Moment of Inertia Calculator

Category: Physics
- March 22, 2025
| |

Calculate the moment of inertia for various shapes about different axes. The moment of inertia is a measure of an object's resistance to changes in its rotation rate.

Select Shape

Shape Diagram

Point Mass Parameters

Advanced Options

About Moment of Inertia

The moment of inertia, also called the mass moment of inertia or rotational inertia, is a measure of an object's resistance to changes in its rotational motion. It is the rotational analog of mass in linear motion.

Key Concepts
  • Moment of Inertia: Depends on both the mass of the object and how the mass is distributed relative to the axis of rotation.
  • Radius of Gyration: The distance from the axis of rotation at which the entire mass of the body could be concentrated without changing its moment of inertia.
  • Parallel Axis Theorem: Relates the moment of inertia about any axis to the moment of inertia about a parallel axis through the center of mass.
  • Perpendicular Axis Theorem: For a planar object, the moment of inertia about an axis perpendicular to the plane equals the sum of the moments of inertia about two perpendicular axes in the plane and through the same point.
Applications

Understanding moments of inertia is important in many fields:

  • Mechanical Engineering: Design of rotating machinery, balancing of wheels and turbines
  • Aerospace Engineering: Aircraft and spacecraft stability analysis
  • Structural Engineering: Analysis of beams and frameworks
  • Robotics: Motion planning and control of robotic arms
  • Sports Engineering: Design of equipment like baseball bats, tennis rackets, etc.
Units

The SI unit of moment of inertia is kilogram square meter (kg¡m²).

System Unit
SI kg¡m²
CGS g¡cm²
Imperial slug¡ft² or lb¡ft¡s²

What Is the Moment of Inertia Calculator?

This calculator helps you determine the moment of inertia for various shapes based on their mass, dimensions, and axis of rotation. Moment of inertia is a physical quantity that measures how much resistance an object offers to a change in its rotation. It plays a key role in mechanical, structural, and physics-based applications.

Basic Formula:
I = m × r²

Where:

  • I is the moment of inertia
  • m is the mass of the object
  • r is the distance from the axis of rotation

Why Use This Calculator?

The moment of inertia varies depending on an object’s shape and how it rotates. This calculator saves time by handling the math for you. Whether you're a student, teacher, engineer, or hobbyist, it simplifies analysis and planning for projects involving rotation or torque.

Key Features

  • Select from common shapes like rods, discs, cylinders, spheres, and more
  • Customize input values and units (e.g., mass in kg or g, length in m or cm)
  • Choose different axes of rotation and see how results vary
  • Get additional insights such as radius of gyration and density
  • See step-by-step calculation breakdowns for learning or verification
  • Supports advanced options like scientific notation and precision control

How to Use the Calculator

Follow these simple steps to get your results:

  1. Select a Shape: Choose the physical shape that represents your object.
  2. Enter Parameters: Input values such as mass, radius, or length based on the selected shape.
  3. Set Axis of Rotation: Pick the relevant axis to calculate the correct moment of inertia.
  4. Adjust Settings (Optional): Choose decimal precision or enable scientific notation as needed.
  5. Click "Calculate": Your results, including a breakdown of calculations, will be displayed instantly.

Who Can Benefit From This?

This tool is useful in a wide range of fields and activities:

  • Students: Understand and explore rotational mechanics through interactive examples.
  • Teachers: Demonstrate core physics concepts with visual and numeric clarity.
  • Engineers: Quickly compute moments for structural or mechanical designs.
  • DIY Builders & Hobbyists: Plan projects involving rotating parts like wheels or gears.

Frequently Asked Questions (FAQ)

What is the moment of inertia?
It’s a measure of how much an object resists rotating around an axis. Heavier and larger objects generally have higher moments of inertia.

Do I need to know the formula to use this tool?
No. The calculator automatically applies the correct formula based on the shape and inputs you provide.

Can I change units?
Yes. You can choose between common units like kilograms or grams, meters or centimeters—whatever matches your data.

What if I want to see how the moment of inertia changes with a different axis?
Simply select a new axis from the dropdown menu. The result updates to reflect that configuration.

Does this support complex shapes?
The calculator supports a wide range of standard shapes. For very irregular forms, custom modeling or software might be more appropriate.

Conclusion

The Moment of Inertia Calculator is a practical and educational tool. It delivers fast, accurate results for rotational inertia calculations, helping users make informed decisions in design, learning, or experimentation. It's intuitive, flexible, and built to make physics more accessible.