Volume Calculator

Rectangular prism dimensions

Volume

30.00 cm³

  • Surface area: 62.00 cm²

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How This Calculator Works

Volume is the amount of three-dimensional space a solid takes up, and each common shape has its own formula for finding it from a few basic measurements. Pick a shape — rectangular prism, cube, sphere, cylinder, or cone — enter its dimensions, and this calculator returns both the volume and the total surface area.

These five shapes are the solid, one-dimension-up counterparts of the Area Calculator’s own flat shapes: a cube is a square with depth, a sphere is a circle with depth, a cylinder is a circle extruded along a straight axis, and a cone tapers that same circle to a point.

The Formula

Each shape has its own volume formula:

Rectangular Prism: Volume=Length×Width×Height\text{Rectangular Prism: Volume} = \vA{\text{Length}} \times \vB{\text{Width}} \times \vC{\text{Height}} Cube: Volume=Side3\text{Cube: Volume} = \vA{\text{Side}}^3 Sphere: Volume=(43)×π×Radius3\text{Sphere: Volume} = \left(\frac{4}{3}\right) \times \pi \times \vA{\text{Radius}}^3 Cylinder: Volume=π×Radius2×Height\text{Cylinder: Volume} = \pi \times \vA{\text{Radius}}^2 \times \vC{\text{Height}} Cone: Volume=(13)×π×Radius2×Height\text{Cone: Volume} = \left(\frac{1}{3}\right) \times \pi \times \vA{\text{Radius}}^2 \times \vC{\text{Height}}

A cone’s volume is exactly one-third of a cylinder with the same radius and height — the same relationship a cone-shaped and cylinder-shaped container of equal base and height always have, regardless of size.

Worked Example

A cylinder with a 5 m radius and 10 m height:

  1. Square the radius: 52=25\vA{5}^2 = 25.
  2. Multiply by π: 25×π78.5425 \times \pi \approx 78.54.
  3. Multiply by the height: 78.54×10785.40 m378.54 \times \vC{10} \approx 785.40 \text{ m}^3.

Its surface area — the two circular ends plus the curved side — works out to about 471.24 m², using 2×π×radius×(radius+height)2 \times \pi \times \text{radius} \times (\text{radius} + \text{height}).

Source: Wikipedia: Volume.

Frequently Asked Questions

What's the difference between this and the Area Calculator?

Area measures the two-dimensional space a flat shape covers; volume measures the three-dimensional space a solid takes up. This calculator's five shapes are the solid, one-dimension-up counterparts of most of the Area Calculator's own shapes — a cube instead of a square, a sphere instead of a circle, and so on.

How is a cone's surface area calculated?

It's the base circle's area plus the lateral (side) surface, which depends on the cone's slant height — the straight-line distance from the rim to the tip, found from the radius and height with the Pythagorean theorem (slant height = √(radius² + height²)), not the vertical height alone.

Can I switch units after entering my numbers?

Yes — changing the unit dropdown converts whatever you've already typed into the new unit rather than reinterpreting the same number, so your shape stays the same real-world size.