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1. Convert Online⇨
2. Maths⇨
3. Geometry⇨
4. Semi-Circle Calculator

{
  "topic": "semi-circle",
  "input_types": [
    "float",
    "float",
    "float",
    "float"
  ],
  "input_labels": [
    "r",
    "d",
    "A",
    "P"
  ],
  "input_descriptions": [
    "radius",
    "diameter",
    "Area",
    "Perimeter"
  ],
  "input_units": [
    "units",
    "units",
    "sq. units",
    "units"
  ],
  "input_values": [
    "",
    "",
    "",
    ""
  ],
  "input_pre_msg": "Enter any one input and click on Calculate button",
  "type": "Calculate",
  "title": "Semi-Circle Calculator",
  "description": "Use our Semi-Circle Calculator to easily calculate radius, diameter, area, and permimeter of a Semi-Circle easily, given only one of these parameters.",
  "category": "Geometry",
  "shape": "Semi-Circle",
  "template": "mathematics_multiple_outputs",
  "formulas": [
    {
      "parameters": [
        "r"
      ],
      "outputs": [
        {
          "label": "d",
          "formula": " 2 * r ",
          "formula_mathjax": "\\( 2r \\)"
        },
        {
          "label": "A",
          "formula": " ( Math.PI * r * r ) / 2 ",
          "formula_mathjax": "\\( \\frac{\\pi r^2}{2} \\)"
        },
        {
          "label": "P",
          "formula": " Math.PI * r + 2 * r ",
          "formula_mathjax": "\\( \\pi r + 2r \\)"
        }
      ]
    },
    {
      "parameters": [
        "d"
      ],
      "outputs": [
        {
          "label": "r",
          "formula": " d / 2 ",
          "formula_mathjax": "\\( \\frac{d}{2} \\)"
        },
        {
          "label": "A",
          "formula": " ( Math.PI * r * r ) / 2 ",
          "formula_mathjax": "\\( \\frac{\\pi r^2}{2} \\)"
        },
        {
          "label": "P",
          "formula": " Math.PI * r + 2 * r ",
          "formula_mathjax": "\\( \\pi r + 2r \\)"
        }
      ]
    },
    {
      "parameters": [
        "A"
      ],
      "outputs": [
        {
          "label": "r",
          "formula": " Math.sqrt( ( 2 * A ) / Math.PI ) ",
          "formula_mathjax": "\\( \\sqrt{ \\frac{2A}{\\pi} } \\)"
        },
        {
          "label": "d",
          "formula": " 2 * r ",
          "formula_mathjax": "\\( 2r \\)"
        },
        {
          "label": "P",
          "formula": " Math.PI * r + 2 * r ",
          "formula_mathjax": "\\( \\pi r + 2r \\)"
        }
      ]
    },
    {
      "parameters": [
        "P"
      ],
      "outputs": [
        {
          "label": "r",
          "formula": " P / ( Math.PI + 2 ) ",
          "formula_mathjax": "\\( \\frac{P}{\\pi + 2} \\)"
        },
        {
          "label": "d",
          "formula": " 2 * r ",
          "formula_mathjax": "\\( 2r \\)"
        },
        {
          "label": "A",
          "formula": " ( Math.PI * r * r ) / 2 ",
          "formula_mathjax": "\\( \\frac{\\pi r^2}{2} \\)"
        }
      ]
    }
  ],
  "content": "<h2>Semi-Circle Calculator</h2>\n<p>A semi-circle is half of a circle, created by cutting a whole circle along its diameter. It shares many of the properties of a circle, such as radius, diameter, area, and perimeter, but each of these properties is adjusted to reflect the fact that the semi-circle represents only half of the circle. Understanding the properties of a semi-circle is essential in various fields such as geometry, engineering, and design, where semi-circular shapes are common.</p>\n\n<p>The semi-circle's properties are directly related to those of a full circle. For example, if you know the radius of a semi-circle, you can easily calculate the diameter, area, and perimeter. Similarly, knowing the area or perimeter allows you to determine the radius and other properties. This makes the semi-circle a versatile and fundamental shape in geometric calculations.