Diagonal of Rectangle Calculator
Calculate the diagonal length of any rectangle by entering its width and height. This calculator uses the Pythagorean theorem and also computes the area, perimeter, diagonal angle, and aspect ratio.
The diagonal of a rectangle connects two opposite corners. Since it divides the rectangle into two right triangles, the Pythagorean theorem gives us the length.
Diagonal Formula:
d = sqrt(width^2 + height^2)
Example:
A rectangle with width 3 and height 4 has diagonal = sqrt(9 + 16) = sqrt(25) = 5. This is the classic 3-4-5 right triangle.
Diagonal Angle:
The diagonal makes an angle with the width side: angle = arctan(height / width). For the 3-4-5 rectangle, the angle is arctan(4/3) = 53.13 degrees.
Common Uses:
- TV and monitor sizes are measured by the diagonal. A "55-inch TV" has a 55-inch diagonal.
- Construction: Finding the diagonal ensures right angles (the 3-4-5 rule is used on job sites).
- Shipping: The diagonal determines whether a long object fits inside a rectangular box.
- Screen resolution: The diagonal, combined with pixel count, determines pixel density (PPI).