What Is a Semicircle?
A semicircle is exactly half of a circle, formed by cutting a circle along its diameter. It consists of a curved arc (half the circumference) and a straight edge (the diameter). Semicircles are among the most common geometric shapes found in architecture, engineering, and everyday objects.
Semicircle Formulas
Area
Half the area of the full circle.
Perimeter
The arc plus the diameter (straight edge).
Arc Length
Half the full circumference.
How to Calculate Semicircle Area
- Determine the radius. If you have the diameter, divide it by 2.
- Square the radius: r².
- Multiply by π: πr².
- Divide by 2: A = πr²/2.
Finding the Perimeter
The perimeter of a semicircle includes both the curved arc and the straight diameter edge:
- Arc length = πr (half the circumference 2πr)
- Straight edge = 2r (the diameter)
- Total perimeter = πr + 2r = r(π + 2)
Example Calculation
For a semicircle with radius 10:
- Area = π(10)²/2 = 100π/2 = 50π ≈ 157.0796 sq units
- Perimeter = π(10) + 2(10) = 10π + 20 ≈ 51.4159 units
- Arc length = π(10) = 10π ≈ 31.4159 units
Applications of Semicircles
- Architecture: arched doorways, windows, and bridges.
- Engineering: tunnel cross-sections and dome designs.
- Sports: the three-point arc in basketball, half-court lines.
- Design: logos, decorative patterns, and protractor shapes.
Semicircle vs. Half-Disk
In geometry, a semicircle technically refers to the curved arc alone, while the region bounded by the arc and diameter is called a half-disk. However, in common usage, "semicircle" usually refers to the entire half-circle region, including its area. Our calculator computes the area and perimeter of the full half-disk region.