Precision Utility
Volume
Calculator
Shapes
6
Output
Volume & SA
Calculate the volume and surface area of any common 3D shape. Choose from cube, cuboid, sphere, cylinder, cone or pyramid, enter your dimensions, and get instant results with the formula used.
Shape & Dimensions
Calculated Volume
1,000.00
cubic units
Volume
1,000.00
Surface Area
600.00
Shape
Cube
Formula
V = s³
How the volume calculator works
Start by selecting one of the six supported 3D shapes from the dropdown: cube, cuboid, sphere, cylinder, cone or pyramid. The calculator automatically shows only the input fields relevant to your chosen shape.
Enter your dimensions using the number fields or the precision sliders. All inputs accept values from 0 to 100 with one decimal place of precision. As you adjust any value, the volume and surface area update instantly.
The result card displays four pieces of information: the calculated volume in cubic units, the surface area in square units, the shape name, and the exact formula used. This makes it easy to verify the calculation or use the formula elsewhere.
You can use any unit of measurement (centimetres, metres, inches, feet) as long as all dimensions use the same unit. The result will be in that unit cubed for volume and squared for surface area.
What you need to know about 3D volumes
Volume is a measure of how much three-dimensional space an object occupies. It is always expressed in cubic units. Surface area measures the total area of all outer faces and is expressed in square units.
Key formulas covered by this calculator:
- Cube: V = s³ and SA = 6s², where s is the side length
- Cuboid: V = l × w × h and SA = 2(lw + lh + wh)
- Sphere: V = 4/3 × π × r³ and SA = 4πr²
- Cylinder: V = πr²h and SA = 2πr(r + h)
- Cone: V = 1/3 × πr²h and SA = πr(r + slant height)
- Pyramid: V = 1/3 × l × w × h (rectangular base)
These formulas are standard geometry and apply regardless of the unit system. They are taught at GCSE level and used widely in engineering, construction, packaging and science.
Frequently asked questions
How do I calculate the volume of a 3D shape?
Select your shape from the dropdown, enter the required dimensions (such as side length, radius or height), and the calculator instantly returns the volume and surface area using the correct geometric formula.
What is the formula for the volume of a sphere?
The volume of a sphere is (4/3) × π × r³, where r is the radius. For example, a sphere with radius 5 has a volume of approximately 523.6 cubic units.
What is the difference between volume and surface area?
Volume measures the three-dimensional space inside a shape (in cubic units), while surface area measures the total area of all outer faces (in square units). Both are useful for different real-world applications like filling containers or wrapping objects.
How do I calculate the volume of a cylinder?
The volume of a cylinder is π × r² × h, where r is the radius of the circular base and h is the height. For example, a cylinder with radius 3 and height 10 has a volume of approximately 282.7 cubic units.
What units should I use?
You can use any unit (cm, m, inches, feet) as long as all dimensions use the same unit. The volume result will be in that unit cubed (e.g. cm³) and the surface area in that unit squared (e.g. cm²).
Why is a cone exactly one-third the volume of a cylinder?
A cone with the same base radius and height as a cylinder has exactly one-third of the cylinder's volume. This relationship is proven using integral calculus — the cross-sectional area of the cone decreases linearly from the base to the apex, resulting in exactly a third of the total volume.