Solid Volume and Mass Properties

Mass properties of one solid

Choose a solid, enter its dimensions and specify its density. The calculator returns material volume, mass, total surface area, centre of gravity and three mass moments of inertia together. For a hollow body, volume means material volume rather than cavity capacity. A prism measuring 2 m by 3 m by 4 m has a volume of 24 m³. With a density of 1 kg/m³, its mass is 24 kg, its centre is 2 m above the base and its inertia about x is 50 kg·m².

Reading the axes

The z axis runs along the height and coincides with the symmetry axis of a body of revolution. x and y are perpendicular transverse axes through the centre of mass. A cone has its centre h/4 above its base. A solid hemisphere has its centre 3R/8 above its flat base. The displayed inertias refer to these centres. To find inertia about a parallel transverse axis through the base, add mass times the square of the centre height.

Scope

These are ideal solids with uniform density. The calculator does not design lifting arrangements, assess strength or tipping, or perform dynamic balancing. Cavities must be concentric. A frustum may have a bottom radius smaller than its top radius. Equal radii produce a cylinder and a zero top radius produces a cone. Mass inertia uses kg·m² and must not be confused with section area inertia in m⁴.

Frequently asked questions

How do you calculate mass with density?

Multiplying volume by density gives 19200 kg for a solid prism measuring 2 m by 3 m by 4 m at an example density of 800 kg/m³. This assumes ideal geometry and uniform density throughout, with no internal voids or regions of different material.

Calculate with these values