Rectangle Calculator

Calculate rectangle properties: area, perimeter, diagonal, aspect ratio, and more. Includes visual representation and comprehensive formulas.

By Dimensions
By Area & Ratio
By Perimeter & Ratio
By Diagonal & Ratio

Rectangle Definition: A rectangle is a quadrilateral with four right angles. Opposite sides are parallel and equal in length.

Length (a)
units
The longer side of the rectangle (if any). Range: 0.01 to 10000
Width (b)
units
The shorter side of the rectangle (if any). Range: 0.01 to 10000
10 × 6
8 × 5
12 × 8
16 × 9 (HD)
1.618 × 1 (Golden)
4 × 3
3 × 2
1 × 1 (Square)
Calculating...

Understanding Rectangles

A rectangle is a quadrilateral with four right angles (90°). It is a special case of a parallelogram where all angles are right angles. The opposite sides of a rectangle are parallel and equal in length.

Key Properties of a Rectangle:

  • Opposite sides are parallel and equal in length
  • All four angles are right angles (90°)
  • The diagonals are equal in length and bisect each other
  • It has two lines of reflectional symmetry
  • It has rotational symmetry of order 2 (through 180°)

Rectangle Formulas

Property Formula Variables
Area A = a × b a = length, b = width
Perimeter P = 2(a + b) a = length, b = width
Diagonal d = √(a² + b²) a = length, b = width
Aspect Ratio AR = a : b a = length, b = width
Length from Area & Width a = A / b A = area, b = width
Width from Area & Length b = A / a A = area, a = length
Length from Perimeter & Width a = P/2 - b P = perimeter, b = width
Length from Diagonal & Width a = √(d² - b²) d = diagonal, b = width

Special Types of Rectangles

1

Square: A rectangle with all sides equal (a = b). All squares are rectangles but not all rectangles are squares.

2

Golden Rectangle: A rectangle whose side lengths are in the golden ratio (approximately 1.618:1). It's considered aesthetically pleasing and appears in art and architecture.

3

Aspect Ratios: Common aspect ratios include 4:3 (traditional TV), 16:9 (widescreen HD), 1.85:1 (cinema), and 2.35:1 (anamorphic widescreen).

Applications of Rectangles

  • Architecture: Floor plans, windows, doors, and building footprints
  • Engineering: Structural components, machine parts, and enclosures
  • Design: Web layouts, graphic design elements, and photo cropping
  • Manufacturing: Sheet metal cutting, packaging design, and material optimization
  • Mathematics: Basis for coordinate geometry and calculus problems

Calculator Features:

  • Calculate all rectangle properties from different inputs (dimensions, area, perimeter, diagonal)
  • Interactive visualization with rotation and labeling options
  • Identify golden rectangles and common aspect ratios
  • Step-by-step calculation explanations
  • Comprehensive formula reference

Frequently Asked Questions

A square is a special type of rectangle where all four sides have equal length. All squares are rectangles, but not all rectangles are squares. A rectangle only requires that opposite sides are equal and all angles are 90°.

The diagonal of a rectangle can be calculated using the Pythagorean theorem: d = √(a² + b²), where 'a' is the length and 'b' is the width of the rectangle. This formula works because the diagonal forms the hypotenuse of a right triangle with the sides of the rectangle.

A golden rectangle is one whose side lengths are in the golden ratio, approximately 1.618:1. This ratio, often denoted by the Greek letter φ (phi), appears frequently in nature, art, and architecture. It is considered aesthetically pleasing and has unique mathematical properties, such as the fact that removing a square from a golden rectangle leaves another golden rectangle.

Yes! If you know the area (A) and aspect ratio (a:b), you can calculate the dimensions as follows: Let the ratio be expressed as a:b = k:1, then b = √(A/k) and a = k × b. Our calculator includes this calculation mode for convenience.

Perimeter is the total distance around the outside of the rectangle (the sum of all four sides). Area is the amount of space enclosed within the rectangle (length × width). Perimeter is measured in linear units (feet, meters), while area is measured in square units (square feet, square meters).