๐ฆ 3D Shape Volume Calculator
Select a common 3D shape โ cube, rectangular box, sphere, cylinder, or cone โ enter its dimensions, and instantly get its volume and surface area. Useful for schoolwork, DIY projects, and estimating packaging sizes.
How to use
- Select the shape you want to calculate (cube, box, sphere, cylinder, or cone).
- Enter the dimensions for that shape (side length, radius, height, etc.).
- The volume and surface area are calculated automatically.
How the calculation works
This tool calculates the volume and surface area of common solids. Cube (side a): volume aยณ, surface 6aยฒ Box (a, b, c): volume abc, surface 2(ab + bc + ca) Sphere (radius r): volume 4/3ฯrยณ, surface 4ฯrยฒ Cylinder (radius r, height h): volume ฯrยฒh, surface 2ฯr(r + h) Cone (radius r, height h): volume 1/3ฯrยฒh, surface ฯr(r + l) (l = โ(rยฒ + hยฒ) is the slant height) A cone's volume is exactly a third of a cylinder with the same base and height, a relationship that can be shown with integration and that also holds between pyramids and prisms.
Worked example
Cube with 5 cm sides: volume 125 cmยณ, surface 150 cmยฒ Sphere of radius 5 cm: volume about 523.6 cmยณ, surface about 314.2 cmยฒ Cylinder, radius 3 cm, height 4 cm: volume about 113.1 cmยณ Cone, radius 3 cm, height 4 cm: slant 5 cm, volume about 37.7 cmยณ (a third of the cylinder) 1,000 cmยณ is 1 litre, so a 10 cm cube holds exactly a litre.
Things to be aware of
- Volume comes out in the cube of your length unit (cmยณ) and surface area in its square (cmยฒ).
- A cylinder's surface includes both ends and the side. For an open container, subtract one end (ฯrยฒ).
- For container capacity, remember the walls' thickness makes the inside dimensions smaller.
FAQ
What units should I use?
This calculator is unit-agnostic. Enter all dimensions in the same unit (e.g. cm), and the results will be in that unit cubed (volume) and squared (surface area).
What does the cone's surface area include?
It's the total surface area: the area of the circular base plus the lateral (side) surface area.
Where do these formulas come from?
These are the standard geometry formulas taught in school (e.g. sphere volume = 4/3 ร ฯ ร radiusยณ).