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

You can calculate the area moment of inertia of all shapes by using these integral calculations. ‘Iz’ and ‘Iy’ refers to the X and Y axes that cross-section resides in.

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

- Second moment of inertia calculation of rectangular cross-section;

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

- Second moment inertia calculation for triangular cross section;

As you understand that, X and Y axes are placed onto center of gravity of triangular cross section. Be aware about the sides and dimensions that are used in area moment of inertia calculation for triangular cross section.

- Second moment inertia calculation for circular cross section;

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

- Second moment inertia calculation for circular cross section;

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

- Second moment inertia calculation for semicircular cross section;

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

From drop down list above, select a cross sectional shape that you want to calculate second moment of inertia. All the cross sections avaliable in calculator are explained above.

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

If you want to do another calcuations, click on ‘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.

The unit of 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.

Check the other engineering calculators that are avaliable in Mechanical Base out!

If you want to change your unit set, you can use MB-Unit Concerter tool.

Mechanical Base does not accept any responsiblity of calculations done on its engineering calculators. All the responsiblity belongs to the calculator users. Every time, good engineers check their calculations by hand calculations.

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