{
  "id": "tire-size",
  "version": "246b960fdc95",
  "status": "published",
  "name": "Tire Size Calculator",
  "question": "How do these tire sizes compare?",
  "summary": "Computes the overall diameter, sidewall height, circumference and revolutions per mile of two metric tire sizes, the difference between them, and how a speedometer reading changes.",
  "category": "everyday-life",
  "url": "https://www.acalculator.org/everyday-life/tire-size-calculator",
  "markdown": "https://www.acalculator.org/everyday-life/tire-size-calculator.md",
  "kind": "function",
  "method": "sidewall = width × aspect ÷ 100; diameter = rim + 2 × sidewall; circumference = π × diameter; revolutions per mile = 1 mile ÷ circumference; true speed = reading × new diameter ÷ current diameter",
  "assumptions": [
    "Sizes are metric tire codes such as 225/45R17: section width in millimetres, aspect ratio in percent, rim diameter in inches.",
    "The diameter is the unloaded design diameter. A tire under load, worn, or at a different pressure is a little smaller.",
    "The speedometer is assumed to read true on the current tires."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "w1": {
        "title": "Current width (mm)",
        "description": "The section width of the current tire, the first number of its size, in millimetres.",
        "type": "number",
        "minimum": 100,
        "maximum": 500
      },
      "a1": {
        "title": "Current aspect ratio (%)",
        "description": "The sidewall height of the current tire as a percent of its width, the second number.",
        "type": "number",
        "minimum": 10,
        "maximum": 100
      },
      "r1": {
        "title": "Current rim (in)",
        "description": "The rim diameter of the current tire in inches, the number after the R.",
        "type": "number",
        "minimum": 8,
        "maximum": 30
      },
      "w2": {
        "title": "New width (mm)",
        "description": "The section width of the new tire, in millimetres.",
        "type": "number",
        "minimum": 100,
        "maximum": 500
      },
      "a2": {
        "title": "New aspect ratio (%)",
        "description": "The sidewall height of the new tire as a percent of its width.",
        "type": "number",
        "minimum": 10,
        "maximum": 100
      },
      "r2": {
        "title": "New rim (in)",
        "description": "The rim diameter of the new tire in inches.",
        "type": "number",
        "minimum": 8,
        "maximum": 30
      },
      "speed": {
        "title": "Speedometer reading",
        "description": "A speed shown on the speedometer, set up for the current tires.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "speed",
        "minimum": 0,
        "maximum": 111.76
      }
    }
  },
  "outputs": {
    "difference": {
      "label": "Diameter difference",
      "description": "How much larger (or smaller, if negative) the new tire’s diameter is, as a percent of the current one.",
      "format": "percent"
    },
    "diameter": {
      "label": "Current diameter",
      "description": "The overall diameter of the current tire: rim + 2 × sidewall.",
      "format": "quantity",
      "unit": "in"
    },
    "newDiameter": {
      "label": "New diameter",
      "description": "The overall diameter of the new tire: rim + 2 × sidewall.",
      "format": "quantity",
      "unit": "in"
    },
    "sidewall": {
      "label": "Current sidewall",
      "description": "The sidewall height of the current tire: width × aspect ratio ÷ 100.",
      "format": "quantity",
      "unit": "in"
    },
    "newSidewall": {
      "label": "New sidewall",
      "description": "The sidewall height of the new tire: width × aspect ratio ÷ 100.",
      "format": "quantity",
      "unit": "in"
    },
    "circumference": {
      "label": "Current circumference",
      "description": "The distance around the current tire: π × diameter.",
      "format": "quantity",
      "unit": "in"
    },
    "newCircumference": {
      "label": "New circumference",
      "description": "The distance around the new tire: π × diameter.",
      "format": "quantity",
      "unit": "in"
    },
    "revs": {
      "label": "Current revolutions per mile",
      "description": "How many times the current tire turns in one mile: 1 mile ÷ circumference.",
      "format": "number"
    },
    "newRevs": {
      "label": "New revolutions per mile",
      "description": "How many times the new tire turns in one mile: 1 mile ÷ circumference.",
      "format": "number"
    },
    "actualSpeed": {
      "label": "Actual speed on the new tires",
      "description": "The true speed when the speedometer shows the reading above: reading × new diameter ÷ current diameter.",
      "format": "quantity",
      "unit": "mph"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "w1": 225,
      "a1": 45,
      "r1": 17,
      "w2": 235,
      "a2": 40,
      "r2": 18,
      "speed": 26.8224
    },
    "outputs": {
      "difference": 1.718429765095375,
      "diameter": 0.6343,
      "newDiameter": 0.6452,
      "sidewall": 0.10125,
      "newSidewall": 0.094,
      "circumference": 1.9927122201720058,
      "newCircumference": 2.0269555800961343,
      "revs": 807.6148596414416,
      "newRevs": 793.971025217865,
      "actualSpeed": 27.283324105312946
    },
    "text": "The new tire’s diameter differs by 1.72%; at a reading of 60 mph you are going 61 mph."
  },
  "examples": [
    {
      "given": {
        "w1": 225,
        "a1": 45,
        "r1": 17,
        "w2": 235,
        "a2": 40,
        "r2": 18,
        "speed": 26.8224
      },
      "expect": {
        "sidewall": 0.10125,
        "diameter": 0.6343,
        "newSidewall": 0.094,
        "newDiameter": 0.6452,
        "difference": 1.7184297650953972,
        "revs": 807.6148596414417,
        "actualSpeed": 27.283324105312946
      },
      "source": "hand calculation in content.mdx: sidewall 225 × 0.45 = 101.25 mm; diameter 431.8 + 202.5 = 634.3 mm (24.97 in); new 457.2 + 188 = 645.2 mm (25.40 in); +1.72%; 60 mph reads 61.03 mph true"
    },
    {
      "given": {
        "w1": 205,
        "a1": 55,
        "r1": 16,
        "w2": 205,
        "a2": 55,
        "r2": 16,
        "speed": 27.77777777777778
      },
      "expect": {
        "difference": 0,
        "diameter": 0.6319,
        "revs": 810.6822368579941,
        "actualSpeed": 27.77777777777778
      },
      "source": "hand calculation in content.mdx: 205 × 0.55 = 112.75 mm; 406.4 + 225.5 = 631.9 mm; 1,609,344 ÷ (π × 631.9) = 810.7 revolutions a mile",
      "tolerance": 1e-12
    }
  ],
  "sources": [
    "Wikipedia, Tire code: the metric size designation (width in mm, aspect ratio in percent, rim in inches) and the overall diameter (2 × W × A ÷ 100) + (R × 25.4) mm. https://en.wikipedia.org/wiki/Tire_code",
    "NIST SP 811 (2008), Appendix B: 1 in = 25.4 mm exactly; 1 mi = 1,609.344 m exactly."
  ],
  "related": [
    "gas"
  ],
  "changelog": []
}