{
  "id": "quarter-mile",
  "version": "608899f5dbfd",
  "status": "published",
  "name": "Quarter Mile Calculator",
  "question": "What is my 1/4 mile time?",
  "summary": "Estimates a car’s quarter-mile (1/4 mile) elapsed time and trap speed from its weight and horsepower with Hale’s formulas, or the horsepower from an ET or trap speed.",
  "category": "sports",
  "url": "https://www.acalculator.org/sports/quarter-mile-calculator",
  "markdown": "https://www.acalculator.org/sports/quarter-mile-calculator.md",
  "kind": "function",
  "method": "Hale: ET (s) = 5.825 × (weight in lb ÷ flywheel hp)^(1/3); trap speed (mph) = 234 × (hp ÷ lb)^(1/3); turned around, lb/hp = (ET ÷ 5.825)³ = (234 ÷ mph)³.",
  "assumptions": [
    "The weight is the race weight with driver and fuel, in pounds; the power is peak flywheel (crank) horsepower, not wheel horsepower.",
    "Hale fitted the constants to cars with good traction; a street car on street tires usually runs slower than the estimate.",
    "1 hp = 550 ft·lbf/s = 745.699872 W; 1 lb = 0.45359237 kg; 1 mph = 0.44704 m/s (NIST SP 811)."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "from": {
        "title": "Start from",
        "description": "Estimate the ET and trap speed from the horsepower, or the horsepower from an ET or a trap speed.",
        "type": "string",
        "enum": [
          "power",
          "et",
          "speed"
        ]
      },
      "w": {
        "title": "Race weight",
        "description": "The car’s weight as it sits at the start line, with the driver and fuel.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "mass",
        "minimum": 226.796185,
        "maximum": 9071.8474
      },
      "hp": {
        "title": "Horsepower (at the flywheel)",
        "description": "The engine’s peak power at the flywheel (crank), not at the wheels.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "power",
        "minimum": 7456.998715822702,
        "maximum": 7456998.715822702
      },
      "et": {
        "title": "Quarter-mile ET",
        "description": "The elapsed time over the quarter mile from a time slip.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "time",
        "minimum": 3,
        "maximum": 60
      },
      "mph": {
        "title": "Trap speed",
        "description": "The speed through the timing lights at the end of the quarter mile.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "speed",
        "minimum": 8.9408,
        "maximum": 178.816
      }
    }
  },
  "outputs": {
    "et": {
      "label": "Quarter-mile ET",
      "description": "Hale’s elapsed time: 5.825 × (pounds ÷ horsepower)^(1/3) seconds.",
      "format": "quantity",
      "unit": "s"
    },
    "speed": {
      "label": "Trap speed",
      "description": "Hale’s speed at the end of the quarter mile: 234 × (horsepower ÷ pounds)^(1/3) mph.",
      "format": "quantity",
      "unit": "mph"
    },
    "power": {
      "label": "Horsepower (at the flywheel)",
      "description": "The flywheel horsepower that fits the weight and the ET or trap speed.",
      "format": "quantity",
      "unit": "hp"
    },
    "ratio": {
      "label": "Pounds per horsepower",
      "description": "The race weight in pounds ÷ the flywheel horsepower.",
      "format": "number"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "from": "power",
      "w": 1587.5732950000001,
      "hp": 298279.9486329081,
      "et": 12,
      "mph": 49.1744
    },
    "outputs": {
      "et": 12.003243435692422,
      "speed": 50.76443506828282,
      "power": 298279.9486329081,
      "ratio": 8.75
    },
    "text": "A 3,500 lb car with 400 hp should run the quarter mile in about 12 s at 113.6 mph."
  },
  "examples": [
    {
      "given": {
        "from": "power",
        "w": 1587.5732950000001,
        "hp": 298279.9486329081
      },
      "expect": {
        "et": 12.003243435692422,
        "mph": 50.76443506828282,
        "ratio": 8.75
      },
      "source": "Patrick Hale’s quarter-mile formulas as given by Stealth 316, Formulas for 1/4 mile ET and mph vs. hp and weight (ET = 5.825 (weight/hp)^(1/3), MPH = 234 (hp/weight)^(1/3)), https://www.stealth316.com/2-calc-hp-et-mph.htm, retrieved 2026-10-02; hand calculation in content.mdx: 5.825 × 8.75^(1/3) = 12.00 s, 234 ÷ 8.75^(1/3) = 113.56 mph",
      "tolerance": 1e-12
    },
    {
      "given": {
        "from": "power",
        "w": 1360.77711,
        "hp": 223709.96147468107
      },
      "expect": {
        "et": 12.549582069435724,
        "mph": 48.55443540897121
      },
      "source": "Patrick Hale’s quarter-mile formulas as given by Stealth 316, Formulas for 1/4 mile ET and mph vs. hp and weight (ET = 5.825 (weight/hp)^(1/3), MPH = 234 (hp/weight)^(1/3)), https://www.stealth316.com/2-calc-hp-et-mph.htm, retrieved 2026-10-02; hand calculation in content.mdx: 10 lb/hp gives 5.825 × 10^(1/3) = 12.55 s and 234 ÷ 10^(1/3) = 108.61 mph",
      "tolerance": 1e-12
    },
    {
      "given": {
        "from": "et",
        "w": 1451.495584,
        "et": 12
      },
      "expect": {
        "hp": 272934.28751449246,
        "mph": 50.778156
      },
      "source": "Patrick Hale’s quarter-mile formulas as given by Stealth 316, Formulas for 1/4 mile ET and mph vs. hp and weight (ET = 5.825 (weight/hp)^(1/3), MPH = 234 (hp/weight)^(1/3)), https://www.stealth316.com/2-calc-hp-et-mph.htm, retrieved 2026-10-02; hand calculation in content.mdx: (12 ÷ 5.825)³ = 8.7429 lb/hp, 3,200 ÷ 8.7429 = 366.0 hp; 1,363.05 ÷ 12 = 113.59 mph",
      "tolerance": 1e-12
    },
    {
      "given": {
        "from": "speed",
        "w": 1542.214058,
        "mph": 49.1744
      },
      "expect": {
        "hp": 263374.3450242354,
        "et": 12.391363636363637
      },
      "source": "Patrick Hale’s quarter-mile formulas as given by Stealth 316, Formulas for 1/4 mile ET and mph vs. hp and weight (ET = 5.825 (weight/hp)^(1/3), MPH = 234 (hp/weight)^(1/3)), https://www.stealth316.com/2-calc-hp-et-mph.htm, retrieved 2026-10-02; hand calculation in content.mdx: 3,400 × (110 ÷ 234)³ = 353.2 hp; 1,363.05 ÷ 110 = 12.39 s",
      "tolerance": 1e-12
    }
  ],
  "sources": [
    "Stealth 316, Formulas for 1/4 mile ET and mph vs. hp and weight (Patrick Hale: ET = 5.825 (weight/hp)^(1/3), MPH = 234 (hp/weight)^(1/3); hp is peak engine output at the clutch, weight with driver), retrieved 2026-10-02. https://www.stealth316.com/2-calc-hp-et-mph.htm",
    "NIST Special Publication 811, Guide for the Use of the International System of Units, Appendix B.8 (pound = 0.45359237 kg, horsepower = 550 ft·lbf/s, mile per hour = 0.44704 m/s), retrieved 2026-10-02. https://www.nist.gov/pml/special-publication-811"
  ],
  "related": [
    "horsepower",
    "pace"
  ],
  "changelog": []
}