Rectangle Calculator
Rectangle Calculator
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About the Rectangle Calculator
A rectangle is a four-sided polygon (quadrilateral) with four right angles. This calculator helps you find all properties of a rectangle including area, perimeter, diagonal, and aspect ratio from the length and width.
You can also find missing dimensions when you know one side and either the area, perimeter, or diagonal. This is useful for construction, design, and engineering applications where you need to work backwards from known measurements.
The calculator automatically detects squares (when length equals width) and calculates aspect ratios commonly used in displays, photography, and design work.
Rectangle Formulas
Basic Formulas
Area = length × width
A = l × w
Perimeter = 2(length + width)
P = 2(l + w) = 2l + 2w
Diagonal = √(length² + width²)
d = √(l² + w²)
Finding Missing Dimensions
From Area: w = A ÷ l
Width equals area divided by length
From Perimeter: w = (P ÷ 2) - l
Width equals half perimeter minus length
From Diagonal: w = √(d² - l²)
Using Pythagorean theorem
Frequently Asked Questions
What is the difference between a rectangle and a square?
A square is a special type of rectangle where all four sides are equal in length. While a rectangle has two pairs of equal sides (length and width), a square has all four sides the same length. Every square is a rectangle, but not every rectangle is a square.
How do I find the diagonal of a rectangle?
Use the Pythagorean theorem: diagonal = √(length² + width²). The diagonal divides the rectangle into two right triangles, where the diagonal is the hypotenuse and the length and width are the other two sides.
What is aspect ratio?
Aspect ratio is the proportional relationship between the width and height of a rectangle, expressed as two numbers separated by a colon (like 16:9 or 4:3). It's commonly used in displays, photography, and video to describe the shape of the frame.
What is the Golden Rectangle?
A Golden Rectangle has an aspect ratio equal to the golden ratio (approximately 1.618:1). It's considered aesthetically pleasing and appears frequently in art, architecture, and nature. When you remove a square from a Golden Rectangle, the remaining rectangle is also a Golden Rectangle.
Examples
Rectangle: 8 × 5
Area: 40 square units
Perimeter: 26 units
Diagonal: 9.434 units
Aspect Ratio: 8:5
Finding Width: l=10, Area=60
Width: 60 ÷ 10 = 6 units
Perimeter: 2(10 + 6) = 32 units
Diagonal: √(100 + 36) ≈ 11.66 units
Common Use Cases
- Construction: Calculate flooring, wall, or roofing materials needed for rectangular areas
- Landscaping: Determine lawn size, fencing requirements, or garden bed dimensions
- Interior Design: Calculate room areas, furniture placement, or carpet sizing
- Screen Displays: Work with aspect ratios for monitors, TVs, and projectors
- Photography: Understand print sizes and cropping dimensions
- Packaging: Design boxes and containers with specific dimensions