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Area of A Sector Calculator

Please provide any two values, and the calculator will calculate the sector area, central angle, radius, diameter, arc length, and chord length of any circle sector.

Select Input Combination:

Central Angle (θ)

deg ▾

Radius (r)

cm ▾

Arc Length (L)

cm ▾

Sector Area (A)

cm² ▾

Chord Length (c)

cm ▾

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Sector Area Calculator

The Sector Area Calculator is an online tool designed to calculate the area of a circle’s sector, arc length, and chord length instantly. Whether you are a student learning geometry or a professional solving practical problems, this calculator helps you get quick and accurate results without complex manual calculations.

What Is a Sector of a Circle?

In geometry, a sector is the portion of a circle enclosed by two radii and the arc between them. It looks like a “slice” of a pizza.

sector of a circle

Arc: The curved boundary of the sector.
Radii: Two straight lines drawn from the center of the circle to the arc.
Central Angle (θ): The angle formed between the two radii.
Chord: A straight line connecting the two endpoints of the arc.

Important Formulas

1. Area of a Sector (Angle in Radians)

Area = (1/2) × r² × θ

2. Area of a Sector (Angle in Degrees)

Area = (θ / 360) × π × r²

Where:

r = radius of the circle
θ = central angle
π ≈ 3.1416

3. Arc Length Formula

Arc Length = r × θ (when θ is in radians)

4. Chord Length Formula

Chord Length = 2 × r × sin(θ / 2)

How To Find the Area of a Sector?

Example 1: Finding Sector Area

Given:

Radius (r) = 3 cm
Angle (θ) = 45°

Step 1: Convert Degrees to Radians

θ (radians) = (θ × π) / 180

θ = (45 × 3.1416) / 180

θ = 0.785 radians

Step 2: Apply Sector Area Formula

Area = (1/2) × r² × θ

Area = (1/2) × 3² × 0.785

Area = (1/2) × 9 × 0.785

Area = 3.53 cm²

Example 2: Finding Arc Length

Given:

Radius (r) = 4 cm
Angle (θ) = 90°

Step 1: Convert to Radians

θ = (90 × 3.1416) / 180

θ = 1.57 radians

Step 2: Apply Arc Length Formula

Arc Length = r × θ

Arc Length = 4 × 1.57

Arc Length = 6.28 cm

Why Use a Sector Area Calculator?

Provides instant and accurate results
Eliminates manual calculation errors
Supports both degrees and radians
Calculates area, arc length, and chord length together

If calculations seem complicated, simply enter the radius and angle into the calculator and get precise results within seconds.

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