Sector Area Calc
A Circular Sector is a portion of a circle connecting the center to the edge, like a slice of pizza. It is bounded by two radii and an arc. The Sector Area Calculator determines the size of this slice based on the circle’s radius and the central angle (the “opening” of the slice). It supports angles in both Degrees () and Radians ().
Features
1. Dual Mode Logic: Calculate sector area using either the Central Angle (standard geometry) or the Arc Length (if the angle is unknown).
2. Multi-Unit Angle Support: Accepts angles in Degrees (deg), Radians (rad), and Gradians (grad).
3. Arc & Chord Outputs: In addition to Area, it automatically calculates the Arc Length (curved edge) and Chord Length (straight line connecting the two radii tips).
4. Visualizer: A dynamic SVG draws the exact pie slice, helping you visually confirm if your 45-degree angle looks correct.
5. Formula Display: The tool shows the exact formula used for your specific calculation, making it an excellent learning aid for students.
Uses
- Landscaping: Calculating the area of a curved garden bed or a corner patio.
- Engineering: Designing mechanical cams, gears, or pie-chart visualizations.
- Food Industry: Determining the exact surface area of a single slice of a 16-inch pizza.
- Surveying: Measuring a corner plot of land defined by a curved road boundary.
Tips
- Degrees vs. Radians: Most real-world measurements use Degrees (). Advanced math often uses Radians (). Ensure you select the correct unit!
- Measuring Arc Length: If you can measure the curved outer edge (Arc) and the Radius, you don’t need to measure the angle at all. Use the “By Arc Length” tab.
- Chord Length: This is useful for construction. It tells you the straight-line distance between the two corners of the arc, which is easier to measure with a tape measure than a curved arc.
FAQs
What is the formula for Sector Area?
For Degrees: . For Radians: .
Can I calculate the angle if I know Area and Radius?
Yes, you can rearrange the formula: .
What is the perimeter of a sector?
The total perimeter is the Arc Length plus two Radii (). This calculator provides the Arc Length (L); simply add to get the total perimeter.
Final Words
The Sector Area Calculator turns complex trigonometry into a simple “plug-and-play” tool. Whether you are dividing a pie or designing a circular driveway, it ensures your curves are calculated with straight-line precision.
