Volume Calculator
Calculate volume of 3D shapes easily
What is it?
This calculator finds the volume of common 3D solids — cube, cuboid, sphere, cylinder, and cone — using the standard geometric formula for each.
Formula
- Cube: V = a³
- Cuboid: V = l × w × h
- Sphere: V = 4/3 × π × r³
- Cylinder: V = π × r² × h
- Cone: V = 1/3 × π × r² × h
Formula Explanation
Volume measures the amount of 3D space a solid occupies — for prism-like shapes (cube, cuboid, cylinder), it's the base area multiplied by height; for tapering shapes (cone, sphere), calculus-derived factors like 1/3 or 4/3 account for how the shape narrows or curves.
Example Calculation
A cube with side 4 has volume 4³ = 64 cubic units.
How to Use
- Select the 3D shape.
- Enter the required measurements (side, radius, height, etc.).
- Click Calculate Volume to see the result and formula used.
Benefits
- Covers five common 3D solids in a single calculator.
- Shows the formula used alongside the result for transparency.
- Handles all needed inputs per shape without extra manual steps.
Use Cases
- Estimating how much liquid, material, or air a container can hold.
- Geometry and engineering coursework involving 3D solids.
- Shipping and packaging calculations requiring volume estimates.
What Your Result Means
The result is the amount of 3D space enclosed by the solid, expressed in cubic units matching your input measurements (e.g. cubic meters if you entered meters).
Tips
- Keep all measurements in the same unit before calculating.
- A cone always has exactly one-third the volume of a cylinder with the same radius and height.
- Volume and surface area measure different things — don't confuse cubic units with square units.
Common Mistakes
- Mixing different units (like meters and centimeters) within the same calculation.
- Using the diameter instead of the radius for spheres, cylinders, or cones.
- Confusing volume (cubic units) with surface area (square units).
FAQs
What units is the result in?
The volume is in cubic units matching whatever unit you entered — for example, cm³ if you entered measurements in centimeters.
Why does a cone have 1/3 the volume of a cylinder with the same base and height?
This comes from calculus (integrating the cone's cross-sectional area) — a cone tapers to a point, so it holds exactly one-third the volume of a cylinder sharing the same radius and height.
Do I need the diameter or radius for a sphere?
This calculator expects the radius — if you only know the diameter, divide it by 2 before entering the value.
How does doubling a cube's side affect its volume?
Doubling the side length increases the volume eightfold, since volume scales with the side length cubed.
Can this calculator find volume for irregular shapes?
No, this calculator only covers cube, cuboid, sphere, cylinder, and cone — irregular shapes typically require integration or displacement-based measurement.
Results are in cubic units matching your input measurements.
Last updated: July 25, 2026