Square Diagonal Calculator
Calculate the diagonal of a square instantly. Features visual geometry overlay and area-based reverse calculations for carpentry and layout tasks.
About
Precise diagonal measurements define the accuracy of tiling, framing, and fabrication layouts. A square that lacks equal diagonals is a rhombus, a structural error that propagates through subsequent construction phases. This tool solves the diagonal length d using the Pythagorean theorem when side length a is known, or reverses the process to find dimensions from a known area.
Carpenters often rely on the 1.414 ratio rule, but rounding errors accumulate over large spans. This calculator computes exact float values, ensuring cuts for trusses or large-format tiles fit perfectly. Correct layouts prevent material waste and structural misalignment.
Formulas
The relationship between the side and diagonal of a square relies on the Pythagorean theorem where width and height are identical.
If calculating from Area A:
Reference Data
| Side Length (a) | Diagonal (d) | Area (A) | Note |
|---|---|---|---|
| 1 | 1.414 | 1 | Unit Square |
| 10 | 14.142 | 100 | Common Tile |
| 12 | 16.971 | 144 | Imperial Foot |
| 24 | 33.941 | 576 | Standard Panel |
| 50 | 70.711 | 2500 | Mid-size Layout |
| 100 | 141.421 | 10000 | Hectometer Base |
| 250 | 353.553 | 62500 | Large Span |
| 500 | 707.107 | 250000 | Structural Base |