Rectangle Calculator -

Calculate area, perimeter, diagonal and more.

Calculate by:

Width (w)

Height (h)

Units (optional)

Rectangle Properties

Width (w):

Height (h):

Area (A):

Perimeter (P):

Diagonal (d):

Circumcircle