Rectangle Calculator — Area, Perimeter, Diagonal & Properties
Calculate the area, perimeter, and diagonal of any rectangle instantly. Enter length and width to get all properties with clear formulas and step-by-step solutions. Ideal for geometry homework, construction planning, and real-world measurements.
Why This Mathematical Concept Matters
Why: Rectangles are the most common shape in the built environment — rooms, screens, books, fields, and construction materials are all rectangular. Calculating their area is essential for flooring, painting, and land measurement. Perimeter matters for fencing and framing. The diagonal — derived from the Pythagorean theorem — is critical for checking squareness in construction (the '3-4-5 rule').
How: Enter the length and width of your rectangle. The calculator instantly computes the area (l × w), perimeter (2l + 2w), and diagonal (√(l² + w²)). All results update in real time as you type. The diagonal formula is a direct application of the Pythagorean theorem applied to the right triangle formed by the length, width, and diagonal.
- ●A rectangle is a special parallelogram where all four angles are exactly 90°
- ●A square is a special rectangle where length equals width
- ●The diagonal divides a rectangle into two congruent right triangles
- ●A rectangle's area is maximized (for a given perimeter) when it's a square — the isoperimetric property
- ●The golden rectangle (ratio ≈ 1.618:1) is considered the most aesthetically pleasing proportion
Area
Perimeter
Diagonal
Rectangle Properties
Area Calculation
The area of a rectangle is the amount of space it occupies in two dimensions.
Perimeter Calculation
The perimeter of a rectangle is the total distance around its edges.
Diagonal Calculation
The diagonal of a rectangle is the straight line connecting opposite corners.
Special Cases
Square
A rectangle with equal length and width is a square. For a square with side length s:
Area = s²
Perimeter = 4s
Diagonal = s√2
Golden Rectangle
A rectangle where the ratio of length to width is the golden ratio (approximately 1.618:1). These rectangles are considered to be aesthetically pleasing and appear in art, architecture, and nature.
⚠️For educational and informational purposes only. Verify with a qualified professional.
🧮 Fascinating Math Facts
Most modern smartphones have screen aspect ratios between 19.5:9 and 20:9 — much more elongated than the classic 16:9 TV ratio.
— GSMArena
A FIFA soccer field is 100–110m × 64–75m, giving an area of 6,400–8,250 m². The penalty area is itself a precisely defined rectangle.
— FIFA Laws of the Game
A4 paper (210 × 297 mm) uses the √2 ratio — so folding it in half gives another rectangle with the same proportions.
— ISO 216
The golden rectangle (≈1.618:1 ratio) appears in ancient Greek architecture, Renaissance art, and the spiral shells of nautilus mollusks.
— Wolfram MathWorld