{
  "id": "specific-heat",
  "version": "e3bcb16f7632",
  "status": "published",
  "name": "Specific Heat Calculator",
  "question": "What is the specific heat?",
  "summary": "Specific heat calculator: finds the specific heat capacity from heat, mass and temperature change (c = Q ÷ mΔT), or the heat, the mass or the final temperature from Q = mcΔT.",
  "category": "physics",
  "subcategory": "energy",
  "url": "https://www.acalculator.org/physics/specific-heat-calculator",
  "markdown": "https://www.acalculator.org/physics/specific-heat-calculator.md",
  "kind": "function",
  "method": "Q = m × c × ΔT, with ΔT = final − start temperature; c = Q ÷ (m × ΔT); m = Q ÷ (c × ΔT); final = start + Q ÷ (m × c).",
  "assumptions": [
    "The material stays in one phase (no melting, freezing or boiling), and c does not change with temperature over the range.",
    "Table values are from OpenStax University Physics Volume 2, Table 1.3, in J/(kg·°C); a change of 1 °C is a change of 1 K."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "find": {
        "title": "Find",
        "description": "Which value to work out from Q = m × c × ΔT.",
        "type": "string",
        "enum": [
          "c",
          "heat",
          "mass",
          "final"
        ]
      },
      "Q": {
        "title": "Heat (Q)",
        "description": "The heat added to the material; type a negative value for heat taken away.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "energy",
        "minimum": -1000000000000000,
        "maximum": 1000000000000000
      },
      "m": {
        "title": "Mass (m)",
        "description": "The mass of the material that heats or cools.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "mass",
        "exclusiveMinimum": 0,
        "maximum": 1000000000
      },
      "sub": {
        "title": "Material",
        "description": "The material, which sets its specific heat (OpenStax Table 1.3, in J/(kg·°C)).",
        "type": "string",
        "enum": [
          "water",
          "ice",
          "aluminum",
          "copper",
          "iron",
          "lead",
          "silver",
          "gold",
          "glass",
          "granite",
          "wood",
          "ethanol",
          "mercury",
          "custom"
        ]
      },
      "c": {
        "title": "Specific heat (c)",
        "description": "The specific heat capacity of the material, in the unit chosen below.",
        "type": "number",
        "exclusiveMinimum": 0,
        "maximum": 1000000
      },
      "cu": {
        "title": "Specific heat unit",
        "description": "The unit of the specific heat you type.",
        "type": "string",
        "enum": [
          "J-kgK",
          "kJ-kgK",
          "J-gK",
          "cal-gK",
          "BTU-lbF"
        ]
      },
      "t1": {
        "title": "Start temperature",
        "description": "The temperature before the heat goes in or out.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "temperature",
        "minimum": 0,
        "maximum": 100000
      },
      "t2": {
        "title": "Final temperature",
        "description": "The temperature after the heat goes in or out.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "temperature",
        "minimum": 0,
        "maximum": 100000
      }
    }
  },
  "outputs": {
    "result": {
      "label": "Answer",
      "description": "The value worked out, to 6 significant figures.",
      "format": "text"
    },
    "c": {
      "label": "Specific heat (J/(kg·°C))",
      "description": "The specific heat capacity in joules per kilogram per degree Celsius (or kelvin).",
      "format": "number"
    },
    "cJg": {
      "label": "Specific heat (J/(g·°C))",
      "description": "The specific heat capacity in joules per gram per degree Celsius.",
      "format": "number"
    },
    "cCal": {
      "label": "Specific heat (cal/(g·°C))",
      "description": "The specific heat capacity in calories per gram per degree Celsius.",
      "format": "number"
    },
    "cBtu": {
      "label": "Specific heat (Btu/(lb·°F))",
      "description": "The specific heat capacity in British thermal units per pound per degree Fahrenheit.",
      "format": "number"
    },
    "joules": {
      "label": "Heat (J)",
      "description": "The heat in joules; negative when heat is taken away.",
      "format": "number"
    },
    "kj": {
      "label": "Heat (kJ)",
      "description": "The heat in kilojoules.",
      "format": "number"
    },
    "btu": {
      "label": "Heat (Btu)",
      "description": "The heat in British thermal units.",
      "format": "number"
    },
    "kg": {
      "label": "Mass (kg)",
      "description": "The mass in kilograms.",
      "format": "number"
    },
    "dT": {
      "label": "Temperature change (°C or K)",
      "description": "Final temperature − start temperature, in °C (the same size as kelvins).",
      "format": "number"
    },
    "dTF": {
      "label": "Temperature change (°F)",
      "description": "The temperature change in degrees Fahrenheit.",
      "format": "number"
    },
    "finalC": {
      "label": "Final temperature (°C)",
      "description": "The final temperature in degrees Celsius.",
      "format": "number"
    },
    "finalF": {
      "label": "Final temperature (°F)",
      "description": "The final temperature in degrees Fahrenheit.",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "find": "c",
      "Q": "41.86 kJ",
      "m": "1 kg",
      "sub": "water",
      "c": 4186,
      "cu": "J-kgK",
      "t1": "20 °C",
      "t2": "30 °C"
    },
    "outputs": {
      "result": "c = 4186 J/(kg·°C)",
      "c": 4186,
      "cJg": 4.186,
      "cCal": 1.0004780114722753,
      "cBtu": 0.999808923282698,
      "joules": 41860,
      "kj": 41.86,
      "btu": 39.675624656315456,
      "kg": 1,
      "dT": 10,
      "dTF": 18,
      "finalC": 30,
      "finalF": 86
    },
    "text": "The answer is c = 4186 J/(kg·°C)."
