# Second Moment of Area Calculator

The area moment of inertia is a geometrical property which shows how its points are distributed and predicts the beam deflection. The beams resistance to bending is represented by second moment area. The objects resistance for being rotated is measured by area moment of inertia calculator. Select the common shapes and enter the width, height, radius in the second moment of area calculator, to find area moment of inertia of semicircle, circle, triangle and rectangle.

## Area Moment of Inertia Calculator

The area moment of inertia is a geometrical property which shows how its points are distributed and predicts the beam deflection. The beams resistance to bending is represented by second moment area. The objects resistance for being rotated is measured by area moment of inertia calculator. Select the common shapes and enter the width, height, radius in the second moment of area calculator, to find area moment of inertia of semicircle, circle, triangle and rectangle.

Code to add this calci to your website

#### Area Moment of Inertia Formula:

**Rectangle**
I_{x} = w × h^{3} / 12
I_{y} = h × w^{3} / 12
**Triangle**
I_{x} = w × h^{3} / 36
**SemiCircle**
I_{x}, I_{y} = π × r^{4} / 8
**Circle**
I_{x}, I_{y} = π × r^{4} / 4
**Where,**
I_{x}, I_{y} = Area Moment Of Inertia
w = Width
h = Height
r = Radius
### Example:

Find the area moment of inertia for the rectangular object of width 8mm and height 5mm.

#### Solution:

I_{x} = 8 × 5^{3} / 12

= 83.3333

I_{y} = 5 × 8^{3} / 12

= 213.3333