diagonal of a square calculator

What is the diagonal of a square?

The diagonal of a square is the straight line that connects one corner (vertex) to the opposite corner. It cuts the square into two congruent right triangles. Because each angle in a square is 90°, the diagonal can be found using the Pythagorean theorem.

Diagonal of a square formula

If the side length of a square is s, then the diagonal d is:

d = s√2

Since √2 is approximately 1.41421356, you can also estimate:

d ≈ 1.414 × s

Why this formula works

A diagonal divides a square into two right triangles where both legs are equal to s. By the Pythagorean theorem:

d² = s² + s² = 2s², so d = s√2

How to use this calculator

• Enter the side length of your square.
• Optionally add a unit such as cm, m, inches, or feet.
• Choose the number of decimal places you want.
• Click Calculate diagonal to get your answer instantly.

Worked examples

Example 1: Side length = 5 cm

d = 5 × √2 = 7.071 cm (rounded to 3 decimals)

Example 2: Side length = 12 m

d = 12 × √2 = 16.971 m (rounded to 3 decimals)

Common mistakes to avoid

• Using side × 2 instead of side × √2.
• Mixing units (for example, entering side length in inches but reading output as centimeters).
• Rounding too early in multi-step calculations.
• Entering negative values for side length.

Where square diagonal calculations are used

Calculating a square’s diagonal is useful in design, carpentry, architecture, construction, engineering layouts, digital graphics, and classroom geometry. It helps when checking whether a frame is truly square and when determining the longest internal distance across a square shape.

Quick FAQ

Can I calculate side length from the diagonal?

Yes. Rearranging the formula gives s = d / √2.

Does the formula change with units?

No. The formula stays the same. Only the measurement unit changes.

Is this calculator accurate?

Yes. It uses JavaScript’s floating-point math and displays values at your chosen precision.