We created a calculator that you can easily calculate the area moment of inertia of certain cross sections. So, you will see that it is very basic to use an area moment of inertia calculator.

## What is the Area Moment of Inertia?

Area moment of inertia is generally used in mechanical and physical problems. Also, the second moment of inertia is about the 2D cross-sectional planes of 3D geometries that show the distribution of points along a specific axis. The most general formulae of an area’s moment of inertia are;

Thus, you can calculate the area moment of inertia of all shapes by using these integral calculations. ‘Iz’ and ‘Iy’ refer to the X and Y axes where the cross-section resides in.

But in engineering practice, some standard shapes are generally used in cross-sections of different mechanical elements. And also, you do not need to do any integral calculations for them. Formulae of the second moment of inertias of these standard cross-sectional shapes are derived already. Here are the formulae of the second moment of inertias of standard shapes:

- The second moment of inertia calculation of rectangular cross-section;

So, as you see, the area moment of inertia of rectangular cross-sections for X and Y axes are defined above. You need to define the sides of the rectangle to calculate the second moment of inertia correctly.

### Triangular and Circular Shapes

- Second-moment inertia calculation for triangular cross-section;

Also again, X and Y axes are placed onto the center of gravity of the triangular cross-section. In addition, be aware of the sides and dimensions that are used in the area moment of inertia calculation for the triangular cross-section.

- Second-moment inertia calculation for circular cross-section;

The second moment of inertia calculation for circular cross-section is very basic as you see. Because the X and Y axes are placed on the center of gravity point of the circular cross-section, the moment of inertia formulae is the same for the two axes for the circular cross-section.

- Second-moment inertia calculation for circular cross-section;

Moreover, if you take a look at the formulae above for hollow circular cross-sections, it is the subtraction of the inner circle from the outer circle. Take care of the inner and outer diameters of the hollow circular cross-section.

- Second-moment inertia calculation for semicircular cross-section;

The semicircular cross section’s second moment of inertia is pretty different from others, because of the position of the center of gravity. Again, be aware of the positions of the X and Y axes, because the area moment of inertia is calculated according to these axes.

## How to Use Area Moment of Inertia Calculator?

Firstly, from the drop-down list above, select a cross-sectional shape that you want to calculate the second moment of inertia. All the cross-sections available in the calculator have been explained above.

And then, for rectangular and triangular area moment of inertia calculators, you need to enter ‘h’ and ‘b’ values inside the required places. Then click on the ‘Calculate!’ button to calculate the area moment of inertia values for ‘X’, ‘Y’, and center points. Areas of them were also calculated.

If you want to do another calculation, click on the ‘Reset’ button, then re-enter values inside the second moments’ inertia calculator.

For, circular, hollow circular, and semicircular cross-sections, you just need to enter diameter ‘d’^value to calculate the area moment of inertia value of them.

## Conclusion

Above all, the unit of an area moment of inertia is the fourth power of length which is ft^4 and m^4. It is very basic but, you need to enter consistent unit sets into the calculators.

Also, check the other engineering calculators that are available in Mechanicalland out!

Mechanicalland does not accept any responsibility for calculations done on its engineering calculators. All the responsibility belongs to the calculator users. Every time, good engineers check their calculations by hand calculations.

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Reference: Researchgate.com