How to use this volume calculator
Select a solid and one common length unit, then enter the dimensions identified by the diagram. Circular solids require radius rather than diameter. Cone and pyramid height is perpendicular to the base, not a sloping side; triangular-prism height belongs to its triangle and is distinct from prism length. Switching shape loads example dimensions, while switching units relabels unchanged numbers. Review the formula and substitution below the result. Use Volume Converter for existing volume quantities and Aquarium Volume Calculator for aquarium fill-height or displacement calculations.
How the calculation works
Volume describes three-dimensional space in cubic units. Lengths in centimeters produce cubic centimeters; lengths in feet produce cubic feet. A geometric solid model uses an ideal boundary supplied by the user. It does not automatically know a container's wall thickness, a safe fill level, an occupied object's mass or how much liquid a porous material displaces. State whether the dimensions describe the full outside solid or an independently measured internal cavity before interpreting the numerical result.
A rectangular prism, also called a cuboid, has volume V=abh from three mutually perpendicular dimensions. A hypothetical 3 m by 2 m by 4 m solid gives 24 m³. A cube is the equal-edge case with V=a³, so edge 3 m gives 27 m³. Replacing one dimension with a face diagonal would not describe the same prism. The schematic marks each dimension to distinguish adjacent edges from an interior cross-measurement.
For a cylinder, multiply circular base area by perpendicular height: V=πr²h. Radius 3 cm and height 5 cm give 45π cm³, about 141.3717 cm³. A cone with the same base radius and perpendicular height has one third of that volume: V=πr²h/3=15π cm³, about 47.1239 cm³. The one-third factor belongs to the full cone model, not a general rule for any tapered object or truncated container.
A complete sphere uses V=4πr³/3. Radius 3 cm gives 36π cm³, about 113.0973 cm³. If the known measurement is diameter 6 cm, divide it by two before entering the radius field. Doubling radius multiplies spherical volume by eight, not two or four. A sphere result does not describe a hemisphere, a hollow shell's material volume or the space above a chosen liquid level inside a ball-shaped vessel.
A triangular prism uses the area of one triangular end multiplied by the distance between the parallel ends. With triangle base b, perpendicular triangle height h and prism length L, V=(bh/2)L. For b=8 cm, h=6 cm and L=10 cm, volume is 240 cm³. The triangle's height is not another name for the prism length. The diagram deliberately uses different labels so the base-face calculation and extrusion distance remain separate.
A rectangular-base pyramid uses V=abh/3, where a and b are base sides and h is perpendicular from the apex to the base plane. Base 8 cm by 6 cm with height 9 cm gives 144 cm³. A slant edge or a triangular face's altitude is not generally the same as the perpendicular solid height. This calculator does not recover missing heights from angles, truncate a pyramid or infer the position of an apex from a photograph.
The result remains in the cube of the selected length unit rather than immediately presenting liters or gallons as if a fluid workflow had been performed. If you already know a volume, Volume Converter can express it in another unit. If you need an aquarium's waterline volume minus independently measured solid displacement, use Aquarium Volume Calculator. The two pages are intentionally linked: common geometric formulas support aquarium reasoning, but a full ideal-solid answer is not automatically the net water used for aquarium dosing or filtration calculations.
Changing the length-unit selector does not convert an existing measurement. A value of 3 interpreted as meters is a different edge from a value of 3 interpreted as centimeters. Convert source lengths into a common unit before calculation, and remember that volume conversion scales with the cube of a length factor. Mixing a width in inches with a length in centimeters without conversion creates an inconsistent multiplication that this unit-label interface cannot repair by guessing.
All required dimensions must be positive, finite and between 1e-9 and 1e12 in the selected unit. Unsupported shapes, zero thickness, negative dimensions and incomplete fields do not produce a result. Arithmetic uses double precision with Math.PI retained internally; displayed figures may be rounded. These are educational geometry calculations, not engineering approval, a load rating, a fluid-dose recommendation or a material quantity guarantee. Verify real boundaries, units and measurement uncertainty separately before using the result in a consequential application.
Formulas
Prisms and cube
Circular solids
Rectangular-base pyramid
Worked examples
Compare a cylinder and cone
With radius 3 cm and perpendicular height 5 cm, cylinder volume is 45π ≈ 141.371669412 cm³. The corresponding full cone is 15π ≈ 47.1238898038 cm³.
Triangular base and a separate prism length
A triangle with base 8 cm and perpendicular height 6 cm has area 24 cm². Extruding it through prism length 10 cm gives 240 cm³, not an aquarium net-water result.
Common uses
Check a solid-geometry calculation
Calculate seven common solids using explicitly labeled base dimensions, radii and perpendicular heights. Cubic units make the three-dimensional interpretation visible.
Compare related shapes
Compare a full cone with a cylinder having the same radius and height, or a rectangular prism with an equal-edge cube. Preserve each model rather than assuming every tapered shape has the same volume ratio.
Choose the appropriate specialist workflow
Use the general solid result for geometry, Volume Converter for known quantities, and Aquarium Volume Calculator for waterline and displacement calculations. Linking them does not merge their assumptions.
Accuracy and limitations
Uses Math.PI and double-precision products with final display rounding. Positive input dimensions must be 1e-9–1e12 in one selected unit; volume is reported in its cubic form.
Does not model partial fills, net aquarium water, displacement, wall thickness, material density, structural load, capacity certification or dosing. Schematic dimensions are not measurements of an actual object.
Sources and methodology
These primary references explain the numerical methods and units used here. Review the calculation assumptions and limitations alongside the result.
Frequently asked questions
Does this calculate aquarium net water?
No. It models full ideal solids. Aquarium Volume Calculator separately supports fill height and independently measured displacement.
Can I use a diameter in the radius field?
No. Divide diameter by two first. Radius enters squared or cubed relationships, so confusing them can create large errors.
Does cone mode use slant height?
No. Use perpendicular height from apex to base plane. The same distinction applies to pyramid mode.
Which solids are supported?
Rectangular prism, cube, cylinder, cone, sphere, triangular prism and rectangular-base pyramid. Other solids and compound shapes need separately specified models.
Why are liters and gallons not primary outputs?
The task here is dimension-based geometry in cubic units. Use Volume Converter afterward for capacity-unit conversions.
Can it infer an internal cavity from outside dimensions?
No. It does not subtract wall thickness or material. Enter independently justified internal dimensions only when an ideal cavity is the intended model.