Major Sector Area Calculator
Formulas Used:
Sector Area = (θ / 360) × πr²
Major Sector = Circle Area − Minor Sector
θ (radians) = Arc Length ÷ Radius
Circles are used in many real‑life designs such as wheels, gardens, roads, tunnels, and round buildings. When a circle is divided using two radii, the part between them is called a sector. Some sectors are small, and some are large. The larger part is known as the major sector.
Finding the area of a major sector can be confusing if you try to calculate it manually. That is why the Major Sector Area Calculator is helpful. It allows you to enter the radius and the angle and instantly gives you the area of the larger section of the circle.
What the Major Sector Area Calculator Is
A Circle Geometry Tool
The Major Sector Area Calculator is an online tool that calculates the area of the larger sector of a circle. A sector is formed by two radii and the curved edge between them.
When the angle given represents the smaller (minor) sector, the calculator automatically finds the larger (major) sector by subtracting that angle from 360 degrees.
Why Major Sector Area Matters
Knowing the major sector area is useful for:
- Architecture and layout planning
- Engineering designs
- Circular land or garden planning
- Geometry homework
- Material estimation
Accurate calculations help avoid design mistakes and save resources.
How the Calculator Works
Step 1: Enter the Radius
The radius is the distance from the center of the circle to its edge.
Step 2: Enter the Central Angle
The central angle is the angle between the two radii that form the minor sector.
Step 3: Get the Major Sector Area
The calculator subtracts the minor angle from 360° and then uses the sector formula to find the major sector area.
Key Formulas Used
Total Circle Area
Circle Area = π × radius²
Sector Area Formula
Sector Area = (π × radius² × θ) ÷ 360
Where θ is the angle in degrees.
Major Sector Area Formula
Major Sector Area = (π × radius² × (360 − θ)) ÷ 360
This formula calculates the larger part of the circle.
Step-by-Step Example
Example: Major Sector Calculation
Given:
- Radius = 7 cm
- Minor sector angle = 90°
Step 1: Find the major angle
360 − 90 = 270°
Step 2: Apply the formula
Major Sector Area = (3.1416 × 7² × 270) ÷ 360
Step 3: Solve
7² = 49
3.1416 × 49 = 153.94
153.94 × 270 ÷ 360 ≈ 115.46 cm²
Result:
The major sector area is 115.46 cm².
Features of the Major Sector Area Calculator
Simple Inputs
Only radius and angle are needed.
Fast Results
The area is calculated instantly.
Accurate Geometry
Uses standard circle formulas.
Beginner Friendly
Easy for students and non‑experts.
Works for Any Circle
Supports all radius sizes and angles.
Uses and Applications
Architecture and Construction
Designers use major sector area calculations when planning curved walls, domes, and circular layouts. Accurate area values help in material planning and cost estimation.
Engineering
Engineers calculate sector areas for machine parts, pipes, and circular components that are not complete circles.
Education
Students use the calculator to solve geometry problems involving sectors and angles.
Landscaping and Design
Garden planners use circular sectors to design curved paths and flower beds.
Helpful Tips for Accurate Results
Measure Radius Correctly
Always measure from the center to the edge.
Use the Minor Angle
Enter the angle of the smaller sector.
Keep Units Consistent
Use the same unit for all measurements.
Double‑Check Inputs
Small errors change the result.
Common Mistakes to Avoid
Confusing Major and Minor Sectors
Major is the larger part of the circle.
Using the Wrong Angle
Always enter the minor sector angle.
Mixing Units
Do not mix cm with m or inches with feet.
Forgetting the Formula
The major sector uses (360 − θ).
FAQs
What is a major sector?
It is the larger part of a circle formed by two radii.
What is a minor sector?
It is the smaller part of the circle.
Does the calculator convert the angle?
Yes, it automatically finds the major angle.
Can students use this tool?
Yes, it is beginner friendly.
Is the result accurate?
Yes, when correct values are used.
Final Words
The Major Sector Area Calculator is a simple and powerful tool for finding the area of the larger portion of a circle. By entering just the radius and the minor angle, you can get fast and accurate results.
Whether you are studying geometry, designing curved structures, or planning circular spaces, this calculator makes major sector area calculations easy and reliable.