What is the formula for the diagonal of a rectangle?

The diagonal of a rectangle is found using the Pythagorean theorem: diagonal = square root of (length squared plus width squared), written as d = sqrt(l^2 + w^2). This works because a rectangle's diagonal splits it into two right-angled triangles, with the diagonal as the hypotenuse and the length and width as the two shorter sides.

Do both diagonals of a rectangle have the same length?

Yes. A rectangle has two diagonals and they are always equal in length, because opposite sides of a rectangle are equal and each diagonal forms a right-angled triangle with the same pair of side lengths. This is one of the defining properties of a rectangle, and it is also true for squares since a square is a special rectangle.

How do I find the length or width if I know the diagonal?

Rearrange the Pythagorean theorem. If you know the diagonal (d) and one side, the other side is found using: missing side = square root of (d^2 minus known side^2). For example, if the diagonal is 5 m and the length is 4 m, the width is the square root of (25 minus 16), which is 3 m.

Diagonal of a Rectangle Calculator

Enter the length and width of any rectangle to instantly find the length of its diagonal, using the Pythagorean theorem. This calculator also works out the perimeter, area and the angle the diagonal makes with the length side.

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Method verified Standard Pythagorean theorem geometry, applicable to any unit of length.

1. Rectangle Dimensions

Length (longer side)

Width (shorter side)

Unit of measurement

2. About the Diagonal

A rectangle's diagonal is the straight line connecting two opposite corners. It splits the rectangle into two identical right-angled triangles, so its length is found with:

d = √(length² + width²)

Rectangle Results

Diagonal Length
-
-

Perimeter

Sum of all 4 sides

Area

Length × width

Diagonal Angle

From the length side

Calculation Breakdown

Length-

Width-

Length squared-

Width squared-

Sum of squares-

Diagonal (square root)-

Other Properties

Perimeter-

Area-

Angle between diagonal and length-

Angle between diagonal and width-

Both diagonals equal?Yes, always

Result: Enter a length and width above.

How to Find the Diagonal of a Rectangle

A rectangle has two diagonals, each connecting a pair of opposite corners. Because a rectangle has four right angles, drawing a diagonal splits it into two right-angled triangles. The diagonal itself becomes the hypotenuse of each triangle, while the length and width form the two shorter sides. This means the Pythagorean theorem applies directly: the diagonal squared equals the length squared plus the width squared.

The Formula

The diagonal (d) of a rectangle with length (l) and width (w) is:

d = √(l² + w²)

For example, a rectangle with a length of 8 m and a width of 6 m has a diagonal of √(8² + 6²) = √(64 + 36) = √100 = 10 m. This is a well-known "3-4-5 triangle" scaled up, which is why it gives a whole number result.

Working Example

Step	Calculation	Result
Square the length	8²	64
Square the width	6²	36
Add the squares	64 + 36	100
Take the square root	√100	10 m

Finding a Missing Side from the Diagonal

If you already know the diagonal and one side, you can rearrange the formula to find the missing side: missing side = √(d² minus known side²). This is useful when measuring a space where the diagonal is easier to check than a single side, such as confirming a door frame, deck, or garden bed is square (a true rectangle has equal diagonals, so if both diagonals match, the corners are 90 degrees).

Where This Is Used

Checking that a building frame, deck, or garden bed is square by comparing the two diagonals
Working out the screen size (diagonal) of a TV, monitor or phone from its width and height
Finding the longest straight object that will fit flat inside a rectangular box or room
Geometry and trigonometry study, including angle and triangle problems

Related Calculators

Maths and Stats Calculators: the full hub of maths tools.
Area of a Rectangle Calculator: work out area from length and width.
Diagonal of a Square Calculator: the special case where all sides are equal.
Pythagorean Theorem Calculator: the underlying formula for any right-angled triangle.
Perimeter Calculator: work out the perimeter of common shapes.

Sources: Pythagorean theorem, standard Euclidean geometry (rectangle diagonal = hypotenuse of two congruent right-angled triangles formed by the length and width).

This calculator applies standard geometry and works with any consistent unit of measurement. Results are rounded for display; use more decimal places for engineering or construction precision.

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