Use this calculator to find the radius, diameter, circumference, and area of a circle. Simply input one known value (radius, diameter, circumference, or area) and specify its unit, then click "Calculate".
Radius
Diameter
Circumference
Area
Understanding Circle Formulas
A circle is a fundamental shape in geometry, defined as the set of all points in a plane that are equidistant from a central point. Understanding its properties—radius, diameter, circumference, and area—is crucial in various fields, from engineering and architecture to art and everyday measurements.
Key Definitions:
Radius (r): The distance from the center of the circle to any point on its boundary. It's half the diameter.
Diameter (d): The distance across the circle passing through its center. It's twice the radius.
Circumference (C): The total distance around the circle, essentially its perimeter.
Area (A): The amount of space enclosed within the circle's boundary.
Pi (π): A mathematical constant approximately equal to 3.14159. It represents the ratio of a circle's circumference to its diameter.
The Formulas:
All circle properties are interconnected through simple formulas involving the constant π (Pi).
1. From Radius (r):
Diameter (d):d = 2 * r
Circumference (C):C = 2 * π * r
Area (A):A = π * r²
2. From Diameter (d):
Radius (r):r = d / 2
Circumference (C):C = π * d
Area (A):A = π * (d/2)²
3. From Circumference (C):
Radius (r):r = C / (2 * π)
Diameter (d):d = C / π
Area (A):A = C² / (4 * π)
4. From Area (A):
Radius (r):r = √(A / π)
Diameter (d):d = 2 * √(A / π)
Circumference (C):C = 2 * π * √(A / π)
How to Use the Calculator:
Enter Value: Input the numerical value you know (e.g., 10).
Select Input Type: Choose whether the value you entered is the Radius, Diameter, Circumference, or Area.
Unit: Optionally, enter the unit of measurement (e.g., "cm", "m", "inches"). This will be used in the output.
Calculate: Click the "Calculate" button to see the derived properties of the circle.
Examples:
Example 1: Known Radius
If a circle has a Radius of 5 cm:
Diameter = 2 * 5 = 10 cm
Circumference = 2 * π * 5 ≈ 31.42 cm
Area = π * 5² ≈ 78.54 cm²
Example 2: Known Diameter
If a circle has a Diameter of 20 meters:
Radius = 20 / 2 = 10 meters
Circumference = π * 20 ≈ 62.83 meters
Area = π * (20/2)² = π * 10² ≈ 314.16 m²
Example 3: Known Circumference
If a circle has a Circumference of 100 inches:
Radius = 100 / (2 * π) ≈ 15.92 inches
Diameter = 100 / π ≈ 31.83 inches
Area = 100² / (4 * π) ≈ 795.77 in²
Example 4: Known Area
If a circle has an Area of 50 square feet:
Radius = √(50 / π) ≈ 3.99 feet
Diameter = 2 * √(50 / π) ≈ 7.98 feet
Circumference = 2 * π * √(50 / π) ≈ 25.07 feet
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font-family: 'Arial', sans-serif;
background-color: #f9f9f9;
padding: 20px;
border-radius: 8px;
box-shadow: 0 2px 10px rgba(0, 0, 0, 0.1);
max-width: 700px;
margin: 20px auto;
border: 1px solid #ddd;
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}
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margin-bottom: 5px;
font-weight: bold;
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padding: 10px;
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width: 100%;
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cursor: pointer;
transition: background-color 0.3s ease;
margin-top: 20px;
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button:hover {
background-color: #0056b3;
}
.result-container {
margin-top: 25px;
padding: 15px;
background-color: #e9f7ef;
border: 1px solid #d4edda;
border-radius: 4px;
min-height: 50px;
color: #155724;
}
.result-container p {
margin: 5px 0;
font-size: 17px;
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.calculator-article h3,
.calculator-article h4 {
color: #333;
margin-top: 20px;
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list-style-type: disc;
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function calculateCircleProperties() {
var valueInput = document.getElementById('valueInput').value;
var inputType = document.getElementById('inputType').value;
var unit = document.getElementById('unitInput').value;
var resultOutput = document.getElementById('resultOutput');
var value = parseFloat(valueInput);
if (isNaN(value) || value <= 0) {
resultOutput.innerHTML = 'Please enter a valid positive number for the value.';
return;
}
var radius, diameter, circumference, area;
var PI = Math.PI;
switch (inputType) {
case 'radius':
radius = value;
diameter = 2 * radius;
circumference = 2 * PI * radius;
area = PI * Math.pow(radius, 2);
break;
case 'diameter':
diameter = value;
radius = diameter / 2;
circumference = PI * diameter;
area = PI * Math.pow(radius, 2);
break;
case 'circumference':
circumference = value;
radius = circumference / (2 * PI);
diameter = circumference / PI;
area = PI * Math.pow(radius, 2);
break;
case 'area':
area = value;
radius = Math.sqrt(area / PI);
diameter = 2 * radius;
circumference = 2 * PI * radius;
break;
}
var unitDisplay = unit ? ' ' + unit : '';
var areaUnitDisplay = unit ? ' ' + unit + '²' : '²';
resultOutput.innerHTML =
'Radius: ' + radius.toFixed(4) + unitDisplay + " +
'Diameter: ' + diameter.toFixed(4) + unitDisplay + " +
'Circumference: ' + circumference.toFixed(4) + unitDisplay + " +
'Area: ' + area.toFixed(4) + areaUnitDisplay + ";
}
// Run calculation on page load with default values
window.onload = function() {
calculateCircleProperties();
};