Sector Area Calculator lets you quickly find the area of a circle’s sector using the radius and angle — in degrees or radians.
It’s fast, accurate, and gives results in square inches, feet, centimeters, and meters with a single click.
Sector Area Calculator – angle & radius.
Sector Area Calculator – Find Area Using Angle & Radius (in Degrees or Radians)
The Sector Area Calculator helps you find the exact area of a circle’s sector by entering just two values — the radius and the angle. Whether your angle is measured in degrees or radians, the tool instantly converts and computes precise results using the standard sector area formula:
Area = π × r² × (θ / 360).
This area of a sector calculator is ideal for geometry students, engineers, designers, and land surveyors who need quick circle sector measurements. You can also calculate results in square inches, square feet, centimeters, or meters — all updated instantly with a single click.
Below, you’ll find step-by-step examples, the sector area formula in both degrees and radians, and explanations for arc length and sector perimeter — so you can fully understand how each result is calculated.
Sector Area Formula
The sector area formula is used to calculate the portion of a circle enclosed by two radii and the connecting arc.
Depending on whether the angle is measured in degrees or radians, the formula slightly changes:
- Degrees:
A = π × r² × (θ / 360) - Radians:
A = ½ × r² × θ
Where:
• A = area of the sector
• r = radius of the circle
• θ = central angle (in degrees or radians)
You can also calculate the sector’s area if you know the arc length (L) using:
A = ½ × r × L
💡 Tip: Use π ≈ 3.1416 for decimal results, or keep π exact for symbolic or algebraic calculations.
This sector area formula works perfectly in both degrees and radians, allowing you to calculate areas in terms of π or exact numeric values depending on your need.
Example – Area of a Sector Calculation
Let’s go through simple examples showing how to apply the sector area formula in both degrees and radians. These help visualize how your calculator works and reinforce geometry concepts from class 10 and beyond.
Example 1 – Using Degrees
Find the area of a sector where radius (r) = 6 inches and angle (θ) = 45°.
Formula: A = π × r² × (θ / 360)
Substitute: A = π × 6² × 45 / 360
→ A = 14.14 in²
✅ The area of the sector is 14.14 square inches.
Example 2 – Using Radians
Find the area of a sector where radius (r) = 10 cm and angle (θ) = 1.2 radians.
Formula: A = ½ × r² × θ
Substitute: A = ½ × 10² × 1.2
→ A = 60 cm²
✅ The area of the sector is 60 square centimeters.
🧮 Conversion Tip: You can easily convert between square inches, square feet, and square meters using the dropdown inside the calculator above — all updates happen instantly.
How to Find Arc Length and Perimeter of a Sector
The arc length calculator part of the tool helps determine the curved edge of the sector — known as the arc — which depends on the radius and the central angle. Once you know the arc, you can easily find the perimeter of the sector using a simple addition formula.
Arc Length Formula
- Degrees:
L = (θ / 360) × 2πr - Radians:
L = r × θ
The perimeter of a sector is simply the sum of both radii and the arc length:
Perimeter = 2r + L
Example Calculation
For a sector with radius (r) = 6 cm and angle (θ) = 60°:
Arc length: L = (60 / 360) × 2π × 6 = 6.28 cm
Perimeter: Perimeter = 2 × 6 + 6.28 = 18.28 cm
💡 Tip: The same formulas apply to any unit — inches, centimeters, or meters.
This makes it easy to calculate both arc length and sector perimeter instantly using the tool above.
Sector Area in Real-Life and Geometry
The area of a sector of a circle represents a specific portion of the total circle’s area, defined by two radii and the connecting arc.
In simple terms, it’s like a “slice” of a circular shape — whether that’s part of a pizza, a wheel, or a land plot.
In geometry (Class 10 and above), this formula is taught to help visualize fractions of circular areas.
It’s essential for solving questions about pie charts, circular gardens, mechanical gear designs, and sectors in engineering drawings.
The standard sector area formula remains consistent for all measurement units — whether in cm², m², or ft² — making it universally applicable in both academic and professional use.
💡 Practical Note: For land or property areas with curved boundaries, this Sector Area Calculator provides close approximations — especially when the boundaries resemble circular arcs.
Whether you’re working on a geometry problem, estimating circular land area, or analyzing rotational parts in machinery, this calculator simplifies the math and ensures accuracy across all use cases.
FAQs – Sector Area Explained
1. What is the formula for area of sector in degrees and radians?
In degrees: A = πr²(θ / 360) | In radians: A = ½r²θ.
Both use π (3.1416) to represent the constant ratio of a circle’s circumference to its diameter.
2. How do you find the sector area from arc length?
If you know arc length (L), use A = ½ × r × L. This formula connects the arc’s length directly to its area.
3. What is the difference between sector and segment area?
A sector is the region between two radii and the arc, while a segment is the smaller area between a chord and the arc.
Segment area = sector area – triangle area.
4. How do I find the perimeter of a sector?
The perimeter is the total boundary of the sector: P = 2r + L, where L is the arc length.
5. Can I calculate sector area in square feet or meters?
Yes, the Sector Area Calculator supports units like square inches, feet, centimeters, and meters — simply select your preferred unit.
6. What is π used for in circle area formulas?
π (pi) represents the constant ratio between a circle’s circumference and its diameter. It’s used in all circle and sector area formulas.
7. How to calculate sector area manually?
Multiply π by the square of the radius, then multiply by the angle (in degrees) divided by 360, or by θ directly if using radians.
8. What is the formula for sector area in radians?
The formula is A = ½ × r² × θ, where θ is in radians. This is the most direct and commonly used method in physics and geometry.
9. How to find area of sector without angle?
If you only know arc length (L) and radius (r), use A = ½ × r × L. This lets you calculate the area without needing the central angle.
Related Tools
- 🔹 Circle Area Calculator – for full circles
- 🔹 Ellipse Area Calculator – for ovals
- 🔹 Arc Length Calculator – coming soon
- 🔹 Trapezoid Area Calculator – for slanted shapes