With this sector area calculator, you'll quickly find any circle sector area, e.g., the area of semicircle or quadrant. In this short article we'll:
So let's start with the sector definition - what is a sector in geometry? A sector is a geometric figure bounded by two radii and the included arc of a circle Sectors of a circle are most commonly visualized in pie charts, where a circle is divided into several sectors to show the weightage of each segment. The pictures below show a few examples of circle sectors - it doesn't necessarily mean that they will look like a pie slice, sometimes it looks like the rest of the pie after you've taken a slice: You may, very rarely, hear about the sector of an ellipse, but the formulas are way, way more difficult to use than the circle sector area equations.
The formula for sector area is simple - multiply the central angle by the radius squared, and divide by 2: But where does it come from? You can find it by using proportions, all you need to remember is circle area formula (and we bet you do!):
Sector Area = α × πr² / 2π = α × r² / 2 The same method may be used to find arc length - all you need to remember is the formula for a circle's circumference. 💡 Note that α should be in radians when using the given formula. If you know your sector's central angle in degrees, multiply it first by π/180° to find its equivalent value in radians. Or you can use this formula instead, where θ is the central angle in degrees: Sector Area = r² × θ × π / 360
Finding the area of a semicircle or quadrant should be a piece of cake now, just think about what part of a circle they are!
We know, we know: "why do we need to learn that, we're never ever gonna use it". Well, we'd like to show you that geometry is all around us:
Apart those simple, real-life examples, the sector area formula may be handy in geometry, e.g. for finding surface area of a cone. |