Calculate all rectangle properties from length and width: area, perimeter, diagonal, aspect ratio, circumradius, and golden rectangle check. Presets for screens, paper sizes, sports fields.
The rectangle is one of the most fundamental shapes in geometry and everyday life. From smartphone screens and sheets of paper to soccer fields and swimming pools, rectangles define the proportions of the objects around us.
A rectangle is a quadrilateral with four right angles. Its opposite sides are equal and parallel, and its diagonals are equal in length and bisect each other. The area is simply length times width, the perimeter is twice the sum of the sides, and the diagonal follows directly from the Pythagorean theorem: d = √(l² + w²).
Beyond these basics, rectangles have rich geometric properties. Every rectangle has a circumscribed circle with radius equal to half the diagonal. The aspect ratio — the ratio of the longer side to the shorter — determines the shape's visual proportions. When the aspect ratio equals the golden ratio φ ≈ 1.618, the rectangle has a unique self-similar property: removing a square from one end leaves a smaller golden rectangle. Golden rectangles appear in art, architecture, and nature.
This calculator computes area, perimeter, diagonal, aspect ratio, circumradius, diagonal angle, and checks for golden rectangle and square status. Presets for common real-world rectangles — paper sizes, screens, sports courts — let you explore instantly. A reference table with common rectangular objects rounds out the tool.
A rectangle looks simple, but practical work often needs more than area alone. Flooring estimates depend on area, trim depends on perimeter, fit checks depend on the diagonal, and screen or print layouts depend on aspect ratio. This calculator puts those related measurements together so you can move from two side lengths to a full geometry summary in one step.
Area: A = l × w Perimeter: P = 2(l + w) Diagonal: d = √(l² + w²) Aspect Ratio: max(l,w) / min(l,w) Circumradius: R = d / 2 Diagonal angle: θ = arctan(w / l)
Result: Area = 623.7 cm^2, perimeter = 101.4 cm, diagonal = 36.3743 cm
With length 29.7 cm and width 21 cm, the calculator finds area = 29.7 x 21 = 623.7 cm^2 and perimeter = 2 x (29.7 + 21) = 101.4 cm. The diagonal is sqrt(29.7^2 + 21^2) = 36.3743 cm, and the aspect ratio is 29.7 / 21 = 1.4143 to 1, which matches the familiar sqrt(2) proportion used by A-series paper sizes.
A rectangle is a parallelogram with four right angles, making it one of the most prevalent shapes in the built environment. Its three principal measurements are fully determined by length L and width W: **area** A = L × W (square units), **perimeter** P = 2(L + W) (linear units), and **diagonal** d = √(L² + W²) (the Pythagorean theorem applied to the two legs). The diagonal bisects the rectangle into two congruent right triangles, and the acute angle θ = arctan(W/L) that the diagonal makes with the length gives the interior composition of the shape.
The **aspect ratio** L/W characterizes the rectangle's proportions. Notable aspect ratios include 1:1 (square), 4:3 (classic TV/monitor format), 16:9 (HD widescreen), 1:√2 (A-series paper, the ISO 216 standard), and φ:1 ≈ 1.618:1 (golden rectangle). The A-series standard (A4: 297 × 210 mm) is ingeniously designed so that folding the sheet in half along its longer axis produces the next smaller size (A5), preserving the same aspect ratio — this requires L/W = √2.
The **golden rectangle** has L/W = φ = (1 + √5)/2 ≈ 1.618. Cutting a square from one end leaves a smaller golden rectangle, and repeating this process generates a logarithmic spiral approximating the Fibonacci spiral. Whether the golden ratio appears naturally in art and architecture or is largely a modern myth is debated, but its mathematical properties (self-similar subdivision, continued-fraction representation 1 + 1/(1 + 1/(1 + …))) are elegant and well-established.
In **construction**, rectangle area drives material estimates: floor tile count, drywall coverage, paint quantity. Perimeter drives framing lumber and baseboard trim. In **screen technology**, diagonal and aspect ratio jointly define display size and pixel density (PPI = √(width_px² + height_px²) / diagonal_inches). In **printing**, paper sizes (A4, Letter, Tabloid) are rectangles with standardized aspect ratios. In **agriculture**, rectangular field measurements directly convert to hectares (1 ha = 10,000 m²) or acres (1 acre ≈ 4,047 m²).
Area = length × width. For a 10 × 6 rectangle, area = 60 square units.
Use the Pythagorean theorem: d = √(l² + w²). For 10 × 6: d = √(100 + 36) = √136 ≈ 11.66.
A rectangle whose aspect ratio equals the golden ratio φ ≈ 1.618. If you cut a square from it, the remaining rectangle is also golden. It appears widely in art and nature.
Yes! A square is a special case of a rectangle where all four sides are equal (aspect ratio = 1).
A 1:1 ratio (a square). Among all rectangles with the same perimeter, the square encloses the most area.
16:9 (≈ 1.778) was chosen as a compromise that works well for both movies and TV broadcasts. It's wider than 4:3 but narrower than cinema's 2.35:1.