Volume of Solids, Tanks, Prisms and Pyramids

Solids vs containers

A solid volume measures how much space an object occupies. A container volume measures how much space is inside the object. The formula can be similar, but the measurement points may be different.

Rectangular tanks and box-shaped containers

Volume = length x width x height

Use inside dimensions when you need capacity. Use outside dimensions when you need the space an object occupies.

Round tanks and cylinders

Volume = pi x radius^2 x height

If a tank is 4 feet across, the diameter is 4 feet and the radius is 2 feet.

Prisms

Volume = base area x length

A prism has the same cross-section along its length. A triangular prism uses half of triangle base times triangle height, then multiplies by prism length.

Triangular prism = 1/2 x triangle base x triangle height x prism length

Pyramids

Volume = 1/3 x base area x height

A pyramid is one-third of a prism with the same base area and height.

Using volume for materials

Volume is often the first estimate for material projects. For construction-style planning, use the Cubic Yard Calculator or Square Feet to Cubic Yards Calculator when cubic yards matter.

Inside capacity vs outside volume

• Outside volume: the space the object occupies.
• Inside capacity: the space the object can hold.
• Wall thickness, rounded corners, lids, slopes, and fill limits can change capacity.

Irregular solids

Some objects do not match simple formulas. For small waterproof objects, water displacement can estimate volume, but do not use it for items that dissolve, absorb water, float, or can be damaged.

Common mistakes

• Using outside dimensions for container capacity.
• Treating a pyramid like a prism and forgetting the one-third factor.
• Forgetting waste, compaction, or fill limits for materials.
• Mixing square feet and cubic feet.