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2. Mathematics
3. Geometry
4. Sector Area

\(r\)

(radius)

units

\(θ\)

(angle of the sector)

degrees

Area

square units

Copy

How to use Sector Area Calculator

1. Enter ✎ value for radius \((r)\).
2. Enter ✎ value for angle of the sector \((θ)\).
3. The result appears beneath the inputs as you enter values.

About this calculation

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."
}