🌗 Semicircle Area Calculator
Calculate the area of a semicircle
How to Use This Calculator
Choose Input Type
Select whether you know the radius or diameter of the semicircle.
Enter Your Value
Input the radius or diameter. Make sure it's a positive number.
Calculate
Click "Calculate Semicircle Area" to get the area, perimeter, and related measurements.
Formula
Area = (π × r²) / 2
Half of a full circle's area
Alternative Formula (using diameter):
Area = (π × d²) / 8
Since d = 2r, we get d² = 4r², so Area = (π × 4r²) / 8 = (π × r²) / 2
Perimeter Formula:
Perimeter = π × r + d = π × r + 2r = r(π + 2)
Perimeter includes the curved arc (Ï€r) plus the straight diameter (d = 2r)
Where:
- r = radius
- d = diameter = 2r
- π ≈ 3.14159...
Example 1: Find area for r = 5 units
Area = (π × 5²) / 2 = (π × 25) / 2 = 39.27 square units
This is exactly half of a full circle with radius 5 (which has area 78.54)
Example 2: Find area for d = 10 units
Step 1: Radius = 10 / 2 = 5 units
Step 2: Area = (π × 5²) / 2 = 39.27 square units
Example 3: Find perimeter for r = 4 units
Perimeter = π × 4 + 8 = 12.57 + 8 = 20.57 units
Includes the semicircular arc (12.57) and the diameter (8)
About Semicircle Area Calculator
The Semicircle Area Calculator finds the area of a semicircle, which is exactly half of a full circle. A semicircle is formed by cutting a circle in half along its diameter.
When to Use This Calculator
- Architecture: Calculate area for semicircular windows, arches, and doorways
- Construction: Determine material needed for semicircular structures
- Design: Plan semicircular gardens, patios, or decorative elements
- Mathematics: Solve geometry problems involving semicircles
- Real Estate: Calculate usable space in semicircular rooms
- Education: Learn and practice semicircle calculations
Why Use Our Calculator?
- ✅ Multiple Input Options: Works with radius or diameter
- ✅ Comprehensive Output: Shows area, perimeter, and related measurements
- ✅ Instant Results: Calculate immediately
- ✅ Educational: Displays formulas and calculation steps
- ✅ Accurate: Precise mathematical calculations
- ✅ 100% Free: No registration required
Understanding Semicircles
A semicircle is exactly half of a circle. It has one curved edge (arc) and one straight edge (diameter). The area is half of the full circle, and the perimeter includes both the curved arc and the straight diameter.
- Semicircle area is always exactly half of the full circle area
- The diameter is a chord that divides the circle into two equal semicircles
- Perimeter includes both the semicircular arc and the diameter
- All semicircles are similar (same shape, different sizes)
Real-World Applications
Architecture: Calculate the area of semicircular windows, arches, or doorways for construction and material planning.
Landscaping: Determine the area of semicircular garden beds or patios for planting and paving calculations.
Design: Plan semicircular elements in furniture, decorations, or artwork.
Engineering: Calculate areas in semicircular components, tanks, or structures.
Frequently Asked Questions
Is semicircle area exactly half of circle area?
Yes! Since a semicircle is formed by dividing a circle along its diameter, its area is exactly (πr²)/2, which is precisely half of the full circle area πr².
What's the difference between semicircle perimeter and circumference?
Semicircle perimeter includes both the curved arc (Ï€r) and the straight diameter (2r), totaling r(Ï€ + 2). Circumference refers only to the curved part of a full circle (2Ï€r).
Can I use diameter instead of radius?
Yes! If you have diameter (d), use Area = (π × d²) / 8. Or convert: radius = diameter / 2, then use Area = (π × r²) / 2.
What if I need to find radius from area?
Rearrange the formula: Area = (π × r²) / 2, so r² = (2 × Area) / π, therefore r = √[(2 × Area) / π].
How is semicircle different from a segment?
A semicircle is always exactly half a circle. A segment is any part of a circle cut off by a chord, which can be larger or smaller than half. All semicircles are segments, but not all segments are semicircles.
What's the formula for semicircle perimeter?
Perimeter = πr + 2r = r(π + 2). This adds the curved arc length (πr) to the straight diameter (2r).