3D Volume Calculator

Nobody works out a cylinder’s volume because they wanted a number in cubic centimetres. They want to know whether the barrel holds enough water, whether the tank on the listing is really a 200-litre one, how many bags of soil will fill the planter. 3D Volume Calculator gives you the cubic figure and then keeps going, converting it into litres, US gallons and cubic metres in the same view.

Six solids are covered: cube, rectangular box, sphere, cylinder, cone and square pyramid. Each reports its surface area next to its volume, which is the number that matters when you are buying paint, wrapping film or sheet metal rather than filling something up.

The unit selector does more than it looks like it does. It is not a label stuck on the answer — it feeds the capacity conversion, so 30 and 90 read as centimetres and the same two numbers read as inches produce two different litre figures, both correct. The arithmetic runs in the page you are on.

A Real Example: A Rain Barrel in Litres

The first press of Load Sample sets up a rain barrel: a cylinder with a 30 cm radius and a 90 cm height. Volume comes back as 254,469 cm³ and surface area as 22,619.5 cm², while the capacity row reads 254.469 litres, 67.2236 US gallons and 0.254469 cubic metres. Below that, the Working line prints V = π × 30² × 90 = 254,469 cm³ with your own numbers substituted in place of the symbols. Press the button again and the pool moves on; it cycles through six real objects, from a 6.5 inch exercise ball up to the Great Pyramid at 230 m across and 146 m tall.

The Six Formulas and Where the Thirds Come From

• Cube and box are the plain ones: V = s³ and V = l × w × h. Their surface areas are 6s² and 2(lw + lh + wh).
• Sphere is V = ⁴⁄₃ × π × r³ with a surface of 4πr². Radius, not diameter: halve the width of the ball before typing it, or the answer comes out eight times too large.
• Cylinder is V = π × r² × h and cone is V = ⅓ × π × r² × h. A cone is exactly one third of the cylinder that encloses it, sharing its base and its height, and a square pyramid stands in that same relation to its box at V = ⅓ × a² × h.
• Cone surface area uses the slant height √(r² + h²) rather than the vertical height. That substitution is the single most common wrecker of a hand calculation, and it is why a cone can report a surface area larger than you expected.

Precision, the Dimension Cap, and What Rounds

Every figure is rounded to 6 significant figures, and anything beyond 1e15 or below 0.0001 switches to exponential notation so the display never clips. Each dimension is capped at 1,000,000 in whichever unit is selected; go past it and the field answers “Base edge is capped at 1,000,000 m — cubing anything larger pushes the volume past 10¹⁸, where a double stops holding whole numbers exactly.” Leave a required dimension empty and you get “A cylinder needs all 2 dimensions before it has a volume.” instead of a half-computed answer. One honest limit on the capacity row: it treats the solid as a hollow container filled level with its opening, so a real tank built to these outside dimensions holds less, because the wall thickness sits inside them.