Moment of Inertia Calculator for Beam Sections

Free Moment of Inertia Calculator / Centroid Calculator

Calculate Moment of Inertia, Centroid, Section Modulus of Multiple Shapes

Welcome to SkyCiv's Free Moment of Inertia Calculator! This free Section Builder is able to accurately and quickly calculate the moment of inertia among other section properties. The following multi-purpose calculator is taken from our Structural Analysis Software and is free to use.

  • Calculate the Moment of Inertia (I) of a beam section (Second Moment of Area)
  • Centroid Calculator used to calculate the Centroid (C) in the X and Y axis of a beam section
  • Calculate the First moment of area (Statical Moment of Inertia) (Q) of a beam section (First Moment of Area)
  • A Section Modulus Calculator to calculate the Section Modulus (Z) of a beam section
  • Calculate the Torsion Constant (J) of a beam section

The Beam Moment of Inertia Calculator is able to find the moment of inertia for a circle, rectangle, hollow rectangular section (HSS), hollow circular section, triangle, I-Beam, T-Beam, L-Sections (angles) and channel sections. SkyCiv also offers other tools such as I beam size tool and free design check software. The dynamic section drawer will also show you a graphical representation of your beam section. So if you want to calculate the moment of inertia of a circle, moment of inertia of a rectangle or any other shapes, feel free to use the below software or our all inclusive SkyCiv Section Builder.

To start using the free centroid calculator to calculate moment of inertia, simply choose the cross section you want to evaluate from the drop down lost, then enter in the dimensions and click Calculate. The results for centroid, moment of inertia, statical moment section modulus and torsion constant will display on your right.



b:
h:

Units:




Notation Value Unit
A - -
Iz - -
Iy - -
Izp - -
Iyp - -
αp - -
Cz - -
Cy - -
Qz - -
Qy - -
Zz - -
Zy - -
J - -




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Hand Calculations

SkyCiv shows you how to calculate the moment of inertia by showing the step-by-step moment of inertia equations and calculations... The also show centroid and area calculations.

Custom and Built-Up Sections

SkyCiv Section Builder uses FEA to calculate key section properties, allowing you to model anything you need. Simply upgrade and get access to powerful software.

Integrated with Analysis Software

The SkyCiv Section Builder is fully integrated with all SkyCiv Analysis Software including SkyCiv Beam and SkyCiv Structural 3D - so you can analyze your section under loads.

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About the Moment of Inertia Calculator

Calculating the moment of inertia of circles, recatngles and aother common cross sections can be a tedious task. This simple, easy to use moment of inertia calculator will find moment of inertia, centroid, section modulus and many more results. You can solve up to three sections before you're required to sign up for a free account - which also gives you access to more software and results.

Moment of Inertia

For instance, if you're looking how to calculate the moment of inertia of a rectangle you can use the tool above simply by selecting rectangle from the drop down list then entering some dimensions for height and width (e.g. 100, 200). After clicking "Calculate", the tool will calculate the moment of inertia. Our paid version will show the full hand calculations of how the tool got to this result. These detailed step-by-step instructions help for you to follow the calculations and learn how to calculate the moment of inertia. Alternatively, we have a tutorial on how to find moment of inertia.

Section Modulus Calculator

The calculator will also produce results like section modulus (Z) and the statical moment of inertia (Q) for your sections. Finally, the result for Torsion Constant (J) will also display using this tool. The SkyCiv Section Builder will also produce these results accurately using FEA analysis of the cross section. So if you need more results, or to add custom shapes - please check out our extra functionality of the SkyCiv Section Builder.

  • aaron lindstrom

    Just some feedback on the statical moment calculation for a circular cross section… seems to be half of what hand calcs generate for me.

    • Hi Aaron. Thanks for the message. It is the property about the neutral axis. This is probably why it is half the value you expected. I imagine you are calculating it as measured from the bottom of the section?

  • Fazli Azizi

    what if the y-axis acting downwards and z-axis acting to the left ? is there any changes in izz and iyy values ? or izz will become iyy and vice versa ?

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