# 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

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

### Area of a Half Circle formula

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

### Perimeter of a Half Circle formula

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

### Radius of a Half Circle formula

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

### Distance from Centroid of a Half Circle formulas

$$C_x \;=\; 0$$

$$C_y \;=\; 4 \; r \;/\; 3 \; \pi$$

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

### Elastic Section Modulus of a Half Circle formula

$$S \;=\; I_x \;/\; C_y$$
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

$$J_{z} \;=\; [\; ( \pi\;/\; 4 ) - ( 8 \;/\; 9 \; \pi )\;] \; r^4$$

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

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

### Radius of Gyration of a Half Circle formulas

$$k_{x} \;=\; r \; \sqrt{ (1 \;/\; 4 ) - (16 \;/\; 9 \; \pi^2 ) }$$

$$k_{y} \;=\; r \;/\; 2$$

$$k_{z} \;=\; r \; \sqrt{ (1 \;/\; 2 ) - (16 \;/\; 9 \; \pi^2 ) }$$

$$k_{x1} \;=\; r \;/\; 2$$

$$k_{y1} \;=\; r \;/\; 2$$

$$k_{z1} \;=\; ( \sqrt {2} \;/\; 2 ) \; r$$

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

### Second Moment of Area of a Half circle formulas

$$I_{x} \;=\; [\; ( \pi \;/\; 8 ) - ( 8 \;/\; 9 \; \pi ) \;] \; r^4$$

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

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

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

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