Torus Moment of Inertia Calculator - Free Online

The moment of inertia (I) measures an object's resistance to rotational acceleration. For a torus, this calculation is complex because mass is distributed around two axes: the major radius (R) and the minor radius (r). Our calculator uses established geometric formulas derived from integral calculus to provide precise results instantly.

You simply input three key parameters:

• Major Radius (R): The distance from the center of the hole to the center of the tube.
• Minor Radius (r): The radius of the circular cross-section (the tube itself).
• Mass (M) or Density: Depending on your input, we calculate I based on the given mass.

The tool applies the correct formula (I = M / (R² + 3r²)) to ensure accuracy, allowing you to quickly determine the rotational inertia without manual derivation.

To maximize the accuracy and usefulness of your calculation, visualize the object's rotation. Consider what axis you are rotating the torus around—our calculator assumes rotation about the central major axis.

• Varying Parameters: If you are testing design iterations, use the tool to quickly compare how a 10% increase in R affects the final moment of inertia value.
• Unit Verification: Before submitting your values, double-check that all inputs (R, r, M) use the same base unit system (SI or Imperial).

If you find yourself needing to calculate this value repeatedly with slight variations, consider using a spreadsheet program alongside our tool for efficient data logging and comparative analysis.