Key takeaways
- The diagonal of a rectangle is d = √(l² + w²).
- It's the Pythagorean theorem, with the length and width as the two legs.
- The diagonal is always longer than either the length or the width alone.
- Equal diagonals confirm a rectangle's corners are true right angles.
In this guide
What is the diagonal of a rectangle?
The diagonal is the straight line that cuts across a rectangle from one corner to the opposite corner. It's always longer than either the length or the width alone.
Why does the diagonal of a rectangle matter?
It's used to check that corners are truly square in construction, and it's the standard way screen sizes are measured and compared.
An 8 m by 6 m driveway has a diagonal of exactly √(8² + 6²) = √100 = 10 m — the same 6-8-10 right triangle you'd meet using the Pythagorean theorem directly on a wall and a ladder.The formula
| Symbol | What it means | Example |
|---|---|---|
| d | The diagonal length you want to find | 10 m |
| l | The length of the rectangle | 8 m |
| w | The width of the rectangle | 6 m |
How to find the diagonal step by step
- 1Measure the length and width of the rectangle.
- 2Square the length and square the width.
- 3Add the two squared values together.
- 4Take the square root of that sum to get the diagonal.
Now try it yourself. Change the length and width in the calculator below and watch the diagonal update, with every step shown.
Try it yourself
Pre-filled with the example — change any value.
Common mistakes to avoid
- Forgetting the square root at the end.
l² + w²gives the squared diagonal, not the actual diagonal length. - Confusing diagonal with perimeter. The perimeter of a rectangle calculator adds up all four sides, which is a completely different measurement.
- Assuming the diagonal alone tells you the shape. Many different rectangles can share the same diagonal length; you need at least one side too.
Tips and tricks
- Recognizing 3-4-5, 6-8-10, or 5-12-13 style side lengths makes the diagonal easy to find without a calculator.
- For a square, the same formula simplifies to
d = s√2, since both sides are equal.
Where you'll use it in real life
- Electronics shopping: checking the advertised screen size of a TV or monitor, measured diagonally.
- Construction: verifying a door frame or picture frame is perfectly square before installing it.
- Furniture: finding the longest straight item that fits inside a rectangular box.
- Landscaping: confirming a rectangular driveway or patio has true right-angle corners.
Quick summary
To find the diagonal of a rectangle, square the length and width, add them together, and take the square root. Equal diagonals confirm the corners are true right angles. Use the calculator above to check your own rectangle instantly.
Worked example
You're checking that a rectangular driveway is perfectly square before pouring concrete. The driveway is 8 meters long and 6 meters wide. What should the diagonal measure if the corners are true right angles?
- 01d = √(l² + w²)
- 02d = √(8² + 6²)
- 03d = √(64 + 36)
- 04d = 10 m
These numbers are pre-filled in the calculator above.
Frequently asked questions
How is the diagonal of a rectangle related to the Pythagorean theorem?
The length and width form the two legs of a right triangle, and the diagonal is the hypotenuse, so d = √(l² + w²) is a direct application of the [Pythagorean theorem](/calculator/pythagorean-theorem).
How do I check if a rectangle is perfectly square (90° corners) using the diagonal?
Measure both diagonals of the rectangle; if they're equal in length, the corners are true right angles. Unequal diagonals mean the shape is slightly skewed.
How do I find a rectangle's side length if I know the diagonal and the other side?
Rearrange the formula to w² = d² - l² (or the reverse for l), then take the square root of the result.
Is the diagonal of a square found the same way?
Yes, since a square is a rectangle with equal sides, its diagonal is d = √(s² + s²), which simplifies to s√2.
