There are input fields for radius \((r)\), diameter \((d)\), Area \((A)\), and Perimeter \((P)\). Enter any one input 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.
Circle Calculator
Circle is one of the most fundamental shapes in geometry, defined as the set of all points in a plane that are equidistant from a given point, known as the center. The distance from the center to any point on the circle is called the radius. Circles are prevalent in both theoretical mathematics and real-world applications, such as in engineering, architecture, and design.
Understanding the properties of a circle—such as its radius, diameter, area, and perimeter (also known as circumference)—is essential for solving various geometric problems. Because of the symmetry of a circle, knowing just one property allows you to calculate all the others. For instance, if you know the radius, you can easily determine the diameter, area, and perimeter. Similarly, knowing the area or perimeter allows you to calculate the radius and other properties.
Let’s explore the fundamental formulas used to calculate the various properties of a circle:
Radius of a Circle
The radius of a circle is the distance from the center to any point on the circle. It is the most basic property of a circle, and knowing the radius allows you to compute the other properties. If the diameter is known, the radius can be found using the formula:
\(r = \dfrac{d}{2}\)
Where:
r is the radius of the circle.
d is the diameter of the circle.
Diameter of a Circle
The diameter of a circle is the distance across the circle through its center, or twice the radius. It represents the longest distance between any two points on the circle. The formula for the diameter is:
\(d = 2r\)
Where:
d is the diameter of the circle.
r is the radius of the circle.
Area of a Circle
The area of a circle represents the amount of space enclosed within its boundaries. It is calculated using the radius with the formula:
\(A = \pi r^2\)
Where:
A is the area of the circle.
r is the radius of the circle.
π (Pi) is a mathematical constant approximately equal to 3.14159.
Perimeter (Circumference) of a Circle
The perimeter or circumference of a circle is the distance around the circle. It is calculated using the radius with the formula:
\(P = 2\pi r\)
Where:
P is the perimeter or circumference of the circle.
r is the radius of the circle.
π (Pi) is a mathematical constant approximately equal to 3.14159.
In many situations, you might only know one of these properties and need to calculate the others. This is where our Circle Calculator becomes incredibly useful. By inputting any one of the radius, diameter, area, or perimeter, the calculator can quickly determine the remaining properties.
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 Circle Calculator an invaluable tool for anyone dealing with circles, whether in geometry or practical applications.
Below are the formulas used in this calculator for various combinations of inputs:
Formulas
1. Given Radius (r):
Diameter: \(d = 2r\)
Area: \(A = \pi r^2\)
Perimeter: \(P = 2\pi r\)
2. Given Diameter (d):
Radius: \(r = \dfrac{d}{2}\)
Area: \(A = \pi r^2\)
Perimeter: \(P = 2\pi r\)
3. Given Area (A):
Radius: \(r = \sqrt{\dfrac{A}{\pi}}\)
Diameter: \(d = 2r\)
Perimeter: \(P = 2\pi r\)
4. Given Perimeter (P):
Radius: \(r = \dfrac{P}{2\pi}\)
Diameter: \(d = 2r\)
Area: \(A = \pi r^2\)
Simply enter any one known value into the Circle Calculator, and it will automatically compute the remaining properties, providing you with a comprehensive understanding of the circle in question. This tool simplifies complex calculations and is perfect for anyone needing quick and accurate results.
{
"topic": "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": "Circle Calculator",
"description": "Use our Circle Calculator to easily calculate radius, diameter, area, and permimeter of a circle easily, given only one of these parameters.",
"category": "Geometry",
"shape": "Circle",
"template": "mathematics_multiple_outputs",
"formulas": [
{
"parameters": [
"r"
],
"outputs": [
{
"label": "d",
"formula": " 2 * r ",
"formula_mathjax": "\\( 2r \\)"
},
{
"label": "A",
"formula": " Math.PI * r * r ",
"formula_mathjax": "\\( \\pi r^2 \\)"
},
{
"label": "P",
"formula": " 2 * Math.PI * r ",
"formula_mathjax": "\\( 2 \\pi r \\)"
}
]
},
{
"parameters": [
"d"
],
"outputs": [
{
"label": "r",
"formula": " d / 2 ",
"formula_mathjax": "\\( \\frac{d}{2} \\)"
},
{
"label": "A",
"formula": " Math.PI * r * r ",
"formula_mathjax": "\\( \\pi r^2 \\)"
