How to Calculate the Area of a Semi-Circle

The semi-circle is a fundamental geometric shape often encountered in real-world applications like architecture, design, and engineering. Calculating its area is useful for estimating space, materials, and design layout. In this article, you’ll learn how to calculate the area of a semi-circle using a simple formula, visualize its parts with an SVG diagram, go through step-by-step examples, and use our free Area of a Semi-Circle Calculator.

What is a Semi-Circle?

A semi-circle is exactly half of a full circle. If you cut a circle along its diameter, you get two equal semi-circles. It has a curved edge (half the circumference of a full circle) and a straight edge (the diameter).

• The radius (r) is the distance from the center to the edge.
• The diameter (d) is twice the radius: d = 2r.

Formula to Calculate Area of a Semi-Circle

The area of a full circle is given by:

Area of full circle = π × r²

Therefore, the area of a semi-circle is half that:

Area of semi-circle = (1/2) × π × r²

Where:

• r = radius of the semi-circle
• π (pi) ≈ 3.14159

Diagram of a Semi-Circle

The following diagram visually explains a semi-circle and its components:

Step-by-Step Examples

Example 1:

Given: Radius r = 7 cm

Solution:

Area = (1/2) × π × r²  
     = (1/2) × 3.1416 × (7 × 7)  
     = 0.5 × 3.1416 × 49  
     ≈ 76.96 cm²
  

Answer: 76.96 cm²

Example 2:

Given: Radius r = 10 meters

Solution:

Area = (1/2) × π × 10²  
     = 0.5 × 3.1416 × 100  
     = 157.08 m²
  

Answer: 157.08 m²

Using the Area of a Semi-Circle Calculator

Instead of calculating manually, you can use our easy-to-use online tool.

Try the Area of a Semi-Circle Calculator where you simply enter the radius, and it will instantly show the calculated area.

This is especially useful when working with decimal or large numbers, saving time and reducing errors.

Real-World Applications

• Architecture: Designing archways, domes, and window frames
• Construction: Estimating the surface area for paving or flooring
• Gardening: Planning semi-circular lawns or flower beds
• Design & Engineering: Used in machine parts, signage, and road structures

Frequently Asked Questions

Can I use diameter instead of radius?

Yes! Since r = d / 2, substitute this into the formula:

Area = (1/2) × π × (d / 2)²

Is the curved part counted in the area?

Yes, the area includes everything enclosed by the curved edge and the diameter line — it is half the full circle.

What is the unit of area?

The area is always expressed in square units, such as cm², m², in², etc.

Conclusion

To calculate the area of a semi-circle, remember this simple formula:

Area = (1/2) × π × r²

For fast and accurate results, use our free Area of a Semi-Circle Calculator.