# Hollow Circle

on . Posted in Plane Geometry

• Two circles each having all points on each circle at a fixed equal distance from a center point.
• Center of a circle having all points on the line circumference are at equal distance from the center point.
• A hollow circle is a structural shape used in construction.

### area of a Hollow Circle formula

$$A \;=\; \pi \; ( R^2 - r^2 )$$
Symbol English Metric
$$A$$ = area  $$in^2$$ $$mm^2$$
$$\pi$$ = Pi $$3.141 592 653 ...$$
$$R$$ = outside radius $$in$$ $$mm$$
$$r$$ = inside radius $$in$$ $$mm$$

### Circumference of a Hollow Circle formulas

$$C \;=\; 2 \; \pi \; r$$     (inside)

$$C \;=\; 2 \; \pi \; R$$     (outside)

Symbol English Metric
$$C$$ = circumference $$in$$ $$mm$$
$$\pi$$ = Pi $$3.141 592 653 ...$$
$$r$$ = inside radius $$in$$ $$mm$$
$$R$$ = outside radius $$in$$ $$mm$$

### Distance from Centroid of a Hollow Circle formulas

$$C_x \;=\; r$$

$$C_y \;=\; r$$

Symbol English Metric
$$C_x, C_y$$ = distance from centroid $$in$$ $$mm$$
$$r$$ = inside radius $$in$$ $$mm$$

### Elastic Section Modulus of a Hollow Circle formula

$$S \;=\; \pi \; ( R^4 - r^4 ) \;/\; 4\;R$$
Symbol English Metric
$$S$$ = elastic section modulus $$in^3$$ $$mm^3$$
$$r$$ = inside radius $$in$$ $$mm$$
$$R$$ = outside radius $$in$$ $$mm$$
$$\pi$$ = Pi $$3.141 592 653 ...$$

### Plastic Section Modulus of a Hollow Circle formula

$$Z \;=\; 4 \; ( R^3 - r^3 ) \;/\; 3$$
Symbol English Metric
$$Z$$ = plastic section modulus $$in^3$$ $$mm^3$$
$$r$$ = inside radius $$in$$ $$mm$$
$$R$$ = outside radius $$in$$ $$mm$$

### Polar Moment of Inertia of a Hollow Circle formulas

$$J_{z} \;=\; ( \pi \;/\; 2 ) \; ( R^4 - r^4 )$$

$$J_{z1} \;=\; [ \; ( \pi \;/\; 2 ) \; ( R^4 - r^4 ) \; ] + [ 2\; \pi \; R^2 \; ( R^2 - r^2 ) \; ]$$

Symbol English Metric
$$J$$ = torsional constant $$in^4$$ $$mm^4$$
$$r$$ = inside radius $$in$$ $$mm$$
$$R$$ = outside radius $$in$$ $$mm$$
$$\pi$$ = Pi $$3.141 592 653 ...$$

### Radius of a Hollow Circle formula

$$r \;=\; C \;/\; 2 \; \pi$$

$$R \;=\; C \;/\;2 \; \pi$$

Symbol English Metric
$$r$$ = inside radius $$in$$ $$mm$$
$$R$$ = outside radius $$in$$ $$mm$$
$$C$$ = circumference $$in$$ $$mm$$
$$\pi$$ = Pi $$3.141 592 653 ...$$

### Radius of Gyration of a Hollow Circle formulas

$$k_{x} \;=\; \frac{1}{2} \; \sqrt { R^2 + r^2 }$$

$$k_{y} \;=\; \frac{1}{2} \; \sqrt { R^2 + r^2 }$$

$$k_{z} \;=\; ( \sqrt{ 2 } \;/\; 2) \; \sqrt{ R^2 + r^2 }$$

$$k_{x1} \;=\; \frac{1}{2} \; \sqrt{ 5 \; R^2 + r^2 }$$

$$k_{y1} \;=\; \frac{1}{2} \; \sqrt{ 5 \; R^2 + r^2 }$$

$$k_{z1} \;=\; ( \sqrt{ 2 } \;/\; 2) \; \sqrt{ 5 \; R^2 + r^2 }$$

Symbol English Metric
$$k$$ = radius of gyration $$in$$ $$mm$$
$$r$$ = inside radius $$in$$ $$mm$$
$$R$$ = outside radius $$in$$ $$mm$$

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

$$I_{x} \;=\; ( \pi \;/\; 4) \; ( R^4 - r^4 )$$

$$I_{y} \;=\; ( \pi \;/\; 4) \; ( R^4 - r^4 )$$

$$I_{x1} \;=\; [ \; ( \pi \;/\; 4 ) \; ( R^4 - r^4 ) \; ] + [ \pi \; R^2 \; ( R^2 - r^2 ) \; ]$$

$$I_{y1} \;=\; [ \; ( \pi \;/\; 4 ) \; ( R^4 - r^4 ) \; ] + [ \pi \; R^2 \; ( R^2 - r^2 ) \; ]$$

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

### Sector of a Hollow Circle formula

$$A \;=\; \pi \; \Delta \; ( r^2 - R^2 ) \;/\; 360$$
Symbol English Metric
$$A$$ = sector area $$in^2$$ $$mm^2$$
$$\Delta$$ = angle $$deg$$ $$rad$$
$$r$$ = inside radius $$in$$ $$mm$$
$$R$$ = outside radius $$in$$ $$mm$$
$$\pi$$ = Pi $$3.141 592 653 ...$$

### Torsional Constant of a Hollow Circle formulas

$$J \;=\; \pi \; ( R^4 - r^4 ) \;/\; 2$$

$$J \;=\; \pi \; ( D^4 - d^4 ) \;/\; 32$$

Symbol English Metric
$$J$$ = torsional constant $$in^4$$ $$mm^4$$
$$d$$ =  inside diameter $$in$$ $$mm$$
$$D$$ =  outside diameter $$in$$ $$mm$$
$$r$$ = inside radius $$in$$ $$mm$$
$$R$$ = outside radius $$in$$ $$mm$$
$$\pi$$ = Pi $$3.141 592 653 ...$$