# Half Circle

on . Posted in Plane Geometry

•  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.

## Arc Length of a Half Circle formula

$$\large{ l = \frac{2 \; \pi \; r}{2} }$$
Symbol English Metric
$$\large{ l }$$ = length  $$\large{ in }$$ $$\large{mm }$$
$$\large{ \pi }$$ = Pi $$\large{3.141 592 653 ...}$$
$$\large{ r }$$ = radius $$\large{ in }$$ $$\large{mm }$$

## Area of a Half Circle formula

$$\large{ A_{area} = \frac{ \pi \; r^2 }{2} }$$
Symbol English Metric
$$\large{ A }$$ = area $$\large{ in^2 }$$ $$\large{ mm^2 }$$
$$\large{ \pi }$$ = Pi $$\large{3.141 592 653 ...}$$
$$\large{ r }$$ = radius $$\large{ in }$$ $$\large{mm }$$

## Perimeter of a Half Circle formula

$$\large{ P = \frac{2 \; \pi \; r}{2} + 2 \; r }$$
Symbol English Metric
$$\large{ P }$$ = perimeter $$\large{ in }$$ $$\large{ mm }$$
$$\large{ \pi }$$ = Pi $$\large{3.141 592 653 ...}$$
$$\large{ r }$$ = radius $$\large{ in }$$ $$\large{mm }$$

## Radius of a Half Circle formula

$$\large{ r = \sqrt {\frac {2 \; A_{area}} {\pi} } }$$
Symbol English Metric
$$\large{ A }$$ = area $$\large{ in^2 }$$ $$\large{ mm^2 }$$
$$\large{ \pi }$$ = Pi $$\large{3.141 592 653 ...}$$
$$\large{ r }$$ = radius $$\large{ in }$$ $$\large{mm }$$

## Distance from Centroid of a Half Circle formulas

$$\large{ C_x = 0 }$$

$$\large{ C_y = \frac {4 \; r} {3 \; \pi} }$$

Symbol English Metric
$$\large{ C_x, C_y }$$ = distance from centroid $$\large{ in }$$ $$\large{ mm }$$
$$\large{ \pi }$$ = Pi $$\large{3.141 592 653 ...}$$
$$\large{ r }$$ = radius $$\large{ in }$$ $$\large{mm }$$

## Elastic Section Modulus of a Half Circle formula

$$\large{ S = \frac { I_x } { C_y } }$$
Symbol English Metric
$$\large{ S }$$ = elastic section modulus $$\large{ in^3 }$$ $$\large{ mm^3 }$$
$$\large{ C_x, C_y }$$ = distance from centroid $$\large{ in }$$ $$\large{ mm }$$

## Polar Moment of Inertia of a Circle formulas

$$\large{ J_{z} = \left( \frac { \pi}{ 4 } - \frac { 8 }{ 9 \; \pi } \right) r^4 }$$

$$\large{ J_{z1} = \frac { \pi \; r^4 } { 4 } }$$

Symbol English Metric
$$\large{ J }$$ = torsional constant $$\large{ in^4 }$$ $$\large{mm^4 }$$
$$\large{ \pi }$$ = Pi $$\large{3.141 592 653 ...}$$
$$\large{ r }$$ = radius $$\large{ in }$$ $$\large{mm }$$

## Radius of Gyration of a Half Circle formulas

$$\large{ k_{x} = r \; \sqrt { \frac { 1 } { 4 } - \frac { 16 } { 9 \; \pi^2 } } }$$

$$\large{ k_{y} = \frac { r } { 2 } }$$

$$\large{ k_{z} = r \; \sqrt { \frac { 1 } { 2 } - \frac { 16 } { 9 \; \pi^2 } } }$$

$$\large{ k_{x1} = \frac { r } { 2 } }$$

$$\large{ k_{y1} = \frac { r } { 2 } }$$

$$\large{ k_{z1} = \frac { \sqrt {2} } { 2 } \; r }$$

Symbol English Metric
$$\large{ k }$$ = radius of gyration $$\large{ in}$$ $$\large{mm }$$
$$\large{ \pi }$$ = Pi $$\large{3.141 592 653 ...}$$
$$\large{ r }$$ = radius $$\large{ in }$$ $$\large{mm }$$

## Second Moment of Area of a Half circle formulas

$$\large{ I_{x} = \left( \frac { \pi}{ 8 } - \frac { 8 }{ 9 \; \pi } \right) r^4 }$$

$$\large{ I_{y} = \frac { \pi \; r^4}{ 8 } }$$

$$\large{ I_{x1} = \frac { \pi \; r^4}{ 8 } }$$

$$\large{ I_{y1} = \frac { \pi \; r^4}{ 8 } }$$

Symbol English Metric
$$\large{ I }$$ = moment of inertia $$\large{ in^4 }$$ $$\large{ mm^4 }$$
$$\large{ \pi }$$ = Pi $$\large{3.141 592 653 ...}$$
$$\large{ r }$$ = radius $$\large{ in }$$ $$\large{mm }$$ 