Convert Online ⇨ Maths ⇨ Geometry ⇨ Sector Calculator
Sector Calculator
How to use this Sector Calculator 🤔 There are input fields for radius \((r)\) , angle of sector \((θ)\) , Arc Length \((l)\) , Area \((A)\) , and Perimeter \((P)\) . Enter any two inputs and click on Calculate button. The calculator uses the formula, substitues given values, and calcuates the missing value. The missing value is calcuated and displayed in the input field. Also, the caculation is displayed under the input section.
{
"topic": "sector",
"input_types": [
"float",
"float",
"float",
"float",
"float"
],
"input_labels": [
"r",
"θ",
"l",
"A",
"P"
],
"input_descriptions": [
"radius",
"angle of sector",
"Arc Length",
"Area",
"Perimeter"
],
"input_units": [
"units",
"degrees",
"units",
"sq. units",
"units"
],
"input_values": [
"",
"",
"",
"",
""
],
"input_pre_msg": "Enter any two inputs and click on Calculate button",
"type": "Calculate",
"title": "Sector Calculator",
"description": "Use our Sector Calculator to easily calculate radius, angle of sector, length of arc, area, and permimeter of a Sector easily, given only two of these parameters.",
"category": "Geometry",
"shape": "Sector",
"template": "mathematics_multiple_outputs",
"formulas": [
{
"parameters": [
"r",
"θ"
],
"outputs": [
{
"label": "l",
"formula": " r * θ * ( Math.PI / 180 ) ",
"formula_mathjax": "\\( r \\theta \\frac{\\pi}{180} \\)"
},
{
"label": "A",
"formula": " (1 / 2) * r * r * θ * ( Math.PI / 180 ) ",
"formula_mathjax": "\\( \\frac{1}{2} r^2 \\theta \\frac{\\pi}{180} \\)"
},
{
"label": "P",
"formula": " r * θ * ( Math.PI / 180 ) + 2 * r ",
"formula_mathjax": "\\( r \\theta \\frac{\\pi}{180} + 2r \\)"
}
]
},
{
"parameters": [
"r",
"l"
],
"outputs": [
{
"label": "θ",
"formula": " ( l / r ) * ( 180 / Math.PI ) ",
"formula_mathjax": "\\( \\frac{l}{r} \\frac{180}{\\pi} \\)"
},
{
"label": "A",
"formula": " (1 / 2) * r * l ",
"formula_mathjax": "\\( \\frac{1}{2} r l \\)"
},
{
"label": "P",
"formula": " l + 2 * r ",
"formula_mathjax": "\\( l + 2r \\)"
}
]
},
{
"parameters": [
"r",
"A"
],
"outputs": [
{
"label": "θ",
"formula": " ( 2 * A ) / ( r * r ) * ( 180 / Math.PI ) ",
"formula_mathjax": "\\( \\frac{2A}{r^2} \\frac{180}{\\pi} \\)"
},
{
"label": "l",
"formula": " ( 2 * A ) / r ",
"formula_mathjax": "\\( \\frac{2A}{r} \\)"
},
{
"label": "P",
"formula": " r * θ * ( Math.PI / 180 ) + 2 * r ",
"formula_mathjax": "\\( r \\theta \\frac{\\pi}{180} + 2r \\)"
}
]
},
{
"parameters": [
"r",
"P"
],
"outputs": [
{
"label": "θ",
"formula": " ( P - 2 * r ) / r * ( 180 / Math.PI ) ",
"formula_mathjax": "\\( \\frac{P - 2r}{r} \\frac{180}{\\pi} \\)"
},
{
"label": "l",
"formula": " P - 2 * r ",
"formula_mathjax": "\\( P - 2r \\)"
},
{
"label": "A",
