Is this the same as area moment of inertia?

No. This calculator uses mass and returns kg m². Beam-section calculations use area moments such as in⁴ or mm⁴.

When should I use the parallel-axis theorem?

Use it when the new axis is parallel to a known center-of-mass axis and shifted by a distance d.

Why does moving mass outward increase inertia?

Mass farther from the axis contributes with distance squared, so rim-heavy objects resist angular acceleration more.

Moment of Inertia Calculator

Calculate mass moment of inertia for rods, disks, rings, cylinders, spheres, plates, boxes and point masses, with the parallel-axis theorem.

Body and axis position

The axis is perpendicular to the disk and passes through its center

Modelmass, dimensions, and selected axis

Mass, kg

Radius, m

Apply the parallel-axis theorem with a parallel offset

Moment of inertia

5.000e-3 kg*m²

In g*cm²

50,000 g*cm²

Extra - energy and torque

Angular speed, rad/s

Angular acceleration, rad/s²

Rotational energy

0.25 J

from the entered speed

Required torque

0.025 N*m

from the entered acceleration

Supported bodies and axes

Body and axis	Notes
Thin rod - axis through center perpendicular	The axis is perpendicular to the rod and passes through its midpoint
Thin rod - axis through end perpendicular	The axis is perpendicular to the rod and passes through one end
Solid disk - symmetry axis	The axis is perpendicular to the disk and passes through its center
Solid disk - diameter axis	The axis lies in the disk plane and passes through the center
Thin hoop / ring - perpendicular axis	The axis is perpendicular to the hoop plane and passes through the center
Solid cylinder - longitudinal axis	The axis is the main symmetry axis of the cylinder
Hollow cylinder (tube) - longitudinal axis	The axis is the main symmetry axis. Thick-walled tube with R1 and R2
Solid sphere - axis through center	Any axis through the center by symmetry
Thin-walled sphere - axis through center	Thin hollow sphere with an axis through the center
Rectangular plate - perpendicular center axis	The axis is perpendicular to the plate plane and passes through its center
Rectangular cuboid - axis through center	The axis is parallel to side c and passes through the body's center
Point mass at distance r	A point mass at distance r from the rotation axis

Mass moment of inertia

English intent for this page is rotational inertia for physical bodies, not the area moment of inertia used for beam sections.

I = \int r^{2} d m

I is mass moment of inertia, r is distance from the axis and dm is a mass element.

I = I_{c m} + m d^{2}

The parallel-axis theorem shifts a known center-of-mass axis by distance d.

Shape and axis matter

Axis-specific result

The same object can have different moments of inertia around different axes. Choose the shape and axis that match the physics problem.

Frequently Asked Questions

Sources and References

Calculations are based on the listed reference sources. Links open in a new tab.

Updated: June 2, 2026

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