Free Moment of Inertia Calculator / Centroid Computer

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

How to use this Moment of Inertia Calculator

This uncomplicated, easy-to-use moment of inertia calculator will find the moment of inertia of a circle, rectangle, hollow rectangular section (HSS), hollow round section, triangle, I-Beam, T-Beam, L-Sections (angles) and aqueduct sections, likewise as centroid, section modulus and many more results.

You can solve up to 3 sections before you're required to sign upwards for a gratis account - which also gives you access to more than software and results.

To starting time using the free centroid calculator to summate moment of inertia, merely choose the cross department you want to evaluate from the drop down listing, then enter in the dimensions and click Calculate. The results for centroid, moment of inertia, statical moment section modulus and torsion abiding volition display on your right.

SkyCiv Moment of Inertia Computer

Units:




Material Backdrop


Need More Functionality?

Hand Calculations


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

Custom and Built-Up Sections


SkyCiv Department Builder uses FEA to summate cardinal section properties, allowing you to model anything you demand. But upgrade and go admission to powerful software.

Integrated with Assay Software


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

Nearly the Moment of Inertia Calculator

Discover the Moment of Inertia with ease

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

  • Calculate the Moment of Inertia (I) of a beam section (2nd Moment of Area)
  • Centroid Reckoner used to calculate the Centroid (C) in the X and Y axis of a beam section
  • Calculate the Kickoff moment of area (Statical Moment of Inertia) (Q) of a beam section (First Moment of Surface area)
  • A Section Modulus Calculator to summate the Section Modulus (Z) of a axle section
  • Calculate the Torsion Constant (J) of a beam section

More than information on these values is provided nether "Section Backdrop Explained"

Moment of Inertia

For example, if you're looking how to calculate the moment of inertia of a rectangle you can use the tool above just past selecting rectangle from the drop down list then inbound 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 total hand calculations of how the tool got to this effect. These detailed stride-by-step instructions assistance for you to follow the calculations and learn how to summate the moment of inertia. Alternatively, we have a tutorial on how to find moment of inertia.

Section Modulus Calculator

The computer will also produce results like section modulus (Z) and the statical moment of inertia (Q) for your sections. Finally, the outcome for Torsion Constant (J) will also display using this tool. The SkyCiv Department Builder will also produce these results accurately using FEA analysis of the cross department. Then if yous need more than results, or to add custom shapes - please bank check out our actress functionality of the SkyCiv Section Builder.

Section Backdrop Explained

  • The moment of inertia calculator will accurately summate a number of important section properties used in structural engineering, including:
    • Surface area of Department (A) -Section area is a adequately simple calculation, only straight used in axial stress calculations (the more cross section expanse, the more than centric forcefulness)
    • Moment of Inertia (Iz, Iy) –also known as second moment of area, is a calculation used to determine the strength of a fellow member and it'south resistance confronting deflection. The college this number, the stronger the section. In that location are two axis hither:
      • Z-Axis (Iz) – This is about the Z axis and is typically considered the major centrality since information technology is ordinarily the strongest direction of the fellow member
      • Y-Axis (Iy) – This is virtually the Y axis and is considered the minor or weak axis. This is because sections aren't designed to have as much forcefulness about this axis
      • As well worth noting that if a shape has the aforementioned dimensions in both directions (square, circular etc..) these values will be the same in both directions. See Moment of Ineria of a circle to learn more.
    • Centroid (Cz, Cy) – this is the middle of mass for the section and usually has a Z and Y component. For symmetrical shapes, this volition exist geometric center. For non-symmetrical shapes (such as angle, Aqueduct) these volition be in different locations. Learn how to calculate the centroid of a axle section
    • Statical Moment of Inertia (Qz, Qy) – Also known every bit First Moment of Area, this measures the distribution of a beam section's area from an centrality. Similar the Moment of Inertia, these are in both the Z and Y direction. These are typically used in shear stress calculations, and so the larger this value the stronger the section is against shearing. The calculator volition provide this value, but click here to learn more near calculating the beginning moment of expanse.
    • Elastic Department Modulus (Sz, Sy) – Likewise known as statical section modulus, and are used in bending stress calculations. They are usually calculated to the top and bottom corner fibres from a particular centrality. For example, Szt is the section modulus about Z to the superlative fibre. For the moment figurer above, this is taken to the height fibres by default.
    • Torsion Constant (J)
    • Other Parameters – These are calculated by the full SkyCiv Department Builder:
      • Product of Inertia (almost Z and Y Axis)
      • Angle of Rotation of Principle Axis
      • Radius of Gyration (almost Z and Y Axis)
      • Plastic Section Modulus (about Z and Y Centrality)
      • Plastic Neutral Axis (virtually Z and Y Axis)
      • Shear Surface area (virtually Z and Y Axis)
      • Altitude of Shear Centre to Centroid (in both Z and Y Axis)
      • Torsion Constant (Using FEA)
      • Torsion Radius
      • Warping Constant
      • Monosymmetry Abiding (almost Z and Y Axis)

About SkyCiv

SkyCiv offers a broad range of Deject Structural Analysis and Design Software for engineers. Every bit a constantly evolving tech company, we're committed to innovating and challenging existing workflows to salvage engineers time in their piece of work processes and designs.

More Free Tools Available

SkyCiv likewise offers other tools such as I beam size tool and free structural pattern software. The dynamic section drawer will likewise bear witness you lot a graphical representation of your beam section. So if you want to summate the moment of inertia of circle, moment of inertia of a rectangle or any other shapes, experience free to use the below software or our all-inclusive SkyCiv Section Builder.

Beam Size Tool

Truss Calculator

Frame Estimator

Beam Calculator

Engineering Professional?

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