Moment of Inertia Calculator
Calculate the second moment of area for various cross-sections
Moment of Inertia Calculator - Calculate Second Moment of Area
The moment of inertia (second moment of area) is a geometrical property that reflects how the area is distributed around an axis. A higher value indicates greater resistance to bending.
The Moment of Inertia (I), also known as the second moment of area, is a fundamental geometric property of a cross-section that reflects how its area is distributed relative to a particular axis. It is a crucial parameter in structural engineering and physics, used to predict the resistance of a beam to bending and deflection.
The calculation depends on the shape of the cross-section and the axis about which it is calculated:
These formulas are derived from integral calculus and represent the distribution of area relative to a specific axis.
Moment of Inertia is used in various engineering applications:
What is moment of inertia? Moment of inertia (I) is a geometrical property of an area that reflects how its points are distributed with regard to an axis. It is also called the second moment of area.
How does moment of inertia affect beam stiffness? A higher moment of inertia means the beam will be stiffer and deflect less under the same load compared to a beam with a lower moment of inertia.
What's the difference between moment of inertia and mass moment of inertia? Moment of area (discussed here) relates to geometry and bending resistance, while mass moment of inertia relates to rotational dynamics and depends on mass distribution.
Why are I-beams shaped the way they are? I-beams are designed to maximize moment of inertia while minimizing material usage, by placing most material away from the centroid where it contributes most to bending resistance.