Diagonal of a Square Calculator - Side, Area & Perimeter

What Is the Diagonal of a Square?

The diagonal of a square is a line segment connecting two opposite corners. It bisects the square into two congruent 45-45-90 right triangles. Knowing the diagonal helps with layout, construction, and geometry problems.

Use our Square Area Calculator or Rectangle Diagonal Angle Calculator for related shapes.

Diagonal of a Square Formula

From side length $a$:

$$d = a\sqrt{2}$$

From area $A$:

$$d = \sqrt{2A}$$

From perimeter $P$:

$$d = \frac{P}{4}\sqrt{2}$$

Worked Example

A square has side 9 units. Its diagonal is $9\sqrt{2} \approx 12.728$ units. The area is $9^2 = 81$ square units.

Frequently Asked Questions

What is the diagonal of a square with side 1?

The diagonal is √2, approximately 1.414. This follows from d = a√2 with a = 1.

How do I find the side from the diagonal?

Divide the diagonal by √2: a = d / √2. For d = 10, a ≈ 7.071.

What is the diagonal of a square with area 50?

Use d = √(2A) = √(100) = 10 units.

Are the diagonals of a square equal?

Yes. Both diagonals have the same length, are perpendicular bisectors of each other, and bisect the corner angles.

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Square Diagonal Calculator

What Is the Diagonal of a Square?

Diagonal of a Square Formula

Worked Example

Frequently Asked Questions

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