Moment of Area Calculator Formula
Understand the math behind the moment of area calculator. Each variable explained with a worked example.
Formulas Used
Ixx (about horizontal axis)
ixx = width_b * pow(height_h, 3) / 12Iyy (about vertical axis)
iyy = height_h * pow(width_b, 3) / 12Ixx in cm^4
ixx_cm4 = width_b * pow(height_h, 3) / 12 / 1e4Variables
| Variable | Description | Default |
|---|---|---|
width_b | Width (b)(mm) | 100 |
height_h | Height (h)(mm) | 200 |
How It Works
Second Moment of Area for a Rectangle
The second moment of area (often called moment of inertia of the cross-section) governs how a beam resists bending.
Formula
Ixx = b h^3 / 12
Iyy = h b^3 / 12
where b is the width and h is the height of the rectangle. The axis with the larger I value provides greater bending resistance. That is why beams are oriented with the taller dimension vertical.
Worked Example
A rectangular timber section 100 mm wide and 200 mm tall.
width_b = 100height_h = 200
- 01Ixx = 100 x 200^3 / 12 = 100 x 8,000,000 / 12 = 66,666,667 mm^4
- 02Iyy = 200 x 100^3 / 12 = 200 x 1,000,000 / 12 = 16,666,667 mm^4
- 03Ixx in cm^4 = 66,666,667 / 10,000 = 6,666.67 cm^4
Ready to run the numbers?
Open Moment of Area Calculator