Accurate Online Tool for Easy Moment of Inertia, Centroid, and Beam Section Calculations
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.
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 Shape Calculator
3. Enter the Shape Parameters
4. Get Instant Results
5. Receive Results by Email
Geometrical characteristics
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
Let’s calculate the moment of inertia of a rectangle with the following dimensions:
The formula for the moment of inertia (I) is:
Substitute the given values:
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.
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.
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.
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.