Segment Calculator: Calculate Segment Area & More 

A  Segment Calculator is a handy tool that helps you find the area of a circular segment with speed and accuracy. Whether you’re working on a geometry problem, designing a curved surface in woodworking, or sketching architectural plans, this tool does the math for you. With the hcalculator Segment Calculator, you can also compute arc length, chord length, segment height, and more—using just a few basic inputs like the radius and central angle. 

Segments are portions of a circle bordered by a chord (a straight line) and the corresponding arc. They appear in various real-world designs and technical fields, making it crucial to calculate them precisely. 

🔍 What Is a Segment of a Circle? 

A segment is a part of a circle formed between a chord and its corresponding arc. Unlike a sector (which includes the center), a segment only covers the curved area between two points on the circle’s edge. 

🔁 Minor vs. Major Segment 

  • Minor Segment: The smaller region cut off by a chord. 
  • Major Segment: The larger area on the opposite side of the chord. 

These two together complete the full area of a circle. 

📏 What Is a Chord? 

A chord is a straight line connecting two points on a circle’s circumference. It doesn’t pass through the center unless it’s the diameter. 

How Chords Relate to Segments: 

A chord splits the circle into two parts—a minor segment and a major segment. 

📐 How to Calculate Segment Area With Segment Calculator?

To find the area of a circular segment, follow this basic principle: 

Segment Area = Sector Area − Triangle Area 

The formula changes slightly depending on whether the angle is in degrees or radians. Don’t worry—hcalculator makes this effortless. 

🧮 Segment Calculator – How It Works 

Our Segment Calculator at hcalculator is designed to make these calculations easy. Enter the radius and central angle, and it automatically computes: 

  • Segment Area 
  • Arc Length 
  • Chord Length 
  • Segment Height 

Want to use it as a Chord Length Calculator? Just input your angle and radius, and you’re set. 

✅ Common Uses of a Segment Calculator 

  • Woodturning & Segmented Turning: Perfect for calculating curved cuts and angles.
  • Engineering: Used in curved beam or gear designs. 
  • Architecture: Helps visualize curved structures. 
  • Geometry Class: Great for solving textbook problems. 

📘 Key Segment Formulas 

  1. Segment Area (Angle in Radians)

Area=12r2(θ−sin⁡(θ)) \text{Area} = \frac {1}{2} r^2 (\theta – \sin(\theta)) Area=21​r2(θ−sin(θ)) 

Where: 

  • rrr is the radius 
  • θ\thetaθ is the central angle in radians 

2. Segment Area (Angle in Degrees) 

Convert the angle from degrees to radians first: 

θrad=θdeg×π180\theta_{rad} = \theta_{deg} \times \frac{\pi} {180} θrad​=θdeg​×180π​ 

Then apply the same area formula. 

3. Arc Length 

Arc Length=r⋅θ\text {Arc Length} = r \cdot \thetaArc Length=r⋅θ 

(θ must be in radians) 

4. Chord Length 

Chord Length=2r⋅sin⁡(θ2) \text {Chord Length} = 2r \cdot \sin\left(\frac{\theta} {2} \right) Chord Length=2r⋅sin(2θ​) 

Use this to find the straight-line distance between the segment’s endpoints. 

5. Segment Height 

Height=r(1−cos⁡(θ2)) \text{Height} = r \left (1 – \cos\left(\frac{\theta} {2} \right) \right) Height=r(1−cos(2θ​)) 

Useful for figuring out how “deep” a segment cuts into the circle. 

🧰 Real-Life Example: What If the Radius Is 5 cm? 

Let’s say: 

  • Radius = 5 cm 
  • Central Angle = 60° 

Step-by-Step: 

  1. Convert 60° to radians: 

θ=60×π180=π3\theta = 60 \times \frac{\pi} {180} = \frac{\pi} {3} θ=60×180π​=3π​ 

  1. Apply the formula: 

Area=12⋅52⋅(π3−sin⁡(π3)) \text{Area} = \frac {1}{2} \cdot 5^2 \cdot \left(\frac{\pi} {3} – \sin\left(\frac{\pi} {3} \right) \right) Area=21​⋅52⋅(3π​−sin(3π​)) 

  1. Calculate the result using a calculator or the hcalculator Segment Calculator. 

🎯 Why Use a Segment Calculator? 

If you’re working with any circular structure—be it a pizza slice, a wheel arch, or a piece of turned wood—you need precise segment measurements. Estimating them manually can lead to errors, wasted materials, or structural misalignments. 

The hcalculator Segment Calculator simplifies these calculations with precision and ease, helping you: 

  • Save time 
  • Avoid errors 
  • Get quick answers for arc, height, and area 

FAQs 

What is a segment in geometry? 

A segment is a region between a chord and the corresponding arc of a circle. 

How do I calculate the segment area? 

Subtract the triangle area from the sector area using the appropriate formula. 

What’s the difference between a segment and a sector? 

A sector includes the center and is shaped like a slice. A segment is the curved area between a chord and an arc. 

Can I use a Segment Calculator for woodturning? 

Absolutely! Many woodworkers use it to measure and cut curved segments accurately. 

Final Thoughts 

Understanding how to calculate the area, arc length, height, and chord length of a segment is incredibly useful in both education and real-world design. Whether you’re designing furniture, solving math problems, or working in architecture, our Segment Calculator by hcalculator makes the job easier and more accurate. 

For best results, pair the tool with geometry visuals or diagrams, and always double-check whether your angles are in degrees or radians before inputting.