# Thin Wall 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 thin wall circle is a structural shape used in construction.

### area of a Thin Walled Circle formula

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

### Perimeter of a Thin Walled Circle formula

$$P \;=\; 2\; \pi \;r$$     (outside)

$$P \;=\; 2\; \pi \; ( r - t )$$     (inside)

Symbol English Metric
$$P$$ = perimeter $$in$$ $$mm$$
$$\pi$$ = Pi $$3.141 592 653 ...$$
$$r$$ = inside radius $$in$$ $$mm$$
$$t$$ = thickness $$in$$ $$mm$$

### Radius of a Thin Walled Circle formula

$$r \;=\; \sqrt{ 2 \; A \;/\; \pi }$$     (Radius of a Thin Walled Circle)

$$A \;=\; r^2 \; \pi \;/\; 2$$

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

### Distance from Centroid of a Thin Walled 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 Thin Walled Circle formula

$$S \;=\; 2 \; \pi \; r \; t \;/\; 3$$     (Elastic Section Modulus of a Thin Walled Circle)

$$r \;=\; S \; 3 \;/\; 2 \; \pi \; t$$

$$t \;=\; S \; 3 \;/\; 2 \; \pi \; r$$

Symbol English Metric
$$S$$ = elastic section modulus $$in^3$$ $$mm^3$$
$$\pi$$ = Pi $$3.141 592 653 ...$$
$$r$$ = inside radius $$in$$ $$mm$$
$$t$$ = thickness $$in$$ $$mm$$

### Plastic Section Modulus of a Thin Walled Circle formula

$$Z \;=\; \pi \; r^2 \; t$$     (Plastic Section Modulus of a Thin Walled Circle)

$$r \;=\; \sqrt{ Z \;/\; \pi \; t }$$

$$t \;=\; Z \;/\; \pi \; r^2$$

Symbol English Metric
$$Z$$ = plastic section modulus $$in^3$$ $$mm^3$$
$$\pi$$ = Pi $$3.141 592 653 ...$$
$$r$$ = inside radius $$in$$ $$mm$$
$$t$$ = thickness $$in$$ $$mm$$

### Polar Moment of Inertia of a Thin Walled Circle formulas

$$J_{z} \;=\; 2\; \pi \;r^3 \;t$$

$$J_{z1} \;=\; 6\; \pi \;r^3 \;t$$

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

### Radius of Gyration of a Thin Walled Circle formulas

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

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

$$k_{z} \;=\; r$$

$$k_{x1} \;=\; ( \sqrt {6} \;/\; 2 ) \; r$$

$$k_{y1} \;=\; ( \sqrt {6} \;/\; 2 ) \; r$$

$$k_{z1} \;=\; \sqrt {3} \; r$$

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

### Second Moment of Area of a Thin Walled Circle formulas

$$I_{x} \;=\; \pi \;r^3 \;t$$

$$I_{x1} \;=\; 3\; \pi \;r^3 \;t$$

$$I_{y1} \;=\; 3\; \pi \;r^3 \;t$$

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

### Torsional Constant of a Thin Walled Circle formula

$$J \;=\; 2\; \pi \;r^3 \; t$$     (Torsional Constant of a Thin Walled Circle)

$$r \;=\; ( J \;/\; 2 \; \pi \; t )^{ \frac{1}{3} }$$

$$t \;=\; J \;/\; 2 \; \pi \; r^3$$

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