Sector Area Calculator
Area = (θ / 360°) × πr²
Or in radians:
Area = (1/2) × r² × θ
Where:
• θ = central angle
• r = radius
Area = (90/360) × π × 8²
= (1/4) × 3.14159 × 64
= 50.27 cm²
This is 1/4 of full circle (90° = quarter)
🔗 Related Calculators
📐 Formula
Area = (θ / 360°) × πr²
Or in radians:
Area = (1/2) × r² × θ
Where:
• θ = central angle
• r = radius
📝 Example Calculation
Area = (90/360) × π × 8²
= (1/4) × 3.14159 × 64
= 50.27 cm²
This is 1/4 of full circle (90° = quarter)
About Sector Area
A sector is a region of a circle bounded by two radii and the arc between them. The area of a sector represents the space enclosed within this region. This calculator helps you find the sector area, arc length, and perimeter when you know the radius and central angle.
Sector Area Formulas
There are two common formulas for calculating sector area:
- A = (1/2) * r^2 * θ (where θ is in radians)
- A = (θdeg/360) * PIr^2 (where θdeg is in degrees)
Where:
- A = sector area
- r = radius of the circle
- θ = central angle in radians
- θdeg = central angle in degrees
Additional Calculations
This calculator also provides:
- Arc Length: s = r * θ (θ in radians)
- Sector Perimeter: P = 2r + s
- Percentage of Circle: (θdeg/360) * 100%
How to Use This Calculator
- Enter the radius of the circle
- Enter the central angle in degrees
- Click "Calculate" to get the sector area
- View detailed results including arc length, perimeter, and percentage of full circle
Understanding Sectors
The sector area is proportional to the central angle. A 180deg sector (semicircle) has half the area of the full circle, while a 90deg sector (quarter circle) has one-fourth the area. The sector's perimeter includes the two straight edges (radii) plus the curved edge (arc).
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. It looks like a slice of pie or pizza. The sector is defined by the central angle between the two radii and the radius of the circle.
What is the formula for sector area?
The sector area formula is A = (1/2) * r^2 * θ, where A is the area, r is the radius, and θ is the central angle in radians. Alternatively, you can use A = (θdeg/360) * PIr^2, where θdeg is the angle in degrees.
How do you find the perimeter of a sector?
The perimeter of a sector consists of two radii plus the arc length. The formula is P = 2r + s, where P is the perimeter, r is the radius, and s is the arc length (s = rθ for θ in radians).
What is the difference between sector area and segment area?
A sector is the region between two radii and an arc, like a pizza slice. A segment is the region between a chord and an arc. The sector includes the triangular portion from the center, while a segment does not.
What are real-world applications of sector area?
Sector area calculations are used in engineering for gear design, in agriculture for irrigation planning (sprinkler coverage), in architecture for designing circular buildings, in surveying for land area measurements, and in statistics for creating pie charts.
How is sector area related to the full circle area?
The sector area is a fraction of the full circle area based on the central angle. If the angle is θ degrees, the sector area is (θ/360) times the full circle area (PIr^2). For a 90deg sector, the area is 1/4 of the circle.