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Rectangle Diagonal & Angle Calculator

Find the length of a rectangle's diagonal and the angles it makes with the sides using the Pythagorean theorem and inverse tangent. Enter the width and height and get the diagonal, both angles, area and perimeter.
Horizontal side length
Vertical side length
Diagonal length
10

Length of the diagonal using the Pythagorean theorem

Diagonal
10
Angle (diagonal vs width)
36.8699°
Angle (diagonal vs height)
53.1301°
Area
48
Perimeter
28
w = 8h = 6d = 10
Diagonal d splits the rectangle into two right triangles: d² = w² + h²
Step by step
  1. 1

    Width squared

    8² = 8 × 8 = 64
  2. 2

    Height squared

    6² = 6 × 6 = 36
  3. 3

    Diagonal

    √(64 + 36) = 10
    Pythagorean theorem: d = √(w² + h²)
Results are estimates for general information only and are not professional advice — always verify important results independently before relying on them. Read the full disclaimer.
Quick answer

How does this calculator work?

The diagonal of a rectangle is d = √(w² + h²). The angle between the diagonal and the width is θ = arctan(h/w); the complementary angle with the height is 90° − θ. Enter width and height to get the diagonal length and both angles instantly.

Formula
d = √(w² + h²) • θ = arctan(h / w)
How this is calculated

Every rectangle can be divided into two congruent right triangles by drawing a diagonal. The diagonal becomes the hypotenuse, and the width and height become the two legs. The Pythagorean theorem gives the diagonal length: d = √(w² + h²).

The angle that the diagonal makes with the width (the base angle θ) is found with the inverse tangent: θ = arctan(h / w), measured in degrees. The angle with the height is the complementary angle 90° − θ. Both diagonals of a rectangle are equal in length and bisect each other, so there are two diagonals forming identical pairs of angles.

This calculator assumes any consistent unit for width and height (cm, m, inches, etc.) — the diagonal is returned in the same unit. For a square (w = h), the angle is always 45°.

Frequently asked questions

Yes. In any rectangle both diagonals are equal in length and bisect each other at their midpoints. This is a defining property of rectangles (and squares).

In a square w = h, so θ = arctan(h/w) = arctan(1) = 45°. Both diagonals always meet the sides at exactly 45°.

To check that a framed rectangle is square, measure both diagonals — if they are equal the corners are right angles. You can also use d = √(w² + h²) to pre-cut diagonal bracing to the exact required length.

Also known as

diagonal of a rectangle
rectangle diagonal length
angle of rectangle diagonal
pythagorean rectangle diagonal
rectangle corner to corner distance
diagonal angle degrees rectangle
rectangle hypotenuse calculator

APA

TG we-Calculate Editorial Team. (2026). Rectangle Diagonal & Angle Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/rectangle-diagonal-angle-calculator

Chicago

TG we-Calculate Editorial Team. "Rectangle Diagonal & Angle Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/rectangle-diagonal-angle-calculator.

IEEE

TG we-Calculate Editorial Team, "Rectangle Diagonal & Angle Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/rectangle-diagonal-angle-calculator

BibTeX

@misc{wecalculate_rectangle_diagonal_angle_calculator, title = {Rectangle Diagonal & Angle Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/rectangle-diagonal-angle-calculator}}, year = {2026}, note = {TG we-Calculate} }

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