Cuboid

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This page provides a diagram and functioning calculator to compute the mass moment of inertia for a cuboid about varying axes.
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Il=112m(w2+h2)I_l = \frac{1}{12} m (w^2 + h^2)Il​=121​m(w2+h2)
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Ih=112m(l2+w2)I_h = \frac{1}{12} m (l^2 + w^2)Ih​=121​m(l2+w2)
Where:
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Iw=112m(l2+h2)I_w = \frac{1}{12} m (l^2 + h^2)Iw​=121​m(l2+h2)
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Id=16m(w2h2+l2h2+l2w2l2+w2+h2)I_d = \frac{1}{6} m \left(\frac{w^2 h^2 + l^2 h^2 + l^2 w^2}{l^2 + w^2 + h^2}\right)Id​=61​m(l2+w2+h2w2h2+l2h2+l2w2​)
﻿﻿Il​
 - Moment of inertia about the length axis (kg·m²)
﻿﻿Iw​
 - Moment of inertia about the width axis (kg·m²)
﻿﻿Ih​
 - Moment of inertia about the height axis (kg·m²)
﻿﻿Id​
 - Moment of inertia about a diagonal axis passing through the centroid (kg·m²)
﻿﻿l
 - Length (m)
﻿﻿w
 - Width (m)
﻿﻿h
 - Height (m)
﻿﻿m
 - Mass of the body  (kg)
Moment of Inertia For A Solid Cylinder About The Central Diameter CalculatorInputs﻿﻿Mass, m
:10.00kg​
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﻿﻿Length, l
:6.00m​
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﻿﻿Width, w
:1.50m​
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﻿﻿Height, h
:3.00m​
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Output﻿﻿Il, kg m^2
:9.375​
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﻿﻿Il​=121​m(w2+h2)
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﻿﻿Ih, kg m^2
:31.875​
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﻿﻿Ih​=121​m(l2+w2)
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﻿﻿Iw, kg m^2
:37.5​
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﻿﻿Iw​=121​m(l2+h2)
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﻿﻿Id, kg m^2
:15​
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﻿﻿Id​=61​m(l2+w2+h2w2h2+l2h2+l2w2​)
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