},
{
"label": "P",
"formula": " 2 * Math.PI * r ",
"formula_mathjax": "\\( 2 \\pi r \\)"
}
]
},
{
"parameters": [
"A"
],
"outputs": [
{
"label": "r",
"formula": " Math.sqrt( A / Math.PI ) ",
"formula_mathjax": "\\( \\sqrt{ \\frac{A}{\\pi} } \\)"
},
{
"label": "d",
"formula": " 2 * r ",
"formula_mathjax": "\\( 2 r } \\)"
},
{
"label": "P",
"formula": " 2 * Math.PI * r ",
"formula_mathjax": "\\( 2 \\pi r \\)"
}
]
},
{
"parameters": [
"P"
],
"outputs": [
{
"label": "r",
"formula": " P / ( 2 * Math.PI ) ",
"formula_mathjax": "\\( \\frac{P}{2 \\pi} \\)"
},
{
"label": "d",
"formula": " 2 * r ",
"formula_mathjax": "\\( 2r \\)"
},
{
"label": "A",
"formula": " Math.PI * r * r ",
"formula_mathjax": "\\( \\pi r^2 \\)"
}
]
}
],
"content": "<h2>Circle Calculator</h2>\n<p>Circle is one of the most fundamental shapes in geometry, defined as the set of all points in a plane that are equidistant from a given point, known as the center. The distance from the center to any point on the circle is called the radius. Circles are prevalent in both theoretical mathematics and real-world applications, such as in engineering, architecture, and design.</p>\n\n<p>Understanding the properties of a circle—such as its radius, diameter, area, and perimeter (also known as circumference)—is essential for solving various geometric problems. Because of the symmetry of a circle, knowing just one property allows you to calculate all the others. For instance, if you know the radius, you can easily determine the diameter, area, and perimeter. Similarly, knowing the area or perimeter allows you to calculate the radius and other properties.</p>\n\n<p>Let’s explore the fundamental formulas used to calculate the various properties of a circle:</p>\n\n<h3>Radius of a Circle</h3>\n<p>The radius of a circle is the distance from the center to any point on the circle. It is the most basic property of a circle, and knowing the radius allows you to compute the other properties. If the diameter is known, the radius can be found using the formula:</p>\n<p class=\"tabspace\">\\(r = \\dfrac{d}{2}\\)</p>\n<p>Where:</p>\n<ul><li><b>r</b> is the radius of the circle.</li>\n<li><b>d</b> is the diameter of the circle.</li></ul>\n\n<h3>Diameter of a Circle</h3>\n<p>The diameter of a circle is the distance across the circle through its center, or twice the radius. It represents the longest distance between any two points on the circle. 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 circle.</li>\n<li><b>r</b> is the radius of the circle.</li></ul>\n\n<h3>Area of a Circle</h3>\n<p>The area of a circle represents the amount of space enclosed within its boundaries. It is calculated using the radius with the formula:</p>\n<p class=\"tabspace\">\\(A = \\pi r^2\\)</p>\n<p>Where:</p>\n<ul><li><b>A</b> is the area of the circle.</li>\n<li><b>r</b> is the radius of the circle.</li>\n<li><b>π</b> (Pi) is a mathematical constant approximately equal to 3.14159.</li></ul>\n\n<h3>Perimeter (Circumference) of a Circle</h3>\n<p>The perimeter or circumference of a circle is the distance around the circle. It is calculated using the radius with the formula:</p>\n<p class=\"tabspace\">\\(P = 2\\pi r\\)</p>\n<p>Where:</p>\n<ul><li><b>P</b> is the perimeter or circumference of the circle.</li>\n<li><b>r</b> is the radius of the 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 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 Circle Calculator an invaluable tool for anyone dealing with 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 = \\pi r^2\\)</li>\n<li><b>Perimeter:</b> \\(P = 2\\pi r\\)</li>\n</ul>\n\n<p><b>2. Given Diameter (d):</b></p>\n<ul>\n<li><b>Radius:</b> \\(r = \\dfrac{d}{2}\\)</li>\n<li><b>Area:</b> \\(A = \\pi r^2\\)</li>\n<li><b>Perimeter:</b> \\(P = 2\\pi r\\)</li>\n</ul>\n\n<p><b>3. Given Area (A):</b></p>\n<ul>\n<li><b>Radius:</b> \\(r = \\sqrt{\\dfrac{A}{\\pi}}\\)</li>\n<li><b>Diameter:</b> \\(d = 2r\\)</li>\n<li><b>Perimeter:</b> \\(P = 2\\pi r\\)</li>\n</ul>\n\n<p><b>4. Given Perimeter (P):</b></p>\n<ul>\n<li><b>Radius:</b> \\(r = \\dfrac{P}{2\\pi}\\)</li>\n<li><b>Diameter:</b> \\(d = 2r\\)</li>\n<li><b>Area:</b> \\(A = \\pi r^2\\)</li>\n</ul>\n\n<p>Simply enter any one known value into the Circle Calculator, and it will automatically compute the remaining properties, providing you with a comprehensive understanding of the circle in question. This tool simplifies complex calculations and is perfect for anyone needing quick and accurate results.</p>",
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