TheCalculatory
Math · Geometry Formula verified

Volume Calculator

Pick a solid, enter its dimensions, and see the volume (and surface area) update instantly, with the formula and a step-by-step proof underneath.

Solid
050100
On-screen number pad
Tap to type into the highlighted field
Volume
64
Cube · side 4
Surface area
96

Step-by-step proofCheck by hand

The formula for each solid

Volume always comes out in cubic units — cubic feet, cubic meters — because it multiplies three lengths together (or a length by itself three times). A cube and a rectangular prism are the same idea: multiply all three dimensions. A cylinder is a circle's area times its height, stacked straight up. A cone and a sphere both taper, which is why their formulas carry a fraction (⅓ for the cone, ⅔ short of a cylinder for the sphere) — they hold less than a cylinder or prism with the same outer dimensions.

The formulas

cube = s³  ·  prism = l × w × h  ·  sphere = 4⁄3πr³  ·  cylinder = πr²h  ·  cone = 1⁄3πr²h

Worked example

A cube with 4-unit sides: volume = 4³ = 64 cubic units, and surface area = 6 × 4² = 96 square units.

Frequently asked questions

Why does a cone need a slant height at all?
The slant height isn't needed for volume — that only depends on the radius and the straight-up height. But it is needed for surface area, since the cone's curved side is really a flattened, unrolled sector of a circle whose size depends on the slant distance from the tip to the rim, not the vertical height. This calculator derives it automatically from the radius and height using the Pythagorean theorem.
Why is a sphere's volume formula so different from a cylinder's?
A cylinder is a stack of identical circles, so its volume is just the base area times height. A sphere has no flat base and its cross-section shrinks toward each pole, so its formula (4⁄3πr³) comes from integrating those shrinking circular slices across the whole sphere rather than multiplying a single area by a length.
What's the difference between volume and surface area?
Volume is how much space a solid takes up on the inside — how much it could hold if it were hollow. Surface area is the total area of its outer skin if you could unfold or unwrap it flat. They use different units too: volume is a length cubed (cubic feet, cubic meters), while surface area is a length squared (square feet, square meters).
Sources and method
  • Standard geometric volume and surface area formulas — general published mathematics.
Last reviewed: 20 Sep 2026 Sources last verified: 20 Sep 2026 Results use the assumptions explained on this page. Report an error How we check calculations

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