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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.

geometry carpentry layout diagonal square

Formulas

The relationship between the side and diagonal of a square relies on the Pythagorean theorem where width and height are identical.

d = a 2

If calculating from Area A:

a = A

Reference Data

Side Length (a)Diagonal (d)Area (A)Note
11.4141Unit Square
1014.142100Common Tile
1216.971144Imperial Foot
2433.941576Standard Panel
5070.7112500Mid-size Layout
100141.42110000Hectometer Base
250353.55362500Large Span
500707.107250000Structural Base

Frequently Asked Questions

The square root of 2 is irrational (approx 1.41421356). In physical construction, this means you can never cut a diagonal with infinite precision, but using 1.414 or 1.4142 provides sufficient accuracy for most engineering tolerances.
No. This specific algorithm assumes all four sides are equal length. For rectangles where width differs from height, use the Rectangle Diagonal Calculator which accounts for two distinct variables.
Measure both diagonals. If diagonal AC equals diagonal BD, and opposite sides are equal length, the corners are exactly 90 degrees.