🍕 Area of a Sector Calculator
Calculate sector area and arc length using radius and central angle
Quick:
Sector = "Pizza Slice" of a Circle
Sector Area Formulas
📐 Understanding Sector Formulas
Using Degrees
When angle θ is in degrees (0° to 360°). Divide by 360 to get the fraction of the full circle.
Using Radians
When angle θ is in radians (0 to 2π). This is the simpler formula mathematically.
Arc Length Formula
The arc length is the curved edge of the sector. Use s = rθ (radians) or s = (θ/360) × 2πr.
🍕 Real-World Applications
| Application | Example | Why Sectors Matter |
|---|---|---|
| Pizza Slices | 8-slice pizza | Each slice = 45° sector (360÷8) |
| Pie Charts | Data visualization | Percentages shown as sector angles |
| Clock Hands | Time elapsed | Hour hand sweeps 30° per hour |
| Windshield Wipers | Wiper coverage | Area cleaned = sector area |
| Radar Systems | Scanning area | Detection zone = sector of circle |
| Agriculture | Pivot irrigation | Circular fields with sector watering |
📊 Common Sector Angles Reference
| Degrees | Radians | Fraction of Circle | Example |
|---|---|---|---|
| 30° | π/6 | 1/12 | Clock: 1 hour |
| 45° | π/4 | 1/8 | 8-slice pizza |
| 60° | π/3 | 1/6 | 6-slice pizza |
| 90° | π/2 | 1/4 | Quarter circle |
| 120° | 2π/3 | 1/3 | 3-slice pizza |
| 180° | π | 1/2 | Semicircle |
| 270° | 3π/2 | 3/4 | Three-quarter |
| 360° | 2π | 1 | Full circle |
❓ Frequently Asked Questions
Q: What is a sector of a circle?
A sector is a "pie slice" or "pizza slice" shaped portion of a circle, bounded by
two radii and an arc. It's defined by the central angle θ that determines what fraction of the full
circle the sector represents.
Q: What is the formula for area of a sector?
For degrees: A = (θ/360) × πr². For radians: A = ½r²θ. Both formulas calculate the
same result—they just use different angle units.
Q: How do I convert degrees to radians?
Multiply degrees by π/180. For example, 90° × (π/180) = π/2 radians. To convert
radians to degrees, multiply by 180/π.
Q: What is the difference between a sector and a segment?
A sector is bounded by two radii and an arc (like a pizza slice). A segment is
bounded by a chord and an arc (like cutting straight across a circle). Segment area = Sector area −
Triangle area.
Q: How do I calculate arc length of a sector?
Arc length s = rθ (when θ is in radians) or s = (θ/360) × 2πr (when θ is in
degrees). The arc length is proportional to the central angle.