Quarter Circle

on . Posted in Plane Geometry

• A part of the interior of a circle having two radius boundries at a 90° angle and an arc.
• Center of a circle having all points on the line circumference are at equal distance from the center point.
• A quarter circle is a structural shape used in construction.

arc Length of a Quarter Circle formula

$$L \;=\; 2 \; \pi \; r\;/\;4$$
Symbol English Metric
$$L$$ = arc length $$in$$ $$mm$$
$$\pi$$ = Pi $$3.141 592 653 ...$$
$$r$$ = radius $$in$$ $$mm$$

area of a Quarter Circle formula

$$A \;=\; \pi \; r^2 \;/\;4$$
Symbol English Metric
$$A$$ = area $$in^2$$ $$mm^2$$
$$\pi$$ = Pi $$3.141 592 653 ...$$
$$r$$ = radius $$in$$ $$mm$$

Distance from Centroid of a Quarter Circle formulas

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

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

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

Elastic Section Modulus of a Quarter Circle formula

$$S \;=\; I_x \;/\; C_y$$
Symbol English Metric
$$S$$ = elastic section modulus $$in^3$$ $$mm^3$$
$$I$$ = moment of inertia $$lbm\;/\;ft^2-sec$$ $$kg\;/\;m^2$$

Perimeter of a Quarter Circle formulas

$$P \;=\; (2 \; \pi \; r\;/\;4)+ 2 \; r$$

$$P \;=\; L + 2 \; r$$

Symbol English Metric
$$P$$ = perimeter $$in$$ $$mm$$
$$L$$ = arc length $$in$$ $$mm$$
$$\pi$$ = Pi $$3.141 592 653 ...$$
$$r$$ = radius $$in$$ $$mm$$

Polar Moment of Inertia of a Circle formulas

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

$$J_{z1} \;=\; \pi \; r^4 \;/\; 8$$

Symbol English Metric
$$L$$ = arc length $$in$$ $$mm$$
$$\pi$$ = Pi $$3.141 592 653 ...$$
$$r$$ = radius $$in$$ $$mm$$

Radius of a Quarter Circle formula

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

Radius of Gyration of a Half Circle formulas

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

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

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

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

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

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

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

Second Moment of Area of a Half circle formulas

$$I_{x} \;=\; [\; ( \pi\;/\; 16 ) - ( 4 \;/\; 9 \; \pi ) \;] \; r^4$$

$$I_{y} \;=\; [\; ( \pi\;/\; 16 ) - ( 4 \;/\; 9 \; \pi ) \;] \; r^4$$

$$I_{x1} \;=\; \pi \; r^4\;/\; 16$$

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

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