Cube, rectangular box, cylinder, sphere, cone and pyramid — volume, plus surface area where it applies.
A rectangular box 4 × 3 × 5 has a volume of 4 × 3 × 5 = 60 and a surface area of 2 × (4×3 + 3×5 + 4×5) = 2 × 47 = 94 — each of the box's three distinct face-pairs counted once, then doubled for the matching face on the opposite side.
This page's cone surface area uses πr(r + √(r² + h²)) — that square root is the slant height, the hypotenuse of a right triangle formed by the radius and the height as the two legs. It is the exact same relationship the Right Triangle Calculator solves directly: lay a cone on its side and the radius, height, and slant edge are just a right triangle's two legs and hypotenuse, wrapped around an axis.
Double every dimension of any solid on this page and volume rises eightfold while surface area only quadruples — volume is a cubic quantity, surface area a square one, and scaling can't change that relationship. That is also why comparing a volume figure to a surface-area figure the way the coincidental sphere example above does is a units mismatch, not a meaningful ratio: one is measured in cubic units, the other in square units, and the two only appear comparable when the units are dropped. The Surface Area Calculator isolates that second quantity on its own, across the same set of solids, and the Area Calculator covers the equivalent flat 2D shapes this page's solids are built from.
| Solid | Volume |
|---|---|
| Cube | a³ |
| Rectangular box | l × w × h |
| Cylinder | πr²h |
| Sphere | ⁴⁄₃πr³ |
| Cone | ⅓πr²h |
| Pyramid | ⅓ × base area × h |
A cone holds exactly one third of the cylinder that encloses it, and a pyramid one third of its enclosing prism — same base, same height. It is worth knowing because it turns two formulas into one idea: anything that tapers to a point holds a third of the straight-sided shape around it.
Double every dimension and volume goes up eightfold, while surface area only quadruples. This square-cube relationship is why large animals have proportionally thicker legs, why a small cup of coffee cools faster than a large one, and why scaling a physical design up is rarely as simple as multiplying every number.
A sphere of radius 3 has a volume of 113.0973 and a surface area of 113.0973 — numerically identical, which is a coincidence of that particular radius rather than anything meaningful, and a good reminder to keep track of units.
Because integrating the cross-sectional area of a shape that tapers linearly to a point yields exactly a third of the constant-area case. The same reasoning gives a pyramid one third of its prism. You can demonstrate it physically: three cone-fulls of water fill the matching cylinder exactly.
Multiply by 1,000 — one cubic metre is exactly 1,000 litres. For cubic feet to gallons, multiply by 7.4805 for US gallons or 6.2288 for imperial.
Because a pyramid’s surface area depends on the slant heights of its faces, which are not determined by base length, base width and vertical height alone unless the pyramid is right and regular. Quoting a single figure would be wrong for most inputs.
Volume rises with the cube of scale while surface area rises with the square. Doubling a shape gives eight times the volume but only four times the surface, which is why heat loss, structural loading and material costs do not scale in step with size.
Every hypotenuse, leg, and slant height computed on this page traces back to the same relationship the Pythagorean Theorem Calculator solves directly — a² + b² = c², applied here to a cone's radius and height instead of a flat triangle's two legs.
For the outside rather than the inside, use the Surface Area Calculator. Two-dimensional shapes are covered by the Area Calculator and the Circle Calculator. To switch between cubic units and litres or gallons, use the Unit Converter. Once you have a volume, the Density Calculator converts it to mass for any material, and the Molarity Calculator does the same for a solution. For material ordering rather than pure geometry, the Concrete Calculator, Mulch Calculator and Gravel Calculator convert volume into cubic yards, bags and tonnage. Landscaping volumes specifically: the Mulch Calculator and Gravel Calculator convert an area and depth straight into cubic yards and bags.