Sector Area Calculator
How to use this Sector Area Calculator 🤔
- Enter ✎ value for radius (r).
- Enter ✎ value for angle of the sector (θ).
- 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).
Calculation
Once you enter the input values in the calculator, the output parameters are calculated.
Examples
The following examples cover how to calcualte the Area when radius, and angle of the sector are given.
1. What is the Area of Sector whose radius is 10 units, and angle of the sector is 180 degrees?
Answer
Given:
- radius, r = 10 units
- angle of the sector, θ = 180 degrees
The formula to find the Area of a Sector is:
A = \( \frac{1}{2} r^2 θ \frac{\pi}{180} \)
Substitute given values in the above formula.
A = \( \frac{1}{2} \times10^2 \times180\times \frac{\pi}{180} \)
A = 157.08 square units
∴ Area, A = 157.08 square units
2. What is the Area of Sector whose radius is 2 units, and angle of the sector is 45 degrees?
Answer
Given:
- radius, r = 2 units
- angle of the sector, θ = 45 degrees
The formula to find the Area of a Sector is:
A = \( \frac{1}{2} r^2 θ \frac{\pi}{180} \)
Substitute given values in the above formula.
A = \( \frac{1}{2} \times2^2 \times45\times \frac{\pi}{180} \)
A = 1.57 square units
∴ Area, A = 1.57 square units
{
"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.",
"examples_data": "<h2>Examples</h2><p>The following examples cover how to calcualte the Area when radius, and angle of the sector are given.</p><div class=\"example\"><h3 class=\"question\"><span class=\"example_n\">1.</span> What is the Area of Sector whose radius is 10 units, and angle of the sector is 180 degrees?</h3><h4 class=\"answer\">Answer</h4><p>Given:</p><ul><li>radius, r = 10 units<li>angle of the sector, θ = 180 degrees</ul><p>The formula to find the Area of a Sector is:</p><p class=\"tabspace\">A = \\( \\frac{1}{2} r^2 θ \\frac{\\pi}{180} \\)</p><p>Substitute given values in the above formula.</p><p class=\"tabspace\">A = \\( \\frac{1}{2} \\times10^2 \\times180\\times \\frac{\\pi}{180} \\)</p><p class=\"tabspace\">A = 157.08 square units</p><p class=\"tabspace answer\">∴ Area, A = 157.08 square units</p></div><div class=\"example\"><h3 class=\"question\"><span class=\"example_n\">2.</span> What is the Area of Sector whose radius is 2 units, and angle of the sector is 45 degrees?</h3><h4 class=\"answer\">Answer</h4><p>Given:</p><ul><li>radius, r = 2 units<li>angle of the sector, θ = 45 degrees</ul><p>The formula to find the Area of a Sector is:</p><p class=\"tabspace\">A = \\( \\frac{1}{2} r^2 θ \\frac{\\pi}{180} \\)</p><p>Substitute given values in the above formula.</p><p class=\"tabspace\">A = \\( \\frac{1}{2} \\times2^2 \\times45\\times \\frac{\\pi}{180} \\)</p><p class=\"tabspace\">A = 1.57 square units</p><p class=\"tabspace answer\">∴ Area, A = 1.57 square units</p></div>",
"schema_data": "\n <script type=\"application/ld+json\">\n {\n \"@context\": \"https://schema.org\",\n \"@type\": \"Article\",\n \"author\": {\n \"@type\": \"Person\",\n \"name\": \"Mallikarjuna M\",\n \"honorificSuffix\": \"B.Tech. (Electronics & Communication)\",\n \"url\": \"https://www.linkedin.com/in/mallikarjuna-mallisetty-7330314a/\"\n },\n \"image\": [\"https://convertonline.org/images/calculators/sector-area.png\"],\n \"dateModified\": \"2024-09-05T00:23:14.014Z\",\n \"datePublished\": \"2024-07-21T07:20:32.526Z\",\n \"description\": \"The sector area calculator calculates the area of a sector by taking its radius and sector angle as inputs.\",\n \"headline\": \"Sector Area Calculator\",\n \"mainEntityOfPage\": {\n \"@id\": \"https://convertonline.org\",\n \"@type\": \"WebPage\"\n },\n \"publisher\": {\n \"@type\": \"Organization\",\n \"name\": \"ConvertOnline.org\",\n \"logo\": {\n \"@type\": \"ImageObject\",\n \"url\": \"https://convertonline.org/images/icon.png\",\n \"width\": \"512px\",\n \"height\": \"512px\"\n }\n }\n }\n </script>\n "
}
ConvertOnline