Sector Area Calculator – Guide & Formulas
Calculate the area of a circle sector (pie slice) using radius and central angle. Supports degrees and radians with complete step math.
Calculate the surface area of a circle sector (wedge shape). Ideal for sizing pizza slices, pie chart sections, and mechanical circular sectors.
Key Takeaway
Use the free Sector Area Calculator to calculate the area of a circle sector (pie slice) using radius and central angle. supports degrees and radians with complete step math. Get instant results with step-by-step explanations.
How to Use the Sector Area Calculator
- Enter the radius of the circle.
- Enter the central angle in degrees or radians.
- Observe the calculated sector area alongside the total circle area.
The Formula
Variable Definitions
- A: Area of the circular sector
- r: Radius of the circle
- θ: Central angle of the sector
Area of a Pizza Slice
A 14-inch pizza (7-inch radius) is cut into 8 equal slices. Find the area of one slice (angle = 45 degrees).
- Step 1: Set radius r = 7 inches and angle θ = 45 degrees.
- Step 2: Apply degrees formula: Area = π * 7² * (45 / 360).
- Step 3: Simplify: Area = 49π * (1/8) ≈ 19.24 square inches.
- Step 4: The surface area of one slice is approximately 19.24 square inches.
Frequently Asked Questions
What is a sector of a circle?
A sector is a portion of a circle enclosed by two radii and an arc, resembling a wedge of pie or cheese.
What is a circle segment?
A segment is the area enclosed between an arc and a straight chord. It is calculated by taking the sector area and subtracting the area of the triangle formed by the center and the two endpoints.
How does doubling the radius affect the sector area?
Since radius is squared in the formula, doubling the radius quadruples (4 times) the resulting sector area for any given angle.