Diagonal do Cubo
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
D = l·√3
About this calculator
The Cube Diagonal calculator determines the length of the space diagonal of a cube, which is the distance between two opposite vertices. This diagonal passes through the interior of the cube, connecting corners that do not share a face. The calculation is useful in various fields such as architecture, engineering, and design, where internal dimensions of cubic structures are needed.
It works simply: enter the side length (edge) of the cube, and the calculator applies the formula D = l × √3, where l is the side. The square root of 3 (approximately 1.732) is a geometric constant derived from the Pythagorean theorem applied in three dimensions. The result is the space diagonal, which is larger than the face diagonal (l × √2).
Use this calculator when you need to dimension objects that fit inside a cube, such as boxes, tanks, or rooms. For example, to check if a long rod can be placed diagonally in a cubic container, or to calculate the distance between opposite corners of a concrete cube. It is also helpful for spatial geometry problems in high school and college.
Cautions: ensure the unit of measurement for the side is consistent with that desired for the diagonal. The formula assumes a perfect cube, with all sides equal and right angles. For rectangular prisms, the formula is different (D = √(a² + b² + c²)). Do not confuse face diagonal with space diagonal: the face diagonal is shorter and uses √2.
Frequently asked questions
What is the difference between face diagonal and cube diagonal?
The face diagonal is the distance between two opposite vertices on the same face, calculated as l × √2. The cube diagonal (space diagonal) connects opposite vertices through the interior, calculated as l × √3, and is longer.
Can I use this calculator for a rectangular prism?
No, the formula D = l × √3 applies only to cubes, where all sides are equal. For rectangular prisms, use D = √(a² + b² + c²), with a, b, c as the three dimensions.
What value of √3 does the calculator use?
The calculator uses √3 ≈ 1.7320508075688772, but you can adjust precision as needed. The exact value is irrational.
How do I convert the diagonal to another unit?
Simply enter the side in the desired unit (e.g., inches) and the result will be in the same unit. To convert later, use a unit converter.
Does this calculator work for cubes with sides in inches?
Yes, it works with any unit of length, as long as it is consistent. The result will be in the same unit as the side entered.