Rectangle Calculator | Area Perimeter Diagonal

How do you calculate the area and perimeter of a rectangle?

Area = width × height; Perimeter = 2(width + height). For a rectangle 10 × 5: area = 50 square units, perimeter = 30 units. The calculator also shows the diagonal √(10² + 5²) = √125 ≈ 11.18 units and the aspect ratio (2:1 in this case).

What is the diagonal of a rectangle and how is it calculated?

The diagonal connects opposite corners of the rectangle. By the Pythagorean theorem, diagonal = √(w² + h²). A 6 × 8 rectangle has diagonal = √(36 + 64) = √100 = 10 units. The diagonal is always longer than either side and shorter than the sum of both sides.

How does a square relate to a rectangle?

A square is a special rectangle where all four sides are equal (w = h). The calculator includes a dedicated square section: area = s², perimeter = 4s, diagonal = s√2, and circumradius (radius of the circumscribed circle) = s√2/2. For s = 5: area = 25, perimeter = 20, diagonal ≈ 7.07.

What is the aspect ratio of a rectangle?

The aspect ratio expresses the proportional relationship between width and height as two integers with no common factor. For a 1920 × 1080 rectangle, the GCD is 120, giving aspect ratio 16:9. Aspect ratios are widely used in screen resolutions, photography, and document layout.

Can I enter decimal values for rectangle dimensions?

Yes. The calculator accepts any positive real number for width and height, including decimals. All results — area, perimeter, diagonal, and aspect ratio — update in real time. Note that the aspect ratio display rounds to the nearest integer ratio, which may not be exact for irrational dimensions.