{
  "id": "circle-skirt",
  "version": "7df6a9258423",
  "status": "published",
  "name": "Circle Skirt Calculator",
  "question": "How do I cut a circle skirt?",
  "summary": "Computes the waist radius, the outer radius, the hem circumference and the fabric rectangle for a full, 3/4, half or quarter circle skirt from the waist measurement and the skirt length.",
  "category": "everyday-life",
  "subcategory": "clothing",
  "url": "https://www.acalculator.org/everyday-life/circle-skirt-calculator",
  "markdown": "https://www.acalculator.org/everyday-life/circle-skirt-calculator.md",
  "kind": "function",
  "method": "waist radius r = waist ÷ (2π × f), f = 1, 3/4, 1/2 or 1/4; outer radius R = r + length + allowance; hem = 2π(r + length) × f; fabric rectangle = 2R × 2R (full, 3/4), 2R × R (half), R × R (quarter).",
  "assumptions": [
    "The waist measurement already includes any ease; the waist seam allowance is part of the optional allowance, added to the outer radius only.",
    "The pattern is cut in one piece; a skirt wider than the fabric is cut in more pieces, which needs seam allowance at each seam.",
    "Fabric stretch and bias drop at the hem are not included."
  ],
  "inputs": {
    "$schema": "https://json-schema.org/draft/2020-12/schema",
    "type": "object",
    "properties": {
      "style": {
        "title": "Skirt",
        "description": "How much of a circle the skirt is: full, three quarters, half, or a quarter.",
        "type": "string",
        "enum": [
          "full",
          "three",
          "half",
          "quarter"
        ]
      },
      "waist": {
        "title": "Waist",
        "description": "The waist measurement where the skirt will sit, with any ease you want added.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "length",
        "exclusiveMinimum": 0,
        "maximum": 5
      },
      "length": {
        "title": "Skirt length",
        "description": "The finished length from the waist seam to the hem.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "length",
        "exclusiveMinimum": 0,
        "maximum": 5
      },
      "hem": {
        "title": "Hem and seam allowance (optional)",
        "description": "Extra length added below the finished length for the hem and the waist seam.",
        "type": [
          "number",
          "string"
        ],
        "x-quantity": "length",
        "minimum": 0,
        "maximum": 1
      }
    }
  },
  "outputs": {
    "radius": {
      "label": "Waist radius",
      "description": "The radius of the waist cut-out: waist ÷ (2π × the fraction of a circle).",
      "format": "quantity",
      "unit": "in"
    },
    "outer": {
      "label": "Outer radius",
      "description": "The waist radius plus the skirt length plus the hem and seam allowance.",
      "format": "quantity",
      "unit": "in"
    },
    "hemCircumference": {
      "label": "Hem circumference",
      "description": "The length of the finished hem edge: 2π × (waist radius + skirt length) × the fraction of a circle.",
      "format": "quantity",
      "unit": "in"
    },
    "fabricWidth": {
      "label": "Fabric rectangle, width",
      "description": "The width of the smallest rectangle that holds the pattern in one piece.",
      "format": "quantity",
      "unit": "in"
    },
    "fabricLength": {
      "label": "Fabric rectangle, length",
      "description": "The length of the smallest rectangle that holds the pattern in one piece.",
      "format": "quantity",
      "unit": "in"
    }
  },
  "defaultAnswer": {
    "inputs": {
      "style": "full",
      "waist": 0.7111999999999999,
      "length": 0.5588
    },
    "outputs": {
      "radius": 0.11319099552695595,
      "outer": 0.671990995526956,
      "hemCircumference": 4.222243949651952,
      "fabricWidth": 1.343981991053912,
      "fabricLength": 1.343981991053912
    },
    "text": "Cut a waist radius of 4.456 in and an outer radius of 26.46 in; the pattern needs a 52.91 in by 52.91 in piece of fabric."
  },
  "examples": [
    {
      "given": {
        "style": "full",
        "waist": 0.7111999999999999,
        "length": 0.5588
      },
      "expect": {
        "radius": 0.11319099552695595,
        "outer": 0.671990995526956,
        "hemCircumference": 4.222243949651952,
        "fabricWidth": 1.343981991053912,
        "fabricLength": 1.343981991053912
      },
      "source": "Circumference of a circle C = 2πr (OpenStax Prealgebra 2e, section 9.5, https://openstax.org/books/prealgebra-2e/pages/9-5-solve-geometry-applications-circles-and-irregular-figures, retrieved 2026-10-01); NIST SP 811: 1 in = 0.0254 m; hand calculation in content.mdx: r = 28 ÷ 2π = 4.4563 in",
      "tolerance": 1e-12
    },
    {
      "given": {
        "style": "half",
        "waist": 0.7,
        "length": 0.6,
        "hem": 0.03
      },
      "expect": {
        "radius": 0.22281692032865347,
        "hemCircumference": 2.584955592153876,
        "outer": 0.8528169203286535,
        "fabricWidth": 1.705633840657307,
        "fabricLength": 0.8528169203286535
      },
      "source": "Circumference of a circle C = 2πr (OpenStax Prealgebra 2e, section 9.5, https://openstax.org/books/prealgebra-2e/pages/9-5-solve-geometry-applications-circles-and-irregular-figures); hand calculation in content.mdx: r = 70 ÷ π = 22.28 cm",
      "tolerance": 1e-12
    },
    {
      "given": {
        "style": "quarter",
        "waist": 0.762,
        "length": 0.508
      },
      "expect": {
        "radius": 0.485104266544097,
        "outer": 0.993104266544097,
        "hemCircumference": 1.5599645340118073
      },
      "source": "Circumference of a circle C = 2πr (OpenStax Prealgebra 2e, section 9.5, https://openstax.org/books/prealgebra-2e/pages/9-5-solve-geometry-applications-circles-and-irregular-figures); hand calculation in content.mdx: r = 30 × 2 ÷ π = 19.099 in, hem = 30 + 10π = 61.416 in",
      "tolerance": 1e-12
    }
  ],
  "sources": [
    "OpenStax, Prealgebra 2e, section 9.5, Solve Geometry Applications: Circles and Irregular Figures (C = 2πr), CC BY 4.0, retrieved 2026-10-01. https://openstax.org/books/prealgebra-2e/pages/9-5-solve-geometry-applications-circles-and-irregular-figures",
    "NIST Special Publication 811, Guide for the Use of the International System of Units, Appendix B (1 in = 0.0254 m exactly). https://www.nist.gov/pml/special-publication-811"
  ],
  "related": [
    "area-of-a-circle",
    "circumference",
    "circle"
  ],
  "changelog": []
}