</p>\n\n<p>Let’s explore the key formulas used to calculate the various properties of a semi-circle:</p>\n\n<h3>Radius of a Semi-Circle</h3>\n<p>The radius of a semi-circle is the distance from the center to any point on the curved edge. It is the same as the radius of the full circle from which the semi-circle is derived. If the diameter is known, the radius can be found using the formula:</p>\n<p class=\"tabspace\">\\(r = \\frac{d}{2}\\)</p>\n<p>Where:</p>\n<ul><li><b>r</b> is the radius of the semi-circle.</li>\n<li><b>d</b> is the diameter of the semi-circle.</li></ul>\n\n<h3>Diameter of a Semi-Circle</h3>\n<p>The diameter of a semi-circle is the distance across the semi-circle through its center, which is also the straight-line distance between the endpoints of the curved edge. The formula for the diameter is:</p>\n<p class=\"tabspace\">\\(d = 2r\\)</p>\n<p>Where:</p>\n<ul><li><b>d</b> is the diameter of the semi-circle.</li>\n<li><b>r</b> is the radius of the semi-circle.</li></ul>\n\n<h3>Area of a Semi-Circle</h3>\n<p>The area of a semi-circle represents the amount of space enclosed within its curved boundary. Since a semi-circle is half of a circle, the area is half of the area of a full circle. The formula for the area is:</p>\n<p class=\"tabspace\">\\(A = \\frac{\\pi r^2}{2}\\)</p>\n<p>Where:</p>\n<ul><li><b>A</b> is the area of the semi-circle.</li>\n<li><b>r</b> is the radius of the semi-circle.</li>\n<li><b>π</b> (Pi) is a mathematical constant approximately equal to 3.14159.</li></ul>\n\n<h3>Perimeter of a Semi-Circle</h3>\n<p>The perimeter of a semi-circle includes both the curved edge (half the circumference of the full circle) and the straight edge (the diameter). The formula for the perimeter is:</p>\n<p class=\"tabspace\">\\(P = \\pi r + 2r\\)</p>\n<p>Where:</p>\n<ul><li><b>P</b> is the perimeter of the semi-circle.</li>\n<li><b>r</b> is the radius of the semi-circle.</li>\n<li><b>π</b> (Pi) is a mathematical constant approximately equal to 3.14159.</li></ul>\n\n<p>In many situations, you might only know one of these properties and need to calculate the others. This is where our Semi-Circle Calculator becomes incredibly useful. By inputting any one of the radius, diameter, area, or perimeter, the calculator can quickly determine the remaining properties.</p>\n\n<p>For example, if you know the area, the calculator can find the radius, diameter, and perimeter. Similarly, if you know the perimeter, it can determine the radius, diameter, and area. This versatility makes the Semi-Circle Calculator an invaluable tool for anyone dealing with semi-circles, whether in geometry or practical applications.</p>\n\n<p>Below are the formulas used in this calculator for various combinations of inputs:</p>\n\n<h3>Formulas</h3>\n<p><b>1. Given Radius (r):</b></p>\n<ul>\n<li><b>Diameter:</b> \\(d = 2r\\)</li>\n<li><b>Area:</b> \\(A = \\frac{\\pi r^2}{2}\\)</li>\n<li><b>Perimeter:</b> \\(P = \\pi r + 2r\\)</li>\n</ul>\n\n<p><b>2. Given Diameter (d):</b></p>\n<ul>\n<li><b>Radius:</b> \\(r = \\frac{d}{2}\\)</li>\n<li><b>Area:</b> \\(A = \\frac{\\pi r^2}{2}\\)</li>\n<li><b>Perimeter:</b> \\(P = \\pi r + 2r\\)</li>\n</ul>\n\n<p><b>3. Given Area (A):</b></p>\n<ul>\n<li><b>Radius:</b> \\(r = \\sqrt{\\frac{2A}{\\pi}}\\)</li>\n<li><b>Diameter:</b> \\(d = 2r\\)</li>\n<li><b>Perimeter:</b> \\(P = \\pi r + 2r\\)</li>\n</ul>\n\n<p><b>4. Given Perimeter (P):</b></p>\n<ul>\n<li><b>Radius:</b> \\(r = \\frac{P}{\\pi + 2}\\)</li>\n<li><b>Diameter:</b> \\(d = 2r\\)</li>\n<li><b>Area:</b> \\(A = \\frac{\\pi r^2}{2}\\)</li>\n</ul>\n\n<p>Simply enter any one known value into the Semi-Circle Calculator, and it will automatically compute the remaining properties, providing you with a comprehensive understanding of the semi-circle in question. This tool simplifies complex calculations and is perfect for anyone needing quick and accurate results.</p>"
}