{ "id": "kinetic-energy", "version": "b4dae8df968d", "status": "published", "name": "Kinetic Energy Calculator", "question": "What is the kinetic energy?", "summary": "Computes kinetic energy from mass and speed (KE = ½ m v²), or the mass or speed from the other two, in metric or US units.", "category": "physics", "subcategory": "energy", "url": "https://www.acalculator.org/physics/kinetic-energy-calculator", "markdown": "https://www.acalculator.org/physics/kinetic-energy-calculator.md", "kind": "function", "method": "KE = ½ × m × v²; m = 2 × KE ÷ v²; v = √(2 × KE ÷ m). Mass in kg and speed in m/s give the energy in joules.", "assumptions": [ "Classical (Newtonian) mechanics: the speed is below 10% of the speed of light, where KE = ½ m v² is within about 0.75% of the relativistic value.", "The energy is the translational kinetic energy of the whole object; spin (rotational energy) is not included.", "Units are converted with exact factors: 1 lb = 0.45359237 kg, 1 mph = 0.44704 m/s, 1 km/h = 1/3.6 m/s, 1 ft·lbf = 1.3558179483314004 J, 1 kcal = 4,184 J." ], "inputs": { "$schema": "https://json-schema.org/draft/2020-12/schema", "type": "object", "properties": { "find": { "title": "Find", "description": "Which value to work out from the other two.", "type": "string", "enum": [ "energy", "mass", "speed" ] }, "m": { "title": "Mass", "description": "The mass of the moving object.", "type": [ "number", "string" ], "x-quantity": "mass", "exclusiveMinimum": 0, "maximum": 1000000000000 }, "v": { "title": "Speed", "description": "How fast the object moves.", "type": [ "number", "string" ], "x-quantity": "speed", "minimum": 0, "maximum": 100000000 }, "ke": { "title": "Kinetic energy", "description": "The kinetic energy of the moving object.", "type": [ "number", "string" ], "x-quantity": "energy", "exclusiveMinimum": 0, "maximum": 1000000000000000000 } } }, "outputs": { "ke": { "label": "Kinetic energy (J)", "description": "The kinetic energy in joules: ½ × mass × speed².", "format": "number" }, "kj": { "label": "Kinetic energy (kJ)", "description": "The same energy in kilojoules.", "format": "number" }, "ftlbf": { "label": "Kinetic energy (ft·lbf)", "description": "The same energy in foot-pounds.", "format": "number" }, "kcal": { "label": "Kinetic energy (kcal)", "description": "The same energy in kilocalories (food Calories).", "format": "number" }, "kg": { "label": "Mass (kg)", "description": "The mass in kilograms: 2 × energy ÷ speed².", "format": "number" }, "lb": { "label": "Mass (lb)", "description": "The same mass in pounds.", "format": "number" }, "mps": { "label": "Speed (m/s)", "description": "The speed in metres per second: √(2 × energy ÷ mass).", "format": "number" }, "kmh": { "label": "Speed (km/h)", "description": "The same speed in kilometres per hour.", "format": "number" }, "mph": { "label": "Speed (mph)", "description": "The same speed in miles per hour.", "format": "number" } }, "defaultAnswer": { "inputs": { "find": "energy", "m": 1000, "v": 25, "ke": 312500 }, "outputs": { "ke": 312500, "kj": 312.5, "ftlbf": 230488.17164914543, "kcal": 74.68929254302103, "kg": 1000, "lb": 2204.622621848776, "mps": 25, "kmh": 90, "mph": 55.92340730136006 }, "text": "A mass of 2,204.62 lb at 55.9234 mph has 312,500 J of kinetic energy." }, "examples": [ { "given": { "find": "energy", "m": 80, "v": 10 }, "expect": { "ke": 4000, "kj": 4 }, "source": "OpenStax, University Physics Volume 1, §7.2 Kinetic Energy, Example 7.6(a): ½ × 80 kg × (10 m/s)² = 4.0 kJ. https://openstax.org/books/university-physics-volume-1/pages/7-2-kinetic-energy" }, { "given": { "find": "energy", "m": 1000, "v": 25 }, "expect": { "ke": 312500, "kj": 312.5, "kmh": 90 }, "source": "OpenStax, University Physics Volume 1, §7.2 Kinetic Energy (K = ½mv²). https://openstax.org/books/university-physics-volume-1/pages/7-2-kinetic-energy; hand calculation in content.mdx: ½ × 1,000 × 25² = 312,500 J" }, { "given": { "find": "energy", "m": 0.145, "v": 40.2336 }, "expect": { "ke": 117.3588362496, "mps": 40.2336 }, "source": "OpenStax, University Physics Volume 1, §7.2 Kinetic Energy (K = ½mv²); NIST Handbook 44 Appendix C (1 mi = 1,609.344 m). https://openstax.org/books/university-physics-volume-1/pages/7-2-kinetic-energy; hand calculation in content.mdx: 90 mph = 40.2336 m/s; ½ × 0.145 × 40.2336² = 117.378 J" }, { "given": { "find": "speed", "ke": 1000, "m": 20 }, "expect": { "mps": 10, "kmh": 36 }, "source": "OpenStax, University Physics Volume 1, §7.2 Kinetic Energy (K = ½mv², so v = √(2K ÷ m)). https://openstax.org/books/university-physics-volume-1/pages/7-2-kinetic-energy; hand calculation in content.mdx: √(2 × 1,000 ÷ 20) = 10 m/s" }, { "given": { "find": "mass", "ke": 450, "v": 3 }, "expect": { "kg": 100, "lb": 220.46226218487757 }, "source": "OpenStax, University Physics Volume 1, §7.2 Kinetic Energy (K = ½mv², so m = 2K ÷ v²). https://openstax.org/books/university-physics-volume-1/pages/7-2-kinetic-energy; hand calculation in content.mdx: 2 × 450 ÷ 3² = 100 kg = 220.462 lb" } ], "sources": [ "OpenStax, University Physics Volume 1, §7.2 Kinetic Energy (K = ½mv², Example 7.6). https://openstax.org/books/university-physics-volume-1/pages/7-2-kinetic-energy (retrieved 2026-10-01)", "NIST Handbook 44 (2026), Appendix C, General Tables of Units of Measurement: 1 lb = 0.45359237 kg; 1 mi = 1,609.344 m; 1 ft = 0.3048 m. https://www.nist.gov/document/2026-nist-handbook-44-appendix-c (retrieved 2026-10-01)", "NIST SP 811 (2008), Appendix B.8, Factors for Units Listed Alphabetically (1 kcal (thermochemical) = 4,184 J; 1 ft·lbf ≈ 1.355818 J, exactly 0.3048 m × 0.45359237 kg × 9.80665 m/s² = 1.3558179483314004 J). https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b8 (retrieved 2026-10-01)" ], "related": [ "power", "speed", "density" ], "changelog": [] }