Free Moment of Inertia, Centroid and Section Modulus Calculator

Accurate Online Tool for Easy Moment of Inertia, Centroid, and Beam Section Calculations

What is Moment of Inertia , Centroid and Section Modulus Calculator

Free Moment of Inertia Calculator Functionality

SDC Verifier’s Free Moment of Inertia Calculator allows you to calculate properties for a wide range of standard profiles commonly used in structural and mechanical engineering:

These options cover both solid and hollow sections, as well as open profiles, making the tool versatile for different engineering scenarios.

Parameters calculated

The calculator provides accurate results for key geometric and structural properties, including:

🔹 Geometrical Characteristics

🔹 Moment of Inertia

Geometric Axes

Principal Axes

🔹 Elastic Section Modulus

🔹 Plastic Section Modulus

🔹 Distance from Centroid to Extreme Fibres

🔹 Radius of Gyration

🔹 Shear Area

🔹 Radius of Gyration
• ry, rz – About geometric Y and Z axes (mm/in): Indicates efficiency of area distribution.
• rx – Radius of gyration about polar axis (mm/in), derived from polar moment of inertia.
• r1, r2 – About principal axes (mm/in): Same as for Y and Z axes but relative to principal axes.
• r3 – Polar radius of gyration about principal axes (mm/in).

🔹 Torsional and Warping Properties

How to Use the Free Moment of Inertia Calculator? Step-by-Step Instructions

How to Use the Shape Calculator

  1. Select the Unit System
    • Choose between Metric or Imperial (default is Metric).
  2. Choose the Shape Type
    • Pick one of the available cross-section shapes:

3. Enter the Shape Parameters

4. Get Instant Results

5. Receive Results by Email

Example: I-beam Section Output

 Basic Properties

  SDC Verifier

Results:

Geometrical characteristics

  SDC Verifier

Moments of Inertia (Geometric Axes)


Moments of Inertia (Principal Axes)


Elastic Section Modulus


Plastic Section Modulus


Distances from Centroid to Extreme Fibers


Radius of Gyration


Shear Areas


Torsional and Warping Properties

See the Formula for Moment of Inertia of a Rectangle

Let’s calculate the moment of inertia of a rectangle with the following dimensions:

The formula for the moment of inertia (I) is:

image 1

Substitute the given values:

image 5
image 6
image 3
image 4

Result:

image 2

This value represents the moment of inertia about the base of the rectangle (horizontal axis). It’s a key parameter in assessing the bending resistance of a section.

Key Benefits of SDC Verifier’s Moment of Inertia Calculator

What Can You Do After Receiving Results on Moment of Inertia?

FAQ

What is moment of inertia?

The moment of inertia is a measure of an object’s resistance to bending or rotation. In structural engineering, it’s used to determine how much a beam or section will deflect under load.

What is the section modulus?

The section modulus is a geometric property that represents the strength of a section in bending. It is calculated as the moment of inertia divided by the distance from the centroid to the outermost fiber.

What is the difference between lz and ly?

Iz is the moment of inertia about the Z-axis, while Iy is the moment of inertia about the Y-axis. The values depend on the geometry and orientation of the cross-section.

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