Segment Area Calculator
2026-02-28 11:07 Diff
https://brightchamps.com/en-us/math/calculators/segment-area-calculator

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Last updated on September 11, 2025

Calculators are reliable tools for solving simple mathematical problems and advanced calculations like trigonometry. Whether you're cooking, tracking BMI, or planning a construction project, calculators can make your life easy. In this topic, we are going to talk about the segment area calculator.

What is a Segment Area Calculator?

A segment area calculator is a tool used to determine the area of a segment of a circle. A segment in a circle is the region bounded by a chord and the arc it subtends.

This calculator makes it easier and faster to find the area of the segment, saving time and effort.

How to Use the Segment Area Calculator?

Given below is a step-by-step process on how to use the calculator:

Step 1: Enter the radius: Input the radius of the circle into the given field.

Step 2: Enter the central angle: Input the central angle in degrees.

Step 3: Click on calculate: Click on the calculate button to find the segment area.

Step 4: View the result: The calculator will display the result instantly.

How to Calculate the Segment Area?

To calculate the segment area of a circle, the calculator uses a specific formula.

The formula for the area of a segment is: Segment Area = (r²/2) × (θ - sin(θ))

Where: - r is the radius of the circle. - θ is the central angle in radians.

The formula subtracts the area of the triangular part from the sector area, giving the segment area.

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Tips and Tricks for Using the Segment Area Calculator

When using a segment area calculator, there are a few tips and tricks we can use to make it easier and avoid mistakes: 

Make sure the angle is in radians if required by the calculator. 

Remember that the segment is part of the circle, so the radius must be accurate. 

Use appropriate units and be consistent throughout the calculation.

Common Mistakes and How to Avoid Them When Using the Segment Area Calculator

We may think that when using a calculator, mistakes will not happen. However, it is possible to make mistakes when using a calculator.

Problem 1

What is the area of a segment of a circle with a radius of 10 and a central angle of 60 degrees?

Okay, lets begin

First, convert the angle to radians:

θ = 60 × (π/180) = π/3

Use the formula: Segment Area = (10²/2) × (π/3 - sin(π/3)) = (100/2) × (π/3 - √3/2) = 50 × (π/3 - √3/2) ≈ 15.47 square units

Explanation

By converting the angle to radians and using the formula, the area of the segment is calculated to be approximately 15.47 square units.

Well explained 👍

Problem 2

Calculate the area of a segment with a radius of 8 and a central angle of 120 degrees.

Okay, lets begin

First, convert the angle to radians:

θ = 120 × (π/180) = 2π/3

Use the formula: Segment Area = (8²/2) × (2π/3 - sin(2π/3)) = (64/2) × (2π/3 - √3/2) = 32 × (2π/3 - √3/2) ≈ 36.38 square units

Explanation

After converting the angle to radians and applying the formula, the segment area is approximately 36.38 square units.

Well explained 👍

Problem 3

Find the segment area of a circle with a radius of 5 and a central angle of 45 degrees.

Okay, lets begin

First, convert the angle to radians:

θ = 45 × (π/180) = π/4

Use the formula: Segment Area = (5²/2) × (π/4 - sin(π/4)) = (25/2) × (π/4 - √2/2) = 12.5 × (π/4 - √2/2) ≈ 3.82 square units

Explanation

Converting the angle to radians and using the formula yields a segment area of approximately 3.82 square units.

Well explained 👍

Problem 4

Determine the segment area for a circle with a radius of 12 and a central angle of 90 degrees.

Okay, lets begin

First, convert the angle to radians:

θ = 90 × (π/180) = π/2

Use the formula: Segment Area = (12²/2) × (π/2 - sin(π/2)) = (144/2) × (π/2 - 1) = 72 × (π/2 - 1) ≈ 56.55 square units

Explanation

After converting the angle to radians and applying the formula, the segment area is approximately 56.55 square units.

Well explained 👍

Problem 5

A circle has a radius of 7 with a central angle of 30 degrees. Find the segment area.

Okay, lets begin

First, convert the angle to radians:

θ = 30 × (π/180) = π/6

Use the formula: Segment Area = (7²/2) × (π/6 - sin(π/6)) = (49/2) × (π/6 - 1/2) = 24.5 × (π/6 - 1/2) ≈ 5.08 square units

Explanation

By converting the angle to radians and using the formula, the segment area is approximately 5.08 square units.

Well explained 👍

FAQs on Using the Segment Area Calculator

1.How do you calculate the segment area?

To calculate the segment area, use the formula: Segment Area = (r²/2) × (θ - sin(θ)), where θ is in radians.

2.What is the segment area of a circle with a central angle of 180 degrees?

For a central angle of 180 degrees, the segment is a semicircle, and the area is half the circle's area.

3.Why should the angle be in radians?

The formula for segment area uses radians for mathematical consistency and accuracy in trigonometric calculations.

4.How do I use a segment area calculator?

Input the circle's radius and the central angle, then click calculate. The calculator will show the segment area.

5.Is the segment area calculator accurate?

The calculator provides a precise result based on the formula, but ensure input values are accurate for the best results.

Glossary of Terms for the Segment Area Calculator

  • Segment: A region in a circle bounded by a chord and the arc.
  • Radians: A unit of angle measurement used in the formula for segment area.
  • Chord: A line segment within a circle, with its endpoints on the circle.
  • Central Angle: The angle subtended at the center of the circle by a segment.
  • Sector: The area of a circle bounded by two radii and an arc.

Seyed Ali Fathima S

About the Author

Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.

Fun Fact

: She has songs for each table which helps her to remember the tables