Second Moment of Area Calculator
I and W for a solid rectangular section and a solid round section.
Results
Second moment of area
416.6667
cm⁴
Section modulus
83.3333
cm³
Second moment of area
12.5664
cm⁴
Section modulus
6.2832
cm³
What this tool does
The second moment of area is what decides how much a beam bends, and it grows with the cube of the height — which is why a plank laid on edge is far stiffer than the same plank laid flat. Section modulus W is the figure used for stress, I is the one used for deflection.
Formula
rectangle: I = b×h³/12 · circle: I = π×d⁴/64
Variables
| Symbol | Meaning | Unit |
|---|---|---|
b | Width | mm |
h | Height | mm |
d | Diameter | mm |
IR | Second moment of area | cm⁴ |
WR | Section modulus | cm³ |
IC | Second moment of area | cm⁴ |
WC | Section modulus | cm³ |
Worked example
- Width50 mm
- Height100 mm
- Diameter40 mm
- Second moment of area416.6667 cm⁴
- Section modulus83.3333 cm³
- Second moment of area12.5664 cm⁴
- Section modulus6.2832 cm³
Limitations
- For work that must comply with a standard or be signed off, check the result against the applicable code and have it reviewed by a qualified engineer.
- Mixing units is the most common source of error. Convert every input to the units shown next to each field before calculating.