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105 LearnersLast updated on September 11, 2025
Segment Area Calculator
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.
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.
Mistake 1
Using Degrees instead of Radians
Ensure you convert degrees to radians if the calculator requires it.
For example, 180 degrees is π radians.
Mistake 2
Incorrect Radius Entry
Ensure the radius is entered correctly, as an incorrect radius will affect the calculation. Double-check your input.
Mistake 3
Forgetting to Subtract the Triangle Area
The segment area involves subtracting the triangle area from the sector area. Forgetting this step will yield incorrect results.
Mistake 4
Misinterpreting the Formula
Ensure you understand the formula and apply each part correctly. Misinterpretation can lead to errors.
Mistake 5
Assuming All Calculators Use the Same Formula
Not all calculators use the same formula. Ensure the calculator you use aligns with the formula provided here.
Segment Area Calculator Examples
Problem 1
What is the area of a segment of a circle with a radius of 10 and a central angle of 60 degrees?
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.
Problem 2
Calculate the area of a segment with a radius of 8 and a central angle of 120 degrees.
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.
Problem 3
Find the segment area of a circle with a radius of 5 and a central angle of 45 degrees.
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.
Problem 4
Determine the segment area for a circle with a radius of 12 and a central angle of 90 degrees.
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.
Problem 5
A circle has a radius of 7 with a central angle of 30 degrees. Find the segment area.
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.
FAQs on Using the Segment Area Calculator
1.How do you calculate the segment area?
2.What is the segment area of a circle with a central angle of 180 degrees?
3.Why should the angle be in radians?
4.How do I use a segment area calculator?
5.Is the segment area calculator accurate?
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.
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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
