Semicircle Calculator
Calculate Area, Perimeter, Radius, or Diameter.
A semicircle is simply half of a circle, formed by cutting a circle along its diameter. While it generally looks simple, its geometry appears everywhere—from the classic Roman archways in architecture to the “D” shape of a protractor on a student’s desk. Calculating its area is essential for construction, design, and geometry problems.
The Semicircle Area Calculator is a precision tool that works backward and forward. Whether you have the radius, the diameter, or even just the length of the curved edge (arc), this tool solves the rest.
How to Use This Calculator
Most calculators only accept Radius. Ours is built for the real world, where you might measure different parts. Select your input mode from the dropdown:
1. Radius (r)
The distance from the center point to any edge. This is the most direct way to calculate area ().
2. Diameter (d)
The measurement straight across the flat bottom edge. If you are measuring a window or a tunnel width, this is usually the number you have. The calculator automatically divides it by 2 to find the radius.
3. Circumference / Arc Length (L)
This is the length of the curved part only. If you have a flexible tape measure and measure around the dome of an igloo or arch, use this mode.
4. Total Perimeter (P)
This is the total distance around the entire shape (Curved Arc + Flat Diameter). This is a tricky calculation to do by hand, but our tool solves for radius instantly using .
Key Features
- Visual Verification
The SVG display updates to show you exactly what “r” and “d” represent, helping students and builders visualize the geometry.
- Precision & Units
Toggle between meters, centimeters, feet, or inches. The calculator converts the area unit automatically (e.g., input in feet, get result in sq ft).
Where do we see Semicircles?
Architecture (Windows & Arches)
The “Palladian Window” style features a central semicircular window. Builders need to calculate the area of glass required or the amount of stone for the archway.
Civil Engineering (Tunnels)
Many road and train tunnels utilize a semicircular cross-section (or horseshoe shape) to distribute the weight of the earth above. Calculating the cross-sectional area is the first step in determining airflow and concrete volume.
Interior Design (Rugs & Mats)
Half-round hearth rugs in front of fireplaces or welcome mats are semicircles. Knowing the area ensures they fit the floor space without overcrowding.
Mathematical Formulas
The mathematics of a semicircle are derived directly from the full circle.
Area:
Or using diameter:
Perimeter (Total):
This sums the curved arc () and the flat diameter ().
Arc Length:
Frequently Asked Questions (FAQ)
Q: Is the perimeter just half the circle’s circumference?
A: No! Just taking half the circle (
) gives you the length of the curved arch. To get the *total* perimeter of the closed shape, you must add the straight diameter (
) across the bottom.
Q: How do I find area if I only have the straight width?
A: That straight width is the diameter. Select “Diameter” mode, enter the value, and the calculator will divide it by 2 to get the radius and solve the area equation.
Q: What implies a “Semi” circle?
A: The prefix “Semi-” means half. A semicircle is strictly a 180° slice of a circle. If the slice is smaller or larger (like a pizza slice), it is called a “Sector” or a “Segment,” not a semicircle.
Final Words
Whether you are framing a beautiful arched doorway or just solving a geometry homework problem, the Semicircle Area Calculator eliminates the guesswork. By handling the complex relationship between arc, diameter, perimeter, and area, it ensures you get the right measurement every time.
