/pages/14-1-fluids-density-and-pressure; NIST SP 811, Appendix B.8 (1 lbf = 4.4482216152605 N; 1 in = 0.0254 m; 1 atm = 101,325 Pa; 1 bar = 100,000 Pa), https://www.nist.gov/pml/special-publication-811; hand calculation in content.mdx: F = 101,325 Pa × 1 m² = 101,325 N"
    },
    {
      "given": {
        "find": "area",
        "F": 700,
        "P": 200000
      },
      "expect": {
        "m2": 0.0035,
        "result": "A = 0.0035 m² (5.42501 in²)"
      },
      "source": "OpenStax, University Physics Volume 1, §14.1 Fluids, Density, and Pressure (p = F ÷ A), https://openstax.org/books/university-physics-volume-1/pages/14-1-fluids-density-and-pressure; hand calculation in content.mdx: A = 700 ÷ 200,000 = 0.0035 m² = 5.42501 in²"
    }
  ],
  "sources": [
    "OpenStax, University Physics Volume 1, §14.1 Fluids, Density, and Pressure (p = F ÷ A; 1 Pa = 1 N/m²). https://openstax.org/books/university-physics-volume-1/pages/14-1-fluids-density-and-pressure (retrieved 2026-10-03)",
    "NIST SP 811, Appendix B.8 Factors for Units Listed Alphabetically (pound-force per square inch, bar, standard atmosphere, millimeter of mercury). https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b8 (retrieved 2026-10-03)"
  ],
  "related": [
    "force",
    "density",
    "tire-pressure"
  ],
  "changelog": []
}