Major Segment Area Calculator
Formulas Used:
Minor Segment = ½r²(θ − sinθ)
Circle Area = πr²
Major Segment = Circle Area − Minor Segment
Circles are everywhere in real life. You see them in wheels, pipes, domes, tunnels, logos, and many design patterns. Sometimes, a straight line cuts through a circle and divides it into two parts. These parts are called segments. One part is smaller (minor segment) and the other is larger (major segment).
When you need to find the area of the larger part, doing the math by hand can be confusing. That is where the Major Segment Area Calculator becomes useful. It helps you quickly calculate the area of the major segment using the circle’s radius and the central angle.
What the Major Segment Area Calculator Is
A Circle Geometry Tool
The Major Segment Area Calculator is an online tool that finds the area of the larger region formed when a chord cuts a circle. The chord creates two regions:
- Minor segment – the smaller part
- Major segment – the larger part
This calculator focuses on the major segment only.
Why Major Segment Area Matters
Knowing the major segment area is useful for:
- Architecture and design
- Engineering layouts
- Material cutting and planning
- Geometry homework
- Circular surface estimation
Accurate calculations help avoid mistakes in real projects.
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 two radii that touch the chord. This angle usually represents the minor segment.
Step 3: Get the Major Segment Area
The calculator finds the minor segment area first and then subtracts it from the full circle area to get the major segment area.
Key Formulas Used
Convert Degrees to Radians
Radians = Degrees × (π ÷ 180)
This step is needed for trigonometric calculations.
Total Circle Area
Circle Area = π × radius²
This gives the full area of the circle.
Minor Segment Area
Minor Segment Area = (radius² ÷ 2) × (θ − sin(θ))
Where θ is in radians.
Major Segment Area
Major Segment Area = Circle Area − Minor Segment Area
This gives the area of the larger segment.
Step-by-Step Example
Example: Circle Segment
Given:
- Radius = 10 cm
- Central Angle = 60°
Step 1: Convert degrees to radians
60 × (π ÷ 180) = π ÷ 3 ≈ 1.047
Step 2: Find circle area
π × 10² = 314.16 cm²
Step 3: Find minor segment area
(100 ÷ 2) × (1.047 − sin(1.047))
= 50 × (1.047 − 0.866)
= 50 × 0.181
= 9.05 cm²
Step 4: Find major segment area
314.16 − 9.05 = 305.11 cm²
Result:
The major segment area is 305.11 cm².
Features of the Major Segment Area Calculator
Simple Inputs
Only radius and angle are required.
Fast Results
The answer appears instantly.
Accurate Geometry
Uses standard circle formulas.
Beginner Friendly
Easy to understand for students.
No Manual Math Needed
The calculator does all calculations for you.
Uses and Applications
Architecture and Design
Architects often work with curved walls, domes, and circular cutouts. Knowing the major segment area helps them plan materials and layouts accurately.
Engineering
Engineers use circle segments in mechanical parts, pipes, and structural components. Accurate area values help in strength and load calculations.
Education
Students use the calculator to solve geometry problems involving circles, chords, and angles.
Manufacturing
When cutting circular materials, the major segment area helps estimate leftover material and waste.
Helpful Tips for Accurate Results
Measure Radius Correctly
Always measure from the center to the edge.
Use Correct Angle
The angle should match the minor segment.
Keep Units Consistent
Do not mix cm with m or inches with feet.
Double-Check Inputs
Small errors change the result.
Common Mistakes to Avoid
Confusing Major and Minor Segments
Major is the larger part.
Using Degrees Instead of Radians
Formulas need radians.
Entering Wrong Angle
Angle must match the chord.
Guessing Measurements
Always measure properly.
FAQs
What is a major segment?
It is the larger part of a circle cut by a chord.
What is a minor segment?
It is the smaller part of the circle.
Does the calculator need radians?
It converts automatically.
Can students use it?
Yes, it is beginner friendly.
Is it accurate?
Yes, when correct values are used.
Final Words
The Major Segment Area Calculator is a helpful tool for anyone working with circular shapes. By entering just the radius and central angle, you can quickly find the area of the larger circle segment.
Whether you are studying geometry, designing curved structures, or planning material use, this calculator makes circle segment calculations simple, fast, and reliable.