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Rectangle Calculator

Calculate rectangle area, perimeter, diagonal, inscribed circle, circumscribed circle, and aspect ratio from any two known values. Includes interactive SVG diagram and step-by-step solutions.

Rectangle Calculator

Try these examples:

10 x 6 Golden Ratio Area 120, L=15 Diagonal 13, L=12

Embed Rectangle Calculator Widget

About Rectangle Calculator

Welcome to the Rectangle Calculator, a comprehensive geometry tool that calculates all properties of a rectangle from any two known values. Whether you know the length and width, the area and one side, the perimeter and one side, or the diagonal and one side, this calculator will find all remaining measurements including area, perimeter, diagonal, inscribed circle radius, circumscribed circle radius, and aspect ratio.

What is a Rectangle?

A rectangle is a quadrilateral (four-sided polygon) with four right angles (90 degrees each). The word comes from the Latin rectus (right) and angulus (angle). Key properties of a rectangle include:

Rectangle Formulas

Area of a Rectangle

The area represents the space enclosed within the rectangle:

Area Formula
$$A = a \times b$$

Where a is the length and b is the width.

Perimeter of a Rectangle

The perimeter is the total distance around the rectangle:

Perimeter Formula
$$P = 2(a + b)$$

Diagonal of a Rectangle

The diagonal connects opposite corners. Using the Pythagorean theorem:

Diagonal Formula
$$d = \sqrt{a^2 + b^2}$$

Inscribed Circle (Largest Circle Inside)

The largest circle that fits inside a rectangle touches the two longer sides:

Inscribed Circle Radius
$$r_{in} = \frac{b}{2}$$

Where b is the shorter side (width).

Circumscribed Circle (Smallest Circle Outside)

The smallest circle that contains the entire rectangle passes through all four corners:

Circumscribed Circle Radius
$$R = \frac{d}{2} = \frac{\sqrt{a^2 + b^2}}{2}$$

How to Use This Calculator

  1. Select calculation mode: Choose what information you know (Length + Width, Area + Side, Perimeter + Side, or Diagonal + Side)
  2. Enter your values: Input the known measurements in the appropriate fields
  3. Optionally add a unit: Specify the unit of measurement for clearer results
  4. Click Calculate: View all rectangle properties, visual diagram, and step-by-step calculations

Understanding the Results

PropertyDescription
Length (a)The longer side of the rectangle
Width (b)The shorter side of the rectangle
Area (A)Space enclosed by the rectangle (in square units)
Perimeter (P)Total distance around the rectangle
Diagonal (d)Distance from one corner to the opposite corner
Inscribed RadiusRadius of the largest circle that fits inside
CircumradiusRadius of the smallest circle containing the rectangle
Aspect RatioRatio of length to width (a:b)

The Golden Rectangle

A golden rectangle is a special rectangle whose sides are in the golden ratio:

Golden Ratio
$$\phi = \frac{1 + \sqrt{5}}{2} \approx 1.618$$

Golden rectangles are considered aesthetically pleasing and appear frequently in art, architecture, and nature. The Parthenon in Athens and Leonardo da Vinci's works feature golden rectangle proportions. This calculator tells you how close your rectangle is to the golden ratio.

Real-World Applications

Frequently Asked Questions

What is a rectangle?

A rectangle is a quadrilateral (four-sided polygon) with four right angles (90 degrees). Opposite sides of a rectangle are equal in length and parallel. The word "rectangle" comes from Latin "rectus" (right) and "angulus" (angle). A square is a special type of rectangle where all four sides are equal.

How do you calculate the area of a rectangle?

The area of a rectangle is calculated by multiplying its length by its width: Area = length x width. For example, a rectangle with length 8 units and width 5 units has an area of 8 x 5 = 40 square units. The area represents the amount of space inside the rectangle.

How do you calculate the diagonal of a rectangle?

The diagonal of a rectangle is calculated using the Pythagorean theorem: Diagonal = sqrt(length^2 + width^2). This works because the diagonal, length, and width form a right triangle. For example, a rectangle with length 8 and width 6 has a diagonal of sqrt(64+36) = sqrt(100) = 10 units.

What is the perimeter of a rectangle?

The perimeter of a rectangle is the total distance around its edges. It is calculated as: Perimeter = 2 x (length + width). For example, a rectangle with length 10 units and width 6 units has a perimeter of 2 x (10 + 6) = 32 units.

What is the golden rectangle?

A golden rectangle is a rectangle whose side lengths are in the golden ratio, approximately 1:1.618 (or more precisely, 1:(1+sqrt(5))/2). Golden rectangles are considered aesthetically pleasing and appear frequently in art, architecture, and nature. When you cut a square from a golden rectangle, the remaining rectangle is also a golden rectangle.

Can you fit a circle inside a rectangle?

Yes, the largest circle that fits inside a rectangle (inscribed circle) has a diameter equal to the shorter side of the rectangle. So the inscribed circle radius = width/2 (where width is the shorter side). This circle will touch the two longer sides but not reach the shorter sides unless the rectangle is a square.

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Additional Resources

Reference this content, page, or tool as:

"Rectangle Calculator" at https://MiniWebtool.com/rectangle-calculator/ from MiniWebtool, https://MiniWebtool.com/

by miniwebtool team. Updated: Jan 30, 2026

You can also try our AI Math Solver GPT to solve your math problems through natural language question and answer.

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