Diagonal of a Rectangle Calculator

Calculate the diagonal of a rectangle precisely — enter your dimensions and get the result with the formula shown.

Quick Facts

Diagonal formula
d = √(l² + w²)
Follows from the Pythagorean theorem — the diagonal is the hypotenuse of the right triangle formed by the length and width.
Equal diagonals
Both diagonals are equal
A rectangle's two diagonals are the same length and bisect each other at the center.
Diagonal angle
θ = arctan(w / l)
The angle the diagonal makes with the length side.

Your Results

Calculated
Diagonal Length
-
d = √(l² + w²)
Angle with Length Side
-
θ = arctan(w / l)
Area
-
A = l × w
Perimeter
-
P = 2(l + w)

Ready

Enter the length and width, then press Calculate.

Formula and Method for the Diagonal of a Rectangle

A rectangle is a four-sided polygon with two pairs of equal, parallel sides and four 90° corners. Drawing a line between two opposite corners splits the rectangle into two right triangles, with the length and width as the legs and the diagonal as the hypotenuse. By the Pythagorean theorem, the diagonal is d = √(l² + w²), where l is the length and w is the width. This calculator also derives the angle the diagonal makes with the length side, the area, and the perimeter from the same two measurements.

How the calculation works

Enter the length and width and choose the unit they are measured in. The calculator squares each value, adds them, and takes the square root to get the diagonal: d = √(l² + w²). It finds the angle between the diagonal and the length side with θ = arctan(w / l), converted to degrees. It also multiplies length by width for the area (A = l × w) and adds all four sides for the perimeter (P = 2(l + w)).

Common mistakes

  • Adding instead of using the Pythagorean theorem: the diagonal is not l + w. For an 8 ft by 6 ft rectangle, the diagonal is √(8² + 6²) = √100 = 10 ft, not 14 ft.
  • Mixing units: keep length and width in one consistent unit — convert inches to feet, or centimeters to meters, before entering the values.
  • Confusing the diagonal with a side: the diagonal is always longer than either the length or the width, since it's the hypotenuse of the right triangle they form.

Real-world applications

  • Carpentry and construction use the 3-4-5 (or measured-diagonal) method to "square" a rectangular frame or foundation: equal diagonals confirm the corners are true 90° angles.
  • TV, monitor, and picture-frame sizes are usually quoted as the diagonal measurement, so this formula converts between diagonal and the actual width/height.
  • Moving furniture or equipment through doorways or stairwells often depends on the diagonal, which is the longest straight-line dimension of a rectangular object.
  • Land surveying and CAD layout use the diagonal and angle to verify rectangular plots and panels are correctly proportioned.

Frequently Asked Questions

What is the formula for the diagonal of a rectangle?
The diagonal of a rectangle is d = √(l² + w²), where l and w are the length and width. This comes directly from the Pythagorean theorem, since the diagonal is the hypotenuse of the right triangle formed by two adjacent sides.
Are the two diagonals of a rectangle the same length?
Yes. Both diagonals of a rectangle are equal in length and bisect each other at the rectangle's center, a property that follows from a rectangle being a parallelogram with four right angles.
How do I find the angle the diagonal makes with the sides?
The angle between the diagonal and the length side is θ = arctan(w / l), and the angle between the diagonal and the width side is 90° − θ (equivalently arctan(l / w)).
Can I find a missing side if I know the diagonal and one side?
Yes. Rearranging the Pythagorean theorem gives w = √(d² − l²) (or l = √(d² − w²)), as long as the diagonal is longer than the known side.

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