# Mass moment of inertia of an Annulus

Calculates the mass moment of inertia of an annulus or a disk with a hole.

`I_z = 1/2*m*(R^2+r^2)` (about central axis)

`I_x=I_y = 1/4*m*(R^2+r^2)` (about diameter)**Enter 'x' in the field to be calculated.**

We use the following formulas to calculate the mass moment of inertia of an annulus (or disk with a hole) that has concentric outer and inner circles.

Case of a rotation about the disc central axis (z-axis on above diagram),

`I_z = 1/2*m * (R^2+r^2)`

Case of a rotation about a disc diameter (x-axis or y-axis on above diagram),

`I_x = I_y = 1/4*m * (R^2+r^2)`

m : mass of the annulus (kg)

R : annulus outer radius in meter (m)

r : annulus inner radius (or hole radius) in meter (m)

## See also

Mass moment of inertia Calculators

Convert mass units

Convert distance units

Convert units of mass moment of inertia

Physics Calculators