Free Moment of Inertia Calculator / Centroid Calculator

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

How to use this Moment of Inertia Calculator

This simple, easy-to-use moment of inertia calculator will find the moment of inertia of a circle, rectangle, hollow rectangular section (HSS), hollow circular section, triangle, I-Beam, T-Beam, L-Sections (angles) and channel sections, as well as 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.

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 list, 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.

SkyCiv Moment of Inertia Calculator



Notation Value Unit
A - -
Iz - -
Iy - -
Izp - -
Iyp - -
αp - -
Cz - -
Cy - -
Qz - -
Qy - -
Sz - -
Sy - -
J - -

Need More Functionality?

Upgrade to a professional plan to unlock full features
SkyCiv Hand Calculations Structural Analysis

SkyCiv Arm Leg Beam, Structural Section Builder Software

SkyCiv Custom Section Builder, Software Cloud

Learn More
Upgrade now!
Learn More
Upgrade now!

About the Moment of Inertia Calculator

Find the Moment of Inertia with ease

This free multi-purpose calculator is taken from our full suite Structural Analysis Software. It allows you to:

  • 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

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.

About SkyCiv

SkyCiv offers a wide range of Cloud Structural Analysis and Design Software for engineers. As a constantly evolving tech company, we're committed to innovating and challenging existing workflows to save engineers time in their work processes and designs.

More Free Tools Available

SkyCiv also offers other tools such as I beam size tool and free structural design 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 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.

Engineering Professional?

If you are an engineering professional, you might benefit more by using our cloud based 3D Structural Analysis Software beyond this calculator. This software includes integrated design modules such as AISC, ACI, AS, Eurocode and CSA.
View Software
View Pricing
View Software
View Pricing