{
  "id": "compression-ratio",
  "version": "40dd467aa3ee",
  "status": "published",
  "name": "Compression Ratio Calculator",
  "question": "What is my compression ratio?",
  "summary": "Computes the static compression ratio of a piston engine from the bore, the stroke and the clearance volume, or any one of them from the other three.",
  "category": "physics",
  "subcategory": "mechanics",
  "url": "https://www.acalculator.org/physics/compression-ratio-calculator",
  "markdown": "https://www.acalculator.org/physics/compression-ratio-calculator.md",
  "kind": "formulas",
  "method": "CR = (Vs + Vc) ÷ Vc, with Vs = π ÷ 4 × bore² × stroke (Heywood 1988).",
  "assumptions": [
    "This is the static (geometric) compression ratio. The dynamic ratio, which depends on when the intake valve closes, is lower.",
    "The clearance volume is the whole volume above the piston at top dead center: the combustion chamber, the compressed head gasket, the deck clearance, and the piston dome (subtract) or dish (add).",
    "The cylinder is a round bore of the given diameter. Every cylinder of the engine is the same, so the ratio for one cylinder is the ratio for the engine."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "bore": {
        "title": "Bore",
        "description": "The diameter of the cylinder.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "length",
        "exclusiveMinimum": 0
      },
      "stroke": {
        "title": "Stroke",
        "description": "How far the piston travels from the bottom to the top of its stroke.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "length",
        "exclusiveMinimum": 0
      },
      "vc": {
        "title": "Clearance volume",
        "description": "The volume above the piston at top dead center: combustion chamber, head gasket, deck clearance, and piston dome or dish.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "volume",
        "exclusiveMinimum": 0
      },
      "cr": {
        "title": "Compression ratio",
        "description": "The cylinder volume at bottom dead center divided by the volume at top dead center.",
        "type": "number",
        "exclusiveMinimum": 1,
        "maximum": 1000
      }
    }
  },
  "solve": {
    "fillAny": 3,
    "variables": [
      "bore",
      "stroke",
      "vc",
      "cr"
    ],
    "inputsOnly": []
  },
  "outputs": {
    "bore": {
      "label": "Bore",
      "description": "The diameter of the cylinder.",
      "format": "quantity"
    },
    "stroke": {
      "label": "Stroke",
      "description": "How far the piston travels from the bottom to the top of its stroke.",
      "format": "quantity"
    },
    "clearance": {
      "label": "Clearance volume",
      "description": "The volume above the piston at top dead center: combustion chamber, head gasket, deck clearance, and piston dome or dish.",
      "format": "quantity"
    },
    "cr": {
      "label": "Compression ratio",
      "description": "The cylinder volume at bottom dead center divided by the volume at top dead center.",
      "format": "number"
    },
    "swept": {
      "label": "Swept volume per cylinder",
      "description": "The volume the piston displaces in one stroke: π ÷ 4 × bore² × stroke.",
      "format": "quantity",
      "unit": "cm3"
    },
    "total": {
      "label": "Cylinder volume at bottom dead center",
      "description": "The swept volume plus the clearance volume.",
      "format": "quantity",
      "unit": "cm3"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "bore": 0.086,
      "stroke": 0.086,
      "vc": 0.00005
    },
    "outputs": {
      "cr": 10.991144284358544,
      "swept": 0.0004995572142179272,
      "total": 0.0005495572142179272
    },
    "text": "A 3.386 in bore and 3.386 in stroke with 50 cm³ of clearance volume gives a compression ratio of 10.99:1."
  },
  "examples": [
    {
      "given": {
        "bore": 0.086,
        "stroke": 0.086,
        "vc": 0.00005
      },
      "expect": {
        "swept": 0.0004995572142179272,
        "cr": 10.991144284358544
      },
      "source": "hand calculation in content.mdx: Vs = π ÷ 4 × 8.6² × 8.6 = 499.56 cm³; CR = (499.56 + 50) ÷ 50 = 10.99 (Heywood 1988, chapter 2)"
    },
    {
      "given": {
        "bore": 0.1016,
        "stroke": 0.088392,
        "cr": 10
      },
      "expect": {
        "vc": 0.00007962468887535292
      },
      "source": "hand calculation in content.mdx: Vs = π ÷ 4 × 4² × 3.48 = 43.731 in³ = 716.62 cm³; Vc = Vs ÷ (10 − 1) = 79.62 cm³"
    },
    {
      "given": {
        "stroke": 0.09,
        "vc": 0.00006,
        "cr": 9.5
      },
      "expect": {
        "bore": 0.08494129788761524
      },
      "source": "hand calculation in content.mdx: bore = √(4 × (9.5 − 1) × 60 cm³ ÷ (π × 9 cm)) = √72.15 cm² = 8.494 cm = 84.94 mm"
    }
  ],
  "sources": [
    "Heywood, J. B. Internal Combustion Engine Fundamentals. McGraw-Hill (1988), chapter 2, Engine design and operating parameters: displaced volume V_d = π ÷ 4 × B² × L and compression ratio r_c = (V_d + V_c) ÷ V_c, with typical values 8 to 12 (spark ignition) and 12 to 24 (compression ignition).",
    "NIST Special Publication 811 (2008), Appendix B.8: 1 in = 2.54 cm exactly and 1 in³ = 16.387064 cm³. https://www.nist.gov/pml/special-publication-811"
  ],
  "related": [
    "gear-ratio",
    "density"
  ],
  "changelog": []
}