  },
  "examples": [
    {
      "given": {
        "find": "c",
        "Q": 41860,
        "m": 1,
        "t1": 293.15,
        "t2": 303.15
      },
      "expect": {
        "c": 4186,
        "cCal": 1.0004780114722753,
        "result": "c = 4186 J/(kg·°C)"
      },
      "source": "OpenStax, University Physics Volume 2, §1.4 Heat Transfer, Specific Heat, and Calorimetry (Q = mcΔT; Table 1.3), https://openstax.org/books/university-physics-volume-2/pages/1-4-heat-transfer-specific-heat-and-calorimetry (retrieved 2026-10-05); hand calculation in content.mdx: c = 41,860 ÷ (1 × 10) = 4,186 J/(kg·°C)",
      "tolerance": 1e-12
    },
    {
      "given": {
        "find": "heat",
        "sub": "aluminum",
        "m": 0.5,
        "t1": 293.15,
        "t2": 423.15
      },
      "expect": {
        "joules": 58500,
        "kj": 58.5
      },
      "source": "OpenStax, University Physics Volume 2, §1.4 Heat Transfer, Specific Heat, and Calorimetry (Q = mcΔT; Table 1.3), https://openstax.org/books/university-physics-volume-2/pages/1-4-heat-transfer-specific-heat-and-calorimetry (retrieved 2026-10-05) (c of aluminum, Table 1.3); hand calculation in content.mdx: 0.5 × 900 × 130 = 58,500 J",
      "tolerance": 1e-12
    },
    {
      "given": {
        "find": "final",
        "sub": "water",
        "Q": 20930,
        "m": 0.25,
        "t1": 288.15
      },
      "expect": {
        "dT": 20,
        "finalC": 35
      },
      "source": "OpenStax, University Physics Volume 2, §1.4 Heat Transfer, Specific Heat, and Calorimetry (Q = mcΔT; Table 1.3), https://openstax.org/books/university-physics-volume-2/pages/1-4-heat-transfer-specific-heat-and-calorimetry (retrieved 2026-10-05); hand calculation in content.mdx: ΔT = 20,930 ÷ (0.25 × 4,186) = 20 °C, so 15 + 20 = 35 °C",
      "tolerance": 1e-12
    },
    {
      "given": {
        "find": "mass",
        "sub": "custom",
        "c": 1,
        "cu": "BTU-lbF",
        "Q": 1055.05585262,
        "t1": 293.15,
        "t2": 293.7055555555555
      },
      "expect": {
        "kg": 0.45359237,
        "c": 4186.8
      },
      "source": "NIST SP 811, Appendix B.8 (1 Btu_IT = 1,055.05585262 J; 1 cal_th = 4.184 J; 1 lb = 0.45359237 kg), https://www.nist.gov/pml/special-publication-811 (retrieved 2026-10-05); hand calculation in content.mdx: 1 Btu/(lb·°F) = 1,055.05585262 ÷ (0.45359237 × 5/9) = 4,186.8 J/(kg·°C); m = 1,055.05585262 ÷ (4,186.8 × 5/9) = 0.45359237 kg",
      "tolerance": 1e-12
    }
  ],
  "sources": [
    "OpenStax, University Physics Volume 2, §1.4 Heat Transfer, Specific Heat, and Calorimetry: Q = mcΔT and Table 1.3 of specific heats, retrieved 2026-10-05. https://openstax.org/books/university-physics-volume-2/pages/1-4-heat-transfer-specific-heat-and-calorimetry",
    "NIST Special Publication 811 (2008), Appendix B.8: 1 Btu (IT) = 1,055.05585262 J, 1 cal (thermochemical) = 4.184 J, 1 lb = 0.45359237 kg, retrieved 2026-10-05. https://www.nist.gov/pml/special-publication-811"
  ],
  "related": [
    "energy",
    "btu",
    "enthalpy"
  ],
  "changelog": []
}