Semi Circle Calc
A Semi-Circle is simply half of a circle, formed by cutting a circle along its diameter. The Semi Circle Area Calculator computes the 2D region enclosed by the arc and the diameter. It is a fundamental shape in architecture (arches), manufacturing (sheet metal), and geometry.
Features
1. Universal Calculation: Determine the Area, Diameter, and Perimeter starting from *any* known variable:
- Radius (r)
- Diameter (d)
- Arc Length (Curved edge only)
- Total Perimeter (Curve + Flat base)
2. Arc vs. Perimeter: Clearly distinguishes between the Arc Length (half-circumference) and the Total Perimeter (Arc + Diameter), a common source of confusion in math exams.
3. Visual Feedback: Displays a labeled diagram of the semi-circle with current dimensions.
4. Step-by-Step Formulas: Shows the exact math logic used for the calculation (e.g., ), helping students verify their hand calculations.
Uses
- Construction: Calculating the area of a semi-circular window or an arched doorway for glass or trim ordering.
- Sports: Measuring the "D" zone area on a basketball court or soccer field.
- Fabrication: Determining the square footage of sheet metal needed to stamp out half-moon washers or brackets.
- Education: Solving trigonometry problems involving composite shapes.
Tips
- Perimeter Trap: The perimeter is NOT just the arc (). You must add the straight edge (Diameter) to close the shape. Formula: .
- Centroid: The center of mass of a semi-circle is not half the height (r/2). It is actually located at above the base.
- Diameter vs Radius: Remember that Diameter is always . If you have one, you have the other.
FAQs
What is the formula for the Area?
It is exactly half the area of a full circle: or .
How do I calculate Radius from Area?
To find the radius, multiply the Area by 2, divide by , then take the square root: .
Is the Arc Length the same as Perimeter?
No. Arc Length is just the curved part. Perimeter includes the straight bottom edge as well.
Final Words
From Roman aqueducts to modern protractors, the semi-circle is everywhere. This calculator removes the "half-circle, double-trouble" confusion, providing instant, accurate geometry solutions for architects, students, and DIYers alike.
