Half of the interior of a circle having a straight chord and an arc.- Center of a circle having all points on the line circumference are at equal distance from the center point.
- A half circle is a structural shape used in construction.
- See Article - Geometric Properties of Structural Shapes
Arc Length of a Half Circle formula |
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| \( l \;=\; \dfrac{ 2 \cdot \pi \cdot r }{ 2 } \) | ||
| Symbol | English | Metric |
| \(\large{ l }\) = length | \( in \) | \( mm \) |
| \(\large{ \pi }\) = Pi | \(3.141 592 653 ...\) | \(3.141 592 653 ...\) |
| \(\large{ r }\) = radius | \( in \) | \( mm \) |
Area of a Half Circle formula |
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| \( A_{area} \;=\; \dfrac{ \pi \cdot r^2 }{ 2 }\) | ||
| Symbol | English | Metric |
| \(\large{ A }\) = area | \( in^2 \) | \( mm^2 \) |
| \(\large{ \pi }\) = Pi | \(3.141 592 653 ...\) | \(3.141 592 653 ...\) |
| \(\large{ r }\) = radius | \( in \) | \( mm \) |
Perimeter of a Half Circle formula |
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| \( P \;=\; \dfrac{ 2 \cdot \pi \cdot r}{ 2 } + (2 \cdot r) \) | ||
| Symbol | English | Metric |
| \(\large{ P }\) = perimeter | \( in \) | \( mm \) |
| \(\large{ \pi }\) = Pi | \(3.141 592 653 ...\) | \(3.141 592 653 ...\) |
| \(\large{ r }\) = radius | \( in \) | \( mm \) |
Radius of a Half Circle formula |
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| \( r \;=\; \sqrt{ \dfrac{ 2 \cdot A_{area} }{ \pi } } \) | ||
| Symbol | English | Metric |
| \(\large{ A }\) = area | \( in^2 \) | \( mm^2 \) |
| \(\large{ \pi }\) = Pi | \(3.141 592 653 ...\) | \(3.141 592 653 ...\) |
| \(\large{ r }\) = radius | \( in \) | \( mm \) |
Distance from Centroid of a Half Circle formulas |
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\( C_x \;=\; 0 \) \( C_y \;=\; \dfrac{ 4 \cdot r }{ 3 \cdot \pi } \) |
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| Symbol | English | Metric |
| \(\large{ C_x, C_y }\) = distance from centroid | \( in \) | \( mm \) |
| \(\large{ \pi }\) = Pi | \(3.141 592 653 ...\) | \(3.141 592 653 ...\) |
| \(\large{ r }\) = radius | \( in \) | \( mm \) |
Elastic Section Modulus of a Half Circle formula |
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| \( S \;=\; \dfrac{ I_x }{ C_y }\) | ||
| Symbol | English | Metric |
| \(\large{ S }\) = elastic section modulus | \( in^3 \) | \( mm^3 \) |
| \(\large{ C_x, C_y }\) = distance from centroid | \( in \) | \( mm \) |
Polar Moment of Inertia of a Circle formulas |
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\( J_{z} \;=\; \left( \dfrac{ \pi}{ 4 } - \dfrac{ 8 }{ 9 \cdot \pi } \right) \cdot r^4 \) \( J_{z1} \;=\; \dfrac{ \pi \cdot r^4 }{ 4 } \) |
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| Symbol | English | Metric |
| \(\large{ J }\) = torsional constant | \( in^4 \) | \( mm^4 \) |
| \(\large{ \pi }\) = Pi | \(3.141 592 653 ...\) | \(3.141 592 653 ...\) |
| \(\large{ r }\) = radius | \( in \) | \( mm \) |
Radius of Gyration of a Half Circle formulas |
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\( k_{x} \;=\; r \cdot \sqrt{ \dfrac{1 }{ 4 } - \dfrac{ 16 }{ 9 \cdot \pi^2 } } \) \( k_{y} \;=\; \dfrac{ r }{ 2 }\) \( k_{z} \;=\; r \cdot \sqrt{ \dfrac{ 1 }{ 2 } - \dfrac{ 16 }{ 9 \cdot \pi^2 } } \) \( k_{x1} \;=\; \dfrac{ r }{ 2 }\) \( k_{y1} \;=\; \dfrac{ r }{ 2 }\) \( k_{z1} \;=\; \dfrac{ \sqrt {2} }{ 2 } \cdot r \) |
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| Symbol | English | Metric |
| \(\large{ k }\) = radius of gyration | \( in \) | \( mm \) |
| \(\large{ \pi }\) = Pi | \(3.141 592 653 ...\) | \(3.141 592 653 ...\) |
| \(\large{ r }\) = radius | \( in \) | \( mm \) |
Second Moment of Area of a Half circle formulas |
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\( I_{x} \;=\; \left( \dfrac{ \pi }{ 8 } - \dfrac{ 8 }{ 9 \cdot \pi } \right) \cdot r^4 \) \( I_{y} \;=\; \dfrac{ \pi \cdot r^4}{ 8 }\) \( I_{x1} \;=\; \dfrac{ \pi \cdot r^4}{ 8 }\) \( I_{y1} \;=\; \dfrac{ \pi \cdot r^4}{ 8 }\) |
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| Symbol | English | Metric |
| \(\large{ I }\) = moment of inertia | \( in^4 \) | \( mm^4 \) |
| \(\large{ \pi }\) = Pi | \(3.141 592 653 ...\) | \(3.141 592 653 ...\) |
| \(\large{ r }\) = radius | \( in \) | \( mm \) |
