Calculate the diagonal of a rectangle from its length and width using the Pythagorean theorem. Also find area, perimeter, diagonal angle, and aspect ratio.
The Diagonal of a Rectangle Calculator uses the Pythagorean theorem to instantly compute the diagonal length of any rectangle from its length and width. In addition to the diagonal, it calculates area, perimeter, the angle the diagonal makes with each side, the aspect ratio, and the half-diagonal (center-to-corner distance).
The diagonal of a rectangle is one of the most commonly needed measurements in everyday life. When you shop for a television, the advertised size is the screen diagonal. When builders check if a room is square, they measure the diagonals. When designers create layouts, they need to know how the diagonal relates to the sides for spacing and alignment.
The formula is elegantly simple — d = √(a² + b²) — but this calculator provides much more than a bare number. It shows a step-by-step Pythagorean theorem breakdown so students can follow the math, displays complementary angles in degrees or radians, and computes the aspect ratio with a simplified integer approximation.
Eight presets let you instantly load common rectangles: A4 paper, letter paper, credit cards, TV screens, smartphones, and sports fields. The reference table lists diagonals and aspect ratios for objects you encounter every day. Visual bars compare length, width, diagonal, and half-diagonal at a glance. Whether you are a student, engineer, designer, or curious learner, this tool makes rectangle geometry quick and intuitive.
The Diagonal of a Rectangle Calculator is useful when you need fast and consistent geometry results without reworking the same algebra repeatedly. It helps you move from raw measurements to Diagonal (d), Area, Perimeter in one pass, with conversions and derived values shown together.
Use it to validate homework steps, check CAD or fabrication dimensions, estimate material requirements, and sanity-check hand calculations before submitting work.
Diagonal d = √(a² + b²) where a is the length and b is the width. Angle α = arctan(b / a). Area = a × b. Perimeter = 2(a + b).
Result: 363.7 mm
An A4 sheet of paper (297 × 210 mm) has a diagonal of √(297² + 210²) = √(88,209 + 44,100) = √132,309 ≈ 363.7 mm. The diagonal angle is arctan(210/297) ≈ 35.26°.
This calculator combines the core geometry formula with the input mode selected in the interface, then derives companion values shown in the output cards, comparison bars, and reference tables. Use it to cross-check both direct calculations and reverse-solving scenarios where one measurement is unknown.
Diagonal of a Rectangle Calculator calculations show up in coursework, drafting, construction layout, packaging, tank sizing, machining, and quality control. Instead of solving each transformation manually, you can test scenarios quickly and verify whether your dimensions remain within tolerance.
Keep units consistent across every input before interpreting area, perimeter, angle, or volume outputs. For best results, measure carefully, round only at the final step, and compare at least one manual calculation with the calculator output when building confidence.
Use the Pythagorean theorem: d = √(length² + width²). For example, a 3 × 4 rectangle has a diagonal of √(9 + 16) = √25 = 5.
The diagonal is the advertised size (e.g., 55"). To find width and height from the diagonal and ratio, use w = d × 16/√(16² + 9²) and h = d × 9/√(16² + 9²).
No. By the Pythagorean theorem, the diagonal is always strictly longer than either side since d = √(a² + b²) > max(a, b).
The angle between the diagonal and the length is α = arctan(width / length). The angle with the width is 90° − α.
For a square with side s, the diagonal is d = s√2 ≈ 1.4142 × s.
Yes. A rectangle (and any parallelogram with right angles) always has two diagonals of equal length, and they bisect each other.