# Quarter Circle

Written by Jerry Ratzlaff on . Posted in Plane Geometry

## Quarter Circle - Geometric Properties

A half circle is also called a semiciecle.

### area of a Quarter Circle  formula

$$\large{ A = \frac { \pi r^2 } {4} }$$

$$\large{ A = \frac { \pi d^2} {16} }$$

### Center of a Quarter Circle

All points on the line circumference are at equal distance from the center point.

### Circumference of a Quarter Circle formula

$$\large{ C = \frac {\pi d} {4} }$$

### Perimeter of a Quarter Circle formula

$$\large{ P = \frac { \pi r } {2} + 2r }$$

$$\large{ P = \frac { \pi d } { 4 } + d }$$

### Radius of a Quarter Circle formula

$$\large{ r = \sqrt {\frac {2A} {\pi} } }$$

### Distance from Centroid of a Quarter Circle formula

$$\large{ C_x = \frac {4r} {3 \pi} }$$

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

### Elastic Section Modulus of a Quarter Circle formula

$$\large{ S = \frac { I_x } { C_y } }$$

### Polar Moment of Inertia of a Circle formula

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

$$\large{ J_{z1} = \frac { \pi r^4 } { 8 } }$$

### Radius of Gyration of a Half Circle formula

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

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

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

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

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

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

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

$$\large{ I_{x} = \left( \frac { \pi}{ 16 } - \frac { 4 }{ 9 \pi } \right) r^4 }$$

$$\large{ I_{y} = \left( \frac { \pi}{ 16 } - \frac { 4 }{ 9 \pi } \right) r^4 }$$

$$\large{ I_{x1} = \frac { \pi r^4}{ 16 } }$$

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

Where:

$$\large{ A }$$ = area

$$\large{ C }$$ = circumference

$$\large{ C_x, C_y }$$ = distance from centroid

$$\large{ d }$$ = diameter

$$\large{ I }$$ = moment of inertia

$$\large{ k }$$ = radius of gyration

$$\large{ P }$$ = perimeter

$$\large{ r }$$ = radius

$$\large{ S }$$ = elastic section modulus

$$\large{ \theta }$$ = angle

$$\large{ \pi }$$ = Pi