Sector Area
Calculate the area of a circle sector using radius and central angle in degrees. Get the sector area, arc length, chord length, and a visual pie-slice breakdown.
About This Calculator
This sector area calculator computes the area of a circle sector -- the region enclosed by two radii and their intercepted arc -- given the radius and central angle in degrees. It also provides the arc length, chord length, and a visual chart showing how the sector compares to the full circle.
The formula used is A = (pi x r^2 x theta) / 360, where r is the radius and theta is the central angle in degrees. This formula is derived from the proportion of the sector's angle to the full circle's angle of 360 deg: since the full circle area is pir^2, the sector area is (theta / 360) x pir^2.
How to Use
Enter the radius of the circle and the central angle of the sector in degrees. Click "Calculate Sector Area" to get the sector area, arc length, and chord length instantly. All inputs are saved to the URL for easy sharing and bookmarking.
Applications
Sector area calculations are used in geometry problems, pizza slice sizing, cake portion planning, pie chart creation, circular garden design, and determining material quantities for curved components in construction and manufacturing.
Frequently Asked Questions
How do you calculate the area of a sector of a circle?
The area of a sector is calculated using the formula A = (pi x r^2 x theta) / 360, where r is the radius and theta is the central angle in degrees. For example, a sector with radius 5 units and a 60 deg central angle has an area of (pi x 25 x 60) / 360 ≈ 13.09 square units.
What is the formula for the arc length of a sector?
The arc length of a sector is given by L = (pi x r x theta) / 180, where r is the radius and theta is the central angle in degrees. For a radius of 5 units and a 60 deg angle, the arc length is (pi x 5 x 60) / 180 ≈ 5.24 units.
What is the difference between a sector and a segment of a circle?
A sector is the region enclosed by two radii and the arc between them -- like a pizza slice. A segment is the region enclosed by a chord and its arc, which is the part of the sector excluding the triangle formed by the two radii and the chord.
How do you find the area of a semicircle using the sector area formula?
A semicircle is a sector with a central angle of 180 deg. Plugging theta = 180 deg into the sector area formula gives A = (pi x r^2 x 180) / 360 = (pi x r^2) / 2, which is the standard area formula for a semicircle.
How do you find the area of a quadrant using the sector area formula?
A quadrant is a sector with a central angle of 90 deg. Using the formula A = (pi x r^2 x theta) / 360 with theta = 90 deg gives A = (pi x r^2 x 90) / 360 = (pi x r^2) / 4, which is one-quarter of the circle's area.
What is the chord length of a sector?
The chord length of a sector is the straight-line distance between the two endpoints of the arc. It is calculated as c = 2 x r x sin(theta/2), where r is the radius and theta is the central angle in radians. For a 60 deg angle with a 5-unit radius, the chord length is 2 x 5 x sin(30 deg) = 5 units.
Is this sector area calculator free to use?
Yes, this sector area calculator is completely free to use. No registration or download is required, and you can calculate as many sectors as you like.
Can I use this tool for math homework and real-world applications?
Yes, the sector area calculator is suitable for students learning geometry, teachers preparing lessons, and professionals in fields like engineering, architecture, and design where sector calculations are needed for circular components, pie charts, or curved structures.