Solid volume and usable capacity
Volume measures space inside a three-dimensional shape. The capacity equivalent assumes the entered dimensions describe usable internal space; external dimensions include the material surrounding it.
For a cylinder or box that is only partly filled, use the Tank Volume Calculator .
The formula
Radius is half the diameter. Height is measured perpendicular to the base. The chosen length unit is cubed for volume conversion; one cubic meter is one thousand liters. A cone or pyramid occupies one third of the volume of its matching cylinder or prism.
Worked example
A box 3 m long, 2 m wide, and 4 m high has volume 24 m³, or 24,000 L. A cone of radius 2 m and height 3 m has volume 4π m³, approximately 12.566371 m³.
How to use this calculator
- Choose the solid and the unit used for every dimension.
- Enter internal dimensions for a capacity estimate or external dimensions for overall geometric size.
- Calculate and compare the cubic-unit result with the liter equivalent.
Perpendicular height and slant height
For a cone, the height runs from the base center straight to the apex. It is not the sloping length along the surface. A pyramid also needs the perpendicular distance from the base plane to its apex. Using a slant measurement in place of height makes the volume too large and describes a different solid.
Volume is not mass
The same volume can contain very different masses depending on the material. A volume calculation alone does not determine weight, density, structural loading, or the amount of dry material required after compaction. If you are estimating a concrete pour, use the concrete calculator to include its specific bag-yield and allowance controls.
Containers and partial filling
This tool returns the full ideal geometric volume, without wall thickness or unused headroom. A sphere is a complete sphere, rather than a hemisphere or cap. For a partially filled cylinder or rectangular tank, use the tank-volume calculator. A liter result here is a unit conversion and does not imply that a container can safely hold that amount.
Assumptions & limitations
What this calculation assumes
- Each solid has ideal dimensions and a positive radius or side length.
What to keep in mind
- No wall thickness, partial-fill geometry, density, or construction allowance.
Common questions
Why does a cone use a factor of one third?
A cone has one third the volume of a cylinder with the same base area and perpendicular height.
Can I mix feet and inches?
Choose one unit and convert every dimension to it before entry. Mixing units in the same formula produces an incorrect volume.