Yarım Daire Alanı Hesaplama
Yarıçap veya çap girerek yarım dairenin alanını, yay uzunluğunu, taban dahil toplam çevresini ve ağırlık merkezini hesaplayın.
Half Circle Area Calculator
What Is a Half Circle (Semicircle)? Anatomy & Core Properties
A semicircle is formed by bisecting a circle along its diameter (central angle θ = 180° or π radians). When enclosed by its flat diameter chord, it forms a planar 2D shape with fundamental architectural utility.
Unlike a full circle, a semicircle is not point-symmetric; it has a single vertical axis of reflectional symmetry. Because it features both a curved boundary and a flat baseline, calculating its physical boundaries requires separating curved arc from the flat diameter chord.
Understanding the distinction between curved arc (πr) and total closed perimeter (πr + 2r) is essential for window framing, garden bed curbing, and structural engineering.
Comprehensive Semicircle Geometric Relations
| Dimension | Formula (Radius r) | Formula (Diameter d) | Example (r = 10 cm) |
|---|---|---|---|
| Enclosed Area (A) | A = (πr²) / 2 | A = (πd²) / 8 | 157.08 cm² |
| Curved Arc Length (L) | L = π × r | L = (πd) / 2 | 31.42 cm |
| Straight Base Edge (b) | b = 2 × r | b = d | 20.00 cm |
| Total Closed Perimeter (P) | P = r(π + 2) ≈ 5.1416r | P = d(π/2 + 1) ≈ 2.5708d | 51.42 cm |
| Centroid Height (ȳ) | ȳ = (4r) / (3π) ≈ 0.4244r | ȳ = (2d) / (3π) ≈ 0.2122d | 4.24 cm |
| Base Moment of Inertia (I) | I_x = (πr⁴) / 8 | I_x = (πd⁴) / 128 | 3,926.99 cm⁴ |
4 Ways to Calculate Semicircle Geometry
Depending on whether you measure the center radius, outer diameter, or arch curve length, use the appropriate formula.
Radius Method: A = (πr²) / 2
The canonical textbook equation. Calculate full circle area (πr²) and divide by 2.
Diameter Method: A = (πd²) / 8
Directly use the flat bottom width (diameter d). Square diameter, multiply by π, and divide by 8.
Curved Arc Method: A = (L × r) / 2
Because a circular sector's area is half of arc length times radius, for a semicircle Area = (L × r) / 2.
Centroid & Pappus: V = 2π ȳ A
Revolving a semicircle of area A around its base generates a sphere of volume (4/3)πr³. Confirms ȳ = (4r) / (3π).
Algebraic Proof: Semicircle Area & Perimeter Formulas
Verifying the fundamental semicircle relationships from Euclidean principles:
Semicircle Dimensions Master Reference Table
Standard radius measurements from 1 to 20 units with arc length, perimeter, and area.
| Radius (r) | Diameter (d) | Arc Length (πr) | Perimeter [r(π+2)] | Centroid (ȳ) | Area [(πr²)/2] |
|---|---|---|---|---|---|
| 1 | 2 | 3.1416 | 5.1416 | 0.4244 | 1.5708 |
| 2 | 4 | 6.2832 | 10.2832 | 0.8488 | 6.2832 |
| 4 | 8 | 12.5664 | 20.5664 | 1.6977 | 25.1327 |
| 6 | 12 | 18.8496 | 30.8496 | 2.5465 | 56.5487 |
| 10 | 20 | 31.4159 | 51.4159 | 4.2441 | 157.0796 |
| 15 | 30 | 47.1239 | 77.1239 | 6.3662 | 353.4292 |
4 Detailed Solved Real-World Examples
Realistic architecture, landscaping, woodworking, and sports ramp calculations with exact steps.
Glass Area & Framing for 6-Foot Arched Top
An arched transom window sits atop a doorway with a 6-foot span (diameter):
Semicircular Patio Against a Garden House
A homeowner builds a stone patio extending 4 meters out from a straight backyard wall:
Half-Moon (Demi-Lune) Console Table
A solid oak entryway table has a flat rear edge of 120 cm (diameter):
Semicircular Halfpipe Section (10-Foot Radius)
Calculate cross-sectional airspace and curved riding surface for a ramp:
Common Mistakes to Avoid in Semicircle Calculations
Wrong: Area = (π × d²) / 4. Correct: Area = (π × d²) / 8. (πd²)/4 is the full circle's area; you must divide by 8 for a half circle.
The curved arc is just πr. If buying trim or fencing for a half circle, you must add the diameter baseline 2r: Total = πr + 2r.
The balance center of a flat semicircle is at 0.4244 × r from the straight base (roughly 42.4% of the radius upward).
Total closed perimeter is always 5.1416 × radius or 2.5708 × diameter. A fast shortcut for job site estimates.
Industry Applications of Semicircle Calculations
Architecture & Windows
Designing Roman arched transoms, Palladian windows, and masonry archway lintels.
Civil Bridge Engineering
Calculating waterway clearance area under semicircular stone and concrete barrel arches.
Custom Woodworking
Drafting drop-leaf tables, demi-lune entry consoles, and radial wooden marquetry veneers.
Skate Park Construction
Framing half-pipe vertical ramps, bowls, and transition curves with plywood sheet layouts.
Culvert Hydraulics
Computing half-full wetted perimeter and hydraulic radius (R_h = r / 2) for drainage culverts.
Landscape Hardscaping
Building circular patios against house foundations, fire pit seating rings, and planting retainers.
Yarım Daire Alanı SSS
Daire alanı, yarıçap, çap formülleri ve birim dönüşümleri hakkında merak edilenler
Yarım dairenin alanı nasıl bulunur?
Yarıçap ile: Alan = (π × r²) / 2. Çap ile: Alan = (π × d²) / 8.
Yarım dairenin toplam çevresi nedir?
Kavisli yay uzunluğu (πr) ile düz taban çapının (2r) toplamıdır: Çevre = πr + 2r = r(π + 2).
Özel Daire Hesaplama Araçlarını Keşfedin
Geometrik parametrelerinize özel olarak tasarlanmış hesaplama aracını seçin
Area of Circle Calculator
Find circle area from radius, diameter, or circumference with instant formulas.
Çap ile Daire Alanı Hesaplama
Calculate circle area directly from diameter using A = (πd²)/4.
Çevre ile Daire Alanı Hesaplama
Determine circle area directly from perimeter using A = C²/(4π).
Daire Dilimi ve Parçası Alan Hesaplama
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Halka (İçi Boş Daire) Alanı Hesaplama
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Dairesel Kesit Alanı Hesaplama
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Dairesel Boru Alanı Hesaplama
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İntegral ile Dairenin Alanı
Calculus derivation of circle area with polar, Cartesian, and shell integrals.