GEOMETRYMathematics Calculator

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.

Concept Fundamentals
A = l × w
Area Formula
P = 2(l + w)
Perimeter
d = √(l² + w²)
Diagonal
4 × 90°
Angles

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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

Key quantities
A = l × w
Area Formula
Key relation
P = 2(l + w)
Perimeter
Key relation
d = √(l² + w²)
Diagonal
Key relation
4 × 90°
Angles
Key relation

Ready to run the numbers?

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

Run the calculator when you are ready.

Rectangle PropertiesLength, width, area, perimeter & diagonal
WidthLengthDiagonal
units
units

Area

-

Perimeter

-

Diagonal

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Rectangle Properties

Area Calculation

The area of a rectangle is the amount of space it occupies in two dimensions.

Area = Length × Width = length × width = ? square units

Perimeter Calculation

The perimeter of a rectangle is the total distance around its edges.

Perimeter = 2 × (Length + Width) = 2 × (length + width) = ? units

Diagonal Calculation

The diagonal of a rectangle is the straight line connecting opposite corners.

Diagonal = √(Length² + Width²) = √(length² + width²) = ? units

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

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