What is the formula for a solid disk?

I = (1/2) × M × R², where M is the total mass in kg and R is the outer radius in meters. The result is in kg·m².

What is the formula for a hollow (annular) disk?

I = (1/2) × M × (R₁² + R₂²), where R₁ is the inner radius and R₂ is the outer radius. M is the total mass of the annular disk.

Why is the hollow disk formula different from the solid one?

A hollow disk has mass distributed farther from the axis on average, so its moment of inertia per unit mass is higher. Integrating the mass distribution over the annular cross-section yields the (R₁² + R₂²) term.

Does the disk thickness matter?

No — the central-axis moment of inertia formula is independent of thickness. Thickness affects mass (and therefore I indirectly), but not the geometric factor.

What units does this calculator use?

Mass in kilograms (kg), radii in meters (m), and the result in kilogram-square-meters (kg·m²), which is the SI unit for moment of inertia.

Can I enter radii in centimeters?

The calculator expects meters. To convert, divide centimeters by 100 (e.g., 25 cm = 0.25 m) before entering the value.

Moment of Inertia — Disk Calculator

Calculate the moment of inertia for a solid disk or hollow annular disk about its central axis.

Disk Parameters

Disk Type

Mass (kg)

Radius R (m)

Result

Fill in the parameters and click Calculate.

Disk Moment of Inertia Reference

Disk Type	Formula	Notes
Solid Disk	I = ½MR²	Uniform density, axis through center
Hollow Annular Disk	I = ½M(R₁² + R₂²)	R₁ = inner radius, R₂ = outer radius

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Summary

The moment of inertia of a disk quantifies its resistance to rotational acceleration about a central axis. For a solid disk, the formula is I = (1/2)MR², while a hollow annular disk uses I = (1/2)M(R₁² + R₂²). This calculator handles both cases, accepting mass in kilograms and radii in meters, and returns the result in kg·m².

How it works

Select either Solid Disk or Hollow (Annular) Disk mode.
Enter the total mass of the disk in kilograms.
For a solid disk, enter the outer radius. For a hollow disk, enter both inner and outer radii.
The calculator instantly applies the appropriate formula and displays I in kg·m².
Use the Copy button to copy the result for use in other calculations.

Use cases

Engineering design of rotating machinery such as flywheels and pulleys.
Physics coursework and homework problems on rotational dynamics.
Robotics joint torque calculations requiring rotational inertia.
Comparing solid vs. hollow disk configurations for a given mass.
Automotive wheel and brake rotor inertia estimation.
Gyroscope and stabilizer design in aerospace applications.

Frequently Asked Questions

Last updated: 2026-06-13 · Reviewed by Nham Vu