"formula": " (1 / 2) * r * l ",
"formula_mathjax": "\\( \\frac{1}{2} r l \\)"
}
]
},
{
"parameters": [
"θ",
"l"
],
"outputs": [
{
"label": "r",
"formula": " l / ( θ * ( Math.PI / 180 ) ) ",
"formula_mathjax": "\\( \\frac{l}{\\theta \\frac{\\pi}{180}} \\)"
},
{
"label": "A",
"formula": " (1 / 2) * ( l / ( θ * ( Math.PI / 180 ) ) ) * l ",
"formula_mathjax": "\\( \\frac{1}{2} \\left( \\frac{l}{\\theta \\frac{\\pi}{180}} \\right) l \\)"
},
{
"label": "P",
"formula": " l + 2 * ( l / ( θ * ( Math.PI / 180 ) ) ) ",
"formula_mathjax": "\\( l + 2 \\left( \\frac{l}{\\theta \\frac{\\pi}{180}} \\right) \\)"
}
]
},
{
"parameters": [
"θ",
"A"
],
"outputs": [
{
"label": "r",
"formula": " Math.sqrt( ( 2 * A ) / ( θ * ( Math.PI / 180 ) ) ) ",
"formula_mathjax": "\\( \\sqrt{ \\frac{2A}{\\theta \\frac{\\pi}{180}} } \\)"
},
{
"label": "l",
"formula": " r * θ * ( Math.PI / 180 ) ",
"formula_mathjax": "\\( r \\theta \\frac{\\pi}{180} \\)"
},
{
"label": "P",
"formula": " r * θ * ( Math.PI / 180 ) + 2 * r ",
"formula_mathjax": "\\( r \\theta \\frac{\\pi}{180} + 2r \\)"
}
]
},
{
"parameters": [
"θ",
"P"
],
"outputs": [
{
"label": "r",
"formula": " P / ( θ * ( Math.PI / 180 ) + 2 ) ",
"formula_mathjax": "\\( \\frac{P}{\\theta \\frac{\\pi}{180} + 2} \\)"
},
{
"label": "l",
"formula": " r * θ * ( Math.PI / 180 ) ",
"formula_mathjax": "\\( r \\theta \\frac{\\pi}{180} \\)"
},
{
"label": "A",
"formula": " (1 / 2) * r * r * θ * ( Math.PI / 180 ) ",
"formula_mathjax": "\\( \\frac{1}{2} r^2 \\theta \\frac{\\pi}{180} \\)"
}
]
},
{
"parameters": [
"l",
"A"
],
"outputs": [
{
"label": "r",
"formula": " ( 2 * A ) / l ",
"formula_mathjax": "\\( \\frac{2A}{l} \\)"
},
{
"label": "θ",
"formula": " l / r * ( 180 / Math.PI ) ",
"formula_mathjax": "\\( \\frac{l}{r} \\frac{180}{\\pi} \\)"
},
{
"label": "P",
"formula": " l + 2 * r ",
"formula_mathjax": "\\( l + 2r \\)"
}
]
},
{
"parameters": [
"l",
"P"
],
"outputs": [
{
"label": "r",
"formula": " ( P - l ) / 2 ",
"formula_mathjax": "\\( \\frac{P - l}{2} \\)"
},
{
"label": "θ",
"formula": " l / r * ( 180 / Math.PI ) ",
"formula_mathjax": "\\( \\frac{l}{r} \\frac{180}{\\pi} \\)"
},
{
"label": "A",
"formula": " (1 / 2) * r * l ",
"formula_mathjax": "\\( \\frac{1}{2} r l \\)"
}
]
},
{
"parameters": [
"A",
"P"
],
"outputs": [
{
"label": "r",
"formula": " ( P + Math.sqrt( P * P - 16 * A ))/4 ",
"formula_mathjax": "\\( ( -P + \\sqrt{P^2 - 16 A})/4 \\)"
},
{
"label": "θ",
"formula": "( 2 * A / ( r * r )) * (180 / Math.PI ) ",
"formula_mathjax": "\\( \\frac{2A}{r^2} \\frac{180}{\\pi} \\)"
},
{
"label": "l",
"formula": " r * θ * ( Math.PI / 180 ) ",
"formula_mathjax": "\\( r \\theta \\frac{\\pi}{180} \\)"
}
]
}
]
} 
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