Cube Calculator (Volume, Surface Area & Diagonal)
Cube Calculator (Volume, Surface Area & Diagonal)
A cube is the simplest 3D shape - six equal square faces, all edges the same length. Enter the side length (in whatever unit you like; the volume comes out in that unit cubed, and the area in that unit squared), and this calculator finds the volume, total surface area, and the space diagonal (the straight line from one corner through the center to the opposite corner), along with a diagram and the full step-by-step working.
- V = a³, so a cube with a 5-unit side has a volume of 5³ = 125 cubic units.
- SA = 6a², since a cube has 6 identical square faces - a 5-unit cube has a surface area of 6 × 5² = 150 square units.
- The space diagonal is d = a√3 (not a√2, which is the diagonal of just one square face) - a 5-unit cube has a space diagonal of 5√3 ≈ 8.66 units, found using the 3D Pythagorean theorem.
How do I find the volume of a cube?
Cube the side length: V = a³. A cube with a side of 5 has a volume of 5³ = 125.
How is a cube's space diagonal different from a face diagonal?
A face diagonal (across one square face) is a√2, while the space diagonal (corner to opposite corner through the cube's interior) is a√3 - it's longer because it also accounts for the cube's depth.
Cube Calculator (Volume, Surface Area & Diagonal)
A cube is the simplest 3D shape - six equal square faces, all edges the same length. Enter the side length (in whatever unit you like; the volume comes out in that unit cubed, and the area in that unit squared), and this calculator finds the volume, total surface area, and the space diagonal (the straight line from one corner through the center to the opposite corner), along with a diagram and the full step-by-step working.
- V = a³, so a cube with a 5-unit side has a volume of 5³ = 125 cubic units.
- SA = 6a², since a cube has 6 identical square faces - a 5-unit cube has a surface area of 6 × 5² = 150 square units.
- The space diagonal is d = a√3 (not a√2, which is the diagonal of just one square face) - a 5-unit cube has a space diagonal of 5√3 ≈ 8.66 units, found using the 3D Pythagorean theorem.
How do I find the volume of a cube?
Cube the side length: V = a³. A cube with a side of 5 has a volume of 5³ = 125.
How is a cube's space diagonal different from a face diagonal?
A face diagonal (across one square face) is a√2, while the space diagonal (corner to opposite corner through the cube's interior) is a√3 - it's longer because it also accounts for the cube's depth.