Przekatnej Rectangle Calculator
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Other tools you may find usefulDiagonal of a rectangle - definition, properties and geometric applications
The diagonal of a rectangle is a segment connecting two opposite (not belonging to the same side) vertices of this geometric figure. Each rectangle has exactly two diagonals that are equal in length and intersect exactly in half of their length. The diagonal divides the rectangle into two congruent (identical) right triangles, in which the sides of the rectangle are the legs and the diagonal is the hypotenuse. Thanks to this property, the calculation of the diagonal length is based directly on the Pythagorean theorem.
Our precise online rectangle diagonal calculator allows you to instantly determine the length of the diagonal (d) based on the given lengths of the sides (a and b) and calculates the angles of the diagonal to the sides of the figure.
Formula for the diagonal of a rectangle and a square
To calculate the length of the diagonal of a rectangle (d) with sidesa i b, we use the formula resulting from the Pythagorean theorem:
d = √(a² + b²)
In the case of a square (a rectangle with all sides equal length, i.e. a = b), the formula is significantly simplified:
d = a × √2
In everyday calculations, the square root approximation of1.4142:
√2 ≈ 1.4142
Conversion table: side dimensions rectangle and the length of the diagonal
The table below shows example lengths of the sides of rectangles and the length of the diagonal calculated on their basis along with the surface area:
| Length of the side (a) | Width of the side (b) | Length of the diagonal (d) | Surface area (a × b) | Practical application / Examples |
|---|---|---|---|---|
| 3 cm | 4 cm | 5.00 cm | 12 cm² | Perfect proportions of the Egyptian triangle (ratio 3:4:5). |
| 5 cm | 12 cm | 13.00 cm | 60 cm² | A classic rectangle with sides that are a Pythagorean triple. |
| 10 cm | 10 cm (Square) | 14.14 cm | 100 cm² | Square with side 10 cm; the diagonal is exactly 10√2. |
| 20 cm | 30 cm | 36.06 cm | 600 cm² | Proportions of a standard sheet of drawing paper. |
| 50 cm | 120 cm | 130.00 cm | 6000 cm² | Dimensions of the door or hanging cabinet. |
| 100 cm (1 m) | 100 cm (Square) | 141.42 cm | 1 m² | A square with sides of 1 meter. |
| 300 cm (3 m) | 400 cm (4 m) | 5.00 m | 12 m² | Dimensions of a living room or terrace. |
Application of diagonal calculation in RTV screens and construction
The diagonal of a rectangle is of key utility in two main industries:
- Sizes of TV and monitor screens:The screen size given in inches (e.g. a 55-inch TV) is actually the length of the diagonal of its screen. Knowing the width and height of the TV, we can easily calculate its diagonal using this calculator and convert it to centimeters.
- Assembly and finishing works:Checking diagonals is the most important activity when laying floor tiles, installing door frames or erecting partition walls. If the diagonals of a rectangular room are equal, it means that all the corners have perfect right angles.
Frequently asked questions (FAQ)
How to calculate the diagonal of a rectangle?
Square the lengths of both sides, add them together and take the square root of the result. The formula is d = √(a² + b²).
What is the formula for the diagonal of a square?
The formula for the diagonal of a square is d = a√2, where "a" is the length of the side of the square.
Do the diagonals of a rectangle intersect at right angles?
No, the diagonals of a rectangle only intersect at right angles if the rectangle is a square. In a classic rectangle, they intersect at acute and obtuse angles.
What does it mean if the diagonals in a room are not equal?
This means that the room is not a perfect rectangle and its walls do not meet at right angles (the room has the shape of a parallelogram or trapezoid).
How to calculate the side of a rectangle, knowing the diagonal and the other side?
We use the transformed formula of the Pythagorean theorem: a = √(d² - b²), i.e. we subtract the square of the known side from the square of the diagonal and take the square root.