Moment of Inertia Calculator
Results
Moment of Inertia (Ix)
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Moment of Inertia (Iy)
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Polar Moment of Inertia (J)
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Radius of Gyration (r)
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About Moment of Inertia
The moment of inertia is a measure of an object's resistance to changes in its rotation. It depends on the mass distribution relative to the axis of rotation.
Rectangle
Ix = (bh³)/12
Iy = (hb³)/12
Where b is the base width and h is the height.
Circle
Ix = Iy = (πr⁴)/4
J = (πr⁴)/2
Where r is the radius.
Triangle
Ix = (bh³)/36
Iy = (hb³)/36
Where b is the base width and h is the height.
Hollow Circle
Ix = Iy = π(R⁴ - r⁴)/4
J = π(R⁴ - r⁴)/2
Where R is the outer radius and r is the inner radius.
Hollow Rectangle
Ix = (BH³ - bh³)/12
Iy = (HB³ - hb³)/12
Where B,H are outer dimensions and b,h are inner dimensions.
Radius of Gyration
r = √(I/A)
Where I is the moment of inertia and A is the cross-sectional area.