Diagonal of a Rectangle Calculator
Enter the length and width of a rectangle to instantly find the diagonal (the straight-line distance from one corner to the opposite corner), the angle the diagonal makes with the length, the area, and the perimeter.
Length of the diagonal from corner to corner
- 1
Square the length
8 × 8 = 64 - 2
Square the width
6 × 6 = 36 - 3
Sum of squares
64 + 36 = 100 - 4
Diagonal = √(l² + w²)
√100 = 10Pythagorean theorem — the diagonal is the hypotenuse of the right triangle formed by length and width.
How does this calculator work?
The diagonal of a rectangle is d = √(l² + w²) — the hypotenuse of the right triangle formed by the two sides. Enter length and width to get the diagonal, the angle it makes with the length, the area (l × w), and the perimeter (2l + 2w) in one step.
Formula
How this is calculated
A rectangle's two diagonals are equal in length and bisect each other. Each diagonal divides the rectangle into two congruent right triangles whose legs are the length and width. The Pythagorean theorem then gives the diagonal directly: d = √(l² + w²). This is the same formula as the hypotenuse of a right triangle with legs l and w.
The angle the diagonal makes with the length side is θ = arctan(w / l). As width approaches length (i.e. the rectangle becomes a square), this angle approaches 45°. Conversely, a very elongated rectangle has a diagonal that runs nearly parallel to the length, so θ approaches 0°.
There are no approximations here — the Pythagorean theorem gives an exact result for any positive length and width. The formula extends naturally to find the space diagonal of a rectangular box: √(l² + w² + h²).
Frequently asked questions
d = √(l² + w²), where l is the length and w is the width. This follows directly from the Pythagorean theorem: the diagonal is the hypotenuse of a right triangle formed by the two sides of the rectangle.
Yes. A rectangle is a parallelogram with right angles, so its two diagonals are always equal in length and they bisect each other at their midpoints. This is not the case for a general parallelogram, where diagonals bisect but are not necessarily equal.
For a square with side s, both sides are equal so the diagonal simplifies to d = s√2. For a rectangle, you apply the general formula d = √(l² + w²). A square's diagonal also makes exactly 45° with each side, whereas a rectangle's diagonal angle depends on the ratio of width to length.
Also known as
TG we-Calculate Editorial Team. (2026). Diagonal of a Rectangle Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/diagonal-of-rectangle-calculator
TG we-Calculate Editorial Team. "Diagonal of a Rectangle Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/diagonal-of-rectangle-calculator.
TG we-Calculate Editorial Team, "Diagonal of a Rectangle Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/diagonal-of-rectangle-calculator
@misc{wecalculate_diagonal_of_rectangle_calculator, title = {Diagonal of a Rectangle Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/diagonal-of-rectangle-calculator}}, year = {2026}, note = {TG we-Calculate} }
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