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1. Convert Online
2. Mathematics
3. Geometry
4. Sector Area

\(r\)

(radius)

units

\(θ\)

(angle of the sector)

degrees

Area

square units

Copy

How to use this Sector Area Calculator 🤔

1. Enter ✎ value for radius \((r)\).
2. Enter ✎ value for angle of the sector \((θ)\).
3. As soon as you enter the required input value(s), the Sector Area is calculated immediately, and displaed in the output section (present under input section).

Sector Area

The area of a sector is defined as the area included between the radii and the arc.

Formula

To calculate the sector area, you can use the following formula.

Area = \( \frac{1}{2} r^2 θ \frac{\pi}{180} \)

where

Calculation

{
  "topic": "sector-area",
  "img": {
    "width": 224,
    "height": 164
  },
  "input_types": [
    "float",
    "float"
  ],
  "input_labels": [
    "r",
    "θ"
  ],
  "input_values": [
    "8",
    "1.5"
  ],
  "input_units": [
    "units",
    "degrees"
  ],
  "input_descriptions": [
    "radius",
    "angle of the sector"
  ],
  "examples": [
    {
      "r": 10,
      "θ": 180
    },
    {
      "r": 2,
      "θ": 45
    }
  ],
  "type": "Calculate",
  "title": "Sector Area",
  "category": "Geometry",
  "shape": "Sector",
  "formula": " (1 / 2) * r * r * θ * ( Math.PI / 180 ) ",
  "formula_mathjax": "\\( \\frac{1}{2} r^2 θ \\frac{\\pi}{180} \\)",
  "formula_mathjax_sub": "\\( \\frac{1}{2} \\times r ^2 \\times θ \\times \\frac{\\pi}{180} \\)",
  "op_label": "Area",
  "output_unit": "square units",
  "description": "The sector area calculator calculates the area of a sector by taking its radius and sector angle as inputs.",
  "explanation": "The area of a sector is defined as the area included between the radii and the arc."
}