A sector of a circle is a portion of a disk enclosed by two radii and an arc. Think of it like a slice of pizza or a piece of pie. The area of this sector can be calculated using its radius and the central angle that defines it.
The Mathematical Formula
The area of a sector is a fraction of the total area of the circle. The fraction is determined by the ratio of the sector's central angle to the total angle in a circle (360 degrees or 2π radians).
The formula for the area of a circle is A = π * r^2, where r is the radius.
To find the area of a sector, we use the following formula:
If the angle is in degrees:
Area of Sector = (θ / 360) * π * r^2
θ is the central angle of the sector in degrees.
r is the radius of the circle.
π (pi) is a mathematical constant, approximately 3.14159.
If the angle is in radians:
Area of Sector = (1/2) * r^2 * θ
θ is the central angle of the sector in radians.
r is the radius of the circle.
Our calculator uses the angle provided in degrees.
When is the Area of a Sector Calculation Useful?
This calculation has practical applications in various fields:
Engineering & Architecture: Calculating the area of curved sections, parts of gears, or designing fan blades.
Design & Art: Creating circular or pie chart segments, designing patterns, or determining the coverage area of circular elements.
Geometry & Education: Understanding circular geometry and practicing mathematical principles.
Resource Management: Estimating coverage areas for sprinklers or distribution patterns.
How to Use the Calculator
Simply enter the radius of the circle and the central angle of the sector in degrees into the fields provided. Click "Calculate Area" to get the result. Ensure your inputs are valid numerical values.
Example Calculation
Let's say you have a circle with a radius of 15 units and you want to find the area of a sector with a central angle of 72 degrees.
Our calculator will perform this computation for you instantly.
function calculateAreaOfSector() {
var radius = document.getElementById("radius").value;
var angleDegrees = document.getElementById("angleDegrees").value;
var resultValueElement = document.getElementById("result-value");
// Clear previous results
resultValueElement.textContent = "–";
// Input validation
if (radius === "" || angleDegrees === "" || isNaN(radius) || isNaN(angleDegrees)) {
resultValueElement.textContent = "Please enter valid numbers.";
return;
}
var r = parseFloat(radius);
var thetaDegrees = parseFloat(angleDegrees);
if (r < 0 || thetaDegrees 360) {
// // You might want to handle angles greater than 360, e.g., modulo 360
// // For simplicity here, we'll allow it as it might represent multiple revolutions
// }
var pi = Math.PI;
// Calculate the area of the sector using the formula for degrees
var sectorArea = (thetaDegrees / 360) * pi * r * r;
// Display the result, formatted to a reasonable number of decimal places
resultValueElement.textContent = sectorArea.toFixed(2) + " square units";
}