Volume Calculator
Calculate the volume and surface area of cubes, boxes, spheres, cylinders, cones and square pyramids.
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Tool guide
What this tool does
Select a solid and enter its dimensions to get volume and total surface area together, with the formula and your numbers shown as working. Covers the six 3D shapes that come up most often in geometry, packaging, construction and everyday capacity questions.
Whether you are figuring out how much water a tank holds, how much material wraps a package, or checking a solid-geometry homework answer, the formulas for volume and surface area differ for every shape. This calculator keeps all six common solids in one place: cube, rectangular box, sphere, cylinder, cone and square pyramid.
Pick the shape, enter its dimensions, and both volume and surface area appear together, each with the formula spelled out using your actual numbers so you can sanity-check the arithmetic or learn the derivation.
How to use Volume Calculator
- Choose the solid from the Shape dropdown.
- Enter the dimensions requested — only the fields relevant to that solid are shown.
- Read the Volume result at the top, highlighted for quick scanning.
- Check the Surface area result directly below it.
- For cones and pyramids, note the slant height shown as an intermediate step toward surface area.
- Switch shapes at any time without losing the values you entered for the others.
Tips for better results
- A cone’s slant height is not the same as its vertical height — the tool derives it from the Pythagorean relationship between radius and height automatically.
- For a square pyramid, the "base" field is the length of one side of the square base, not its full area.
- Surface area for a closed box adds all six rectangular faces; if your container is open on top, subtract that one face’s area yourself.
- Keep all dimensions for one shape in the same unit (all centimeters or all inches) since results are computed in whatever unit you entered.
Common use cases
- Estimating how much liquid a cylindrical tank, spherical tank or conical container can hold.
- Working out how much wrapping material or paint covers a box, cylinder or pyramid-shaped surface.
- Checking solid-geometry homework for volume and surface-area problems.
- Comparing packaging options by volume-to-surface-area ratio for shipping or storage efficiency.
Common mistakes to avoid
- Entering a cone or pyramid’s slant height into the Height field — the tool wants the perpendicular (vertical) height and computes slant height itself.
- Using diameter where the radius field is expected for spheres and cylinders, which doubles the error in volume.
- Forgetting that a square pyramid’s volume formula divides by three, unlike a rectangular box of the same footprint and height.
- Mixing centimeters for one dimension and inches for another on the same shape, which silently produces a meaningless result.
Frequently asked questions
What is the difference between a cone’s height and slant height?
Height is the straight vertical distance from the base to the apex; slant height runs along the cone’s curved surface from the base edge to the apex. The calculator derives slant height from the radius and height for you.
Does the box volume formula work for a cube too?
Yes, but the Cube option is simpler to use since it only needs one side length instead of three separate dimensions.
How is a square pyramid’s surface area computed?
It adds the square base area to four identical triangular faces, each using the pyramid’s slant height along the face.
Can I compute an open-top cylinder, like a cup?
The surface area shown includes both circular ends. For an open-top shape, subtract the area of one circular face (πr²) from the result yourself.
Feedback & suggestions
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