Volume Calculator
Cube, Prism, Sphere, Cylinder & Cone
Choose a 3D shape, enter its dimensions, and calculate its total volume.
Understanding Volume
Volume tells you how much three-dimensional space a solid occupies — how much water it could hold, how much material it takes to fill it, or how much cargo it can carry.
This calculator covers the cube, rectangular prism (box), sphere, cylinder, and cone — the five 3D shapes you'll encounter most often in geometry, packaging, and engineering.
Because volume measures three-dimensional space, results are always expressed in cubic units (in³, cm³, m³, and so on) — never linear or square units.
The Five Formulas
Cube
Rectangular Prism
Sphere
Cylinder
Cone
Why the Cone and Sphere Formulas Have Fractions
A cone's volume is exactly one-third that of a cylinder sharing the same base radius and height — a relationship provable with calculus, but also demonstrable by filling three cones and pouring them into a cylinder of matching dimensions. A sphere's 4/3 factor comes from a similar integral derivation. Both fractions are constants baked into the geometry itself, not rounding artifacts, so the calculator applies them exactly.
Cube, rectangular prism, sphere, cylinder, and cone.
Volume measures a solid's interior capacity, not its exterior covering.
Spheres, cylinders, and cones all rely on π for their curved volume.
Key Takeaways
- Volume is always in cubic units — it measures capacity, not a surface covering.
- A cone's volume is exactly one-third of a matching cylinder's, and a sphere's carries a 4/3 factor — both exact, not approximate.
- Need the exterior covering instead? Use the companion Surface Area Calculator for the same five shapes.
Frequently Asked Questions
- Choose a shape from the dropdown — Cube, Rectangular Prism, Sphere, Cylinder, or Cone.
- Enter the required dimensions for that shape (all values must be positive numbers).
- Click "Calculate" to see the total volume.
Volume is the amount of three-dimensional space enclosed inside a solid, measured in cubic units. It's how much the shape can hold — think of it as how much water it would take to completely fill the object.
Volume measures the three-dimensional space a solid occupies (in cubic units, like cm³), while surface area measures the two-dimensional "skin" that wraps around it (in square units, like cm²). A shape can have a large volume but a relatively small surface area, or vice versa. Use our Surface Area Calculator to find how much surface covers a shape instead of how much space it holds.
A cone's volume is exactly one-third of a cylinder with the same base radius and height. This can be proven with integral calculus, but it's also demonstrable physically: three cones of identical base and height, filled with a substance and emptied into a cylinder of the same base and height, will fill it exactly. The sphere's 4/3 factor comes from a related derivation using the same underlying calculus.
No — this calculator is unit-agnostic. Enter all dimensions for a single calculation in the same unit (all in centimeters, all in inches, etc.), and the result will be in that unit cubed. Mixing units within one calculation will give an incorrect result.
A cube is just a special case of a rectangular prism where length, width, and height are all equal, so its volume formula s³ is a simplified version of the general l × w × h formula used for any box shape.