Summarize this article:
124 LearnersLast updated on September 2, 2025
Area Of Sector 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 will make your life easy. In this topic, we are going to talk about the area of sector calculators.
What is an Area Of Sector Calculator?
An area of sector calculator is a tool to determine the area of a sector in a circle. A sector is a part of a circle bounded by two radii and the arc between them. This calculator makes the calculation much easier and faster, saving time and effort.
How to Use the Area Of Sector 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 angle: Input the central angle of the sector in degrees.
Step 3: Click on calculate: Click on the calculate button to get the area of the sector.
Step 4: View the result: The calculator will display the result instantly.
How to Calculate the Area of a Sector?
To calculate the area of a sector, there is a simple formula that the calculator uses.
The formula is: Area of Sector = (θ/360) × π × r² where θ is the central angle in degrees and r is the radius of the circle.
This formula takes a fraction of the circle's area (πr²) based on the angle θ, which represents the sector's portion of the full circle.
Tips and Tricks for Using the Area Of Sector Calculator
When we use an area of sector calculator, there are a few tips and tricks that we can use to make it a bit easier and avoid silly mistakes:
Ensure the angle is in degrees. If it's in radians, convert it to degrees first.
Double-check your radius input; a mistake here can significantly affect the result.
Remember that a sector's area is always part of the total circle's area.
Common Mistakes and How to Avoid Them When Using the Area Of Sector Calculator
We may think that using a calculator prevents mistakes, but errors can still occur. Here are common mistakes and how to avoid them:
Mistake 1
Entering the wrong angle measurement
Ensure that the angle is entered in degrees, not radians or any other unit. A wrong unit will lead to incorrect calculations.
Mistake 2
Misplacing the radius value
A common error is inputting the wrong radius value. Always double-check that the radius corresponds to the correct circle.
Mistake 3
Forgetting to use the π constant correctly
Ensure that the calculator uses the accurate value of π (around 3.14159) for the calculation to get a precise result.
Mistake 4
Relying solely on the calculator for complex scenarios
While calculators are helpful, they may not consider specific conditions like sectors from concentric circles. Always verify results when dealing with non-standard problems.
Mistake 5
Ignoring the units of measurement
Make sure that all measurements are in the same unit system (e.g., all in centimeters or all in meters) to ensure consistency in the result.
Area Of Sector Calculator Examples
Problem 1
What is the area of a sector with a radius of 10 cm and a central angle of 45 degrees?
Use the formula:
Area of Sector = (θ/360) × π × r²
Area of Sector = (45/360) × π × 10² ≈ 7.85 cm²
So, the area of the sector is approximately 7.85 cm².
Explanation
By substituting the values into the formula, we calculate the area of the sector as approximately 7.85 cm².
Problem 2
Find the area of a sector with a 15-degree angle in a circle with a radius of 20 cm.
Use the formula:
Area of Sector = (θ/360) × π × r²
Area of Sector = (15/360) × π × 20² ≈ 52.36 cm²
Therefore, the area is approximately 52.36 cm².
Explanation
The formula calculates the area by considering the 15-degree angle representing a fraction of the entire circle.
Problem 3
Calculate the area of a sector with a radius of 8 meters and an angle of 90 degrees.
Use the formula:
Area of Sector = (θ/360) × π × r²
Area of Sector = (90/360) × π × 8² ≈ 50.27 m²
Therefore, the area of the sector is approximately 50.27 m².
Explanation
The 90-degree angle is a quarter of the circle, so the area is a quarter of the circle's total area.
Problem 4
Determine the area of a sector in a circle with a radius of 5 inches and a central angle of 120 degrees.
Use the formula:
Area of Sector = (θ/360) × π × r²
Area of Sector = (120/360) × π × 5² ≈ 26.18 in²
Thus, the area of the sector is approximately 26.18 in².
Explanation
The 120-degree central angle covers one-third of the circle, so the area is one-third of the total.
Problem 5
If a sector of a circle has a radius of 12 meters and a central angle of 200 degrees, what is its area?
Use the formula:
Area of Sector = (θ/360) × π × r²
Area of Sector = (200/360) × π × 12² ≈ 251.33 m²
Hence, the area is approximately 251.33 m².
Explanation
The 200-degree angle accounts for more than half the circle, impacting the area proportionately.
FAQs on Using the Area Of Sector Calculator
1.How do you calculate the area of a sector?
2.Is the area of a sector always less than the area of the circle?
3.Why do we use the angle in degrees for the formula?
4.How do I use an area of sector calculator?
5.Is the area of sector calculator accurate?
Glossary of Terms for the Area Of Sector Calculator
- Sector: A portion of a circle bounded by two radii and the arc between them.
- Radius: The distance from the center of a circle to any point on its circumference.
- Central Angle: The angle formed at the center of the circle by two radii.
- π (Pi): A mathematical constant approximately equal to 3.14159, representing the ratio of a circle's circumference to its diameter.
- Degrees: A unit of measurement for angles, with a full circle encompassing 360 degrees.
Explore More calculators
![Important Math Links Icon]()
Previous to Area Of Sector Calculator
![Important Math Links Icon]()
Next to Area Of Sector Calculator
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
