{
  "id": "muzzle-energy",
  "version": "3fee43a648b8",
  "status": "published",
  "name": "Muzzle Energy Calculator",
  "question": "What is the muzzle energy?",
  "summary": "Computes the muzzle energy of a bullet from its weight and muzzle velocity (E = ½mv²) in foot-pounds and joules, or the velocity or weight from the energy, with the momentum.",
  "category": "physics",
  "subcategory": "mechanics",
  "url": "https://www.acalculator.org/physics/muzzle-energy-calculator",
  "markdown": "https://www.acalculator.org/physics/muzzle-energy-calculator.md",
  "kind": "formulas",
  "method": "E = ½ × m × v²; m = 2E ÷ v²; v = √(2E ÷ m); momentum = m × v.",
  "assumptions": [
    "The energy is the kinetic energy of the bullet alone at the muzzle; spin and the powder gases are left out.",
    "Units are converted exactly: 1 grain = 64.79891 mg, 1 ft = 0.3048 m, 1 ft·lbf = 1.3558179483314004 J (NIST SP 811)."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "m": {
        "title": "Bullet weight",
        "description": "The mass of the bullet (the projectile alone, not the cartridge).",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "mass",
        "exclusiveMinimum": 0,
        "maximum": 100
      },
      "v": {
        "title": "Muzzle velocity",
        "description": "The speed of the bullet as it leaves the muzzle.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "speed",
        "exclusiveMinimum": 0,
        "maximum": 3000
      },
      "e": {
        "title": "Muzzle energy",
        "description": "The kinetic energy of the bullet at the muzzle.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "energy",
        "exclusiveMinimum": 0,
        "maximum": 500000000
      }
    }
  },
  "solve": {
    "fillAny": 2,
    "variables": [
      "m",
      "v",
      "e"
    ],
    "inputsOnly": []
  },
  "outputs": {
    "m": {
      "label": "Bullet weight",
      "description": "The mass of the bullet (the projectile alone, not the cartridge).",
      "format": "quantity"
    },
    "v": {
      "label": "Muzzle velocity",
      "description": "The speed of the bullet as it leaves the muzzle.",
      "format": "quantity"
    },
    "e": {
      "label": "Muzzle energy",
      "description": "The kinetic energy at the muzzle, ½ × m × v².",
      "format": "quantity",
      "unit": "ftlbf"
    },
    "ftlbf": {
      "label": "Energy in foot-pounds",
      "description": "The energy in foot-pounds (ft·lbf): joules ÷ 1.355 817 948 331 400 4.",
      "format": "number"
    },
    "joules": {
      "label": "Energy in joules",
      "description": "The energy in joules: ½ × kilograms × (metres per second)².",
      "format": "number"
    },
    "momentum": {
      "label": "Momentum",
      "description": "The momentum of the bullet, m × v, in newton-seconds (kg·m/s).",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "m": 0.009719836499999999,
      "v": 859.5360000000001
    },
    "outputs": {
      "e": 3590.5179804639993,
      "ftlbf": 2648.230158689694,
      "joules": 3590.5179804639993,
      "momentum": 8.354549385863999
    },
    "text": "A 150 gr bullet at 2,820 ft/s has a muzzle energy of 2,648.23 ft·lbf."
  },
  "examples": [
    {
      "given": {
        "m": 0.009719836499999999,
        "v": 859.5360000000001
      },
      "expect": {
        "e": 3590.5179804639993,
        "ftlbf": 2648.230158689694,
        "momentum": 8.354549385863999
      },
      "source": "OpenStax University Physics Volume 1, section 7.2, Kinetic Energy, K = ½mv² (https://openstax.org/books/university-physics-volume-1/pages/7-2-kinetic-energy, retrieved 2026-10-01); NIST SP 811 (1 gr = 64.79891 mg, 1 ft·lbf = 1.3558179483314004 J); hand calculation in content.mdx",
      "tolerance": 1e-12
    },
    {
      "given": {
        "m": 80,
        "v": 10
      },
      "expect": {
        "e": 4000
      },
      "source": "OpenStax University Physics Volume 1, section 7.2, Kinetic Energy, example: 80 kg at 10 m/s is 4.0 kJ (https://openstax.org/books/university-physics-volume-1/pages/7-2-kinetic-energy)",
      "tolerance": 1e-12
    },
    {
      "given": {
        "m": 0.0035639400499999996,
        "e": 1738.1586097608551
      },
      "expect": {
        "v": 987.6305260586619
      },
      "source": "OpenStax University Physics Volume 1, section 7.2, Kinetic Energy (v = √(2K ÷ m)); NIST SP 811 units; hand calculation in content.mdx: 3,240.26 ft/s",
      "tolerance": 1e-12
    }
  ],
  "sources": [
    "OpenStax, University Physics Volume 1, section 7.2, Kinetic Energy (K = ½mv²; example: 80 kg at 10 m/s is 4.0 kJ), CC BY 4.0, retrieved 2026-10-01. https://openstax.org/books/university-physics-volume-1/pages/7-2-kinetic-energy",
    "NIST Special Publication 811, Guide for the Use of the International System of Units, Appendix B.8 (grain = 64.79891 mg, foot = 0.3048 m, pound-force = 4.4482216152605 N), retrieved 2026-10-01. https://www.nist.gov/pml/special-publication-811"
  ],
  "related": [
    "power",
    "speed"
  ],
  "changelog": []
}