Moment of Inertia Calculator
Calculate the area moment of inertia (second moment of area) for various shapes. Get Ix and Iy values with step-by-step solutions.
Shape Diagram
About Moment of Inertia Calculator
Our free Moment of Inertia Calculator helps engineers, students, and professionals calculate the area moment of inertia (second moment of area) for various geometric shapes. This property is crucial for analyzing structural strength and beam deflection.
The area moment of inertia describes how area is distributed about an axis. It's measured in meters to the fourth power (m⁴) and is essential in structural engineering, mechanical design, and construction analysis.
Key Features
- Multiple Shapes: Rectangle, circle, triangle support
- Ix and Iy Calculation: Both horizontal and vertical axes
- Step-by-Step Solutions: Detailed working shown
- Visual Diagrams: SVG diagrams for each shape
- Instant Results: Real-time calculations
- Mobile Friendly: Works on all devices
Moment of Inertia Formulas
Rectangle:
Ix = width × height³ / 12
Iy = height × width³ / 12
Circle:
Ix = Iy = π/4 × radius⁴
Triangle:
Ix = width × height³ / 36
Applications
Engineering Uses
- Structural analysis
- Beam design
- Material strength
- Cross-section analysis
- Deflection calculations
Educational Uses
- Engineering courses
- Mechanics of materials
- Structural engineering
- Homework help
- Exam preparation
Whether you're designing beams, analyzing structures, or studying engineering, our calculator provides accurate moment of inertia values instantly!
Frequently Asked Questions
The area moment of inertia (second moment of area) is a geometrical property describing how area is distributed about an axis. Units are meters to the fourth power (m⁴). It's crucial for analyzing structural strength and beam deflection.
For a rectangle: Ix = width × height³ / 12 and Iy = height × width³ / 12. These formulas assume the origin is at the centroid (center) of the rectangle.
Ix is the moment of inertia about the horizontal x-axis, while Iy is about the vertical y-axis. They measure how the area is distributed relative to each respective axis.
For a circle: Ix = Iy = π/4 × radius⁴. Circles have the same moment of inertia about both axes due to their symmetry.
The parallel axis theorem states that the moment of inertia about any axis parallel to an axis through the centroid equals: I = Ic + A×d², where Ic is the centroidal moment, A is area, and d is the distance between axes.
Moment of inertia is crucial for analyzing structural strength, beam deflection, and material cross-sections in construction and mechanical engineering. It helps determine how resistant a shape is to bending.
Yes, this calculator is completely free with no limitations, registration requirements, or hidden fees. Calculate unlimited shapes and access all features without any cost.