Inputs
Formula and steps
The space diagonal of a rectangular cuboid with edges L, W, and H is given by:
d = √(L² + W² + H²)
Face diagonals for each side are:
- Front/Back (L × H): √(L² + H²)
- Left/Right (W × H): √(W² + H²)
- Top/Bottom (L × W): √(L² + W²)
Results
Enter dimensions then press Calculate to see the space and face diagonals.
Quick notes
- All dimensions must be positive real numbers.
- Use the same unit for all three dimensions.
- Change decimal places to control rounding.
- Space diagonal is always longer than any face diagonal.
FAQs
The space diagonal is d = √(L² + W² + H²), derived from applying the Pythagorean theorem twice.
Use the same unit for length, width, and height. The results will be in that same unit.
Each face of the cuboid has a diagonal: √(L² + W²), √(L² + H²), and √(W² + H²).
Decimal places control rounding in the displayed results. Increase for more precision or lower for simpler values.
No. All dimensions must be strictly positive for a physical cuboid. The tool enforces this with validation.
Yes. If L = W = H = a, then the space diagonal is √(3a²) = a√3.
Results are computed using double precision floating point arithmetic. Display rounding is controlled by the decimal places setting.
By the Pythagorean relationship, √(L² + W² + H²) is strictly greater than L, W, or H when all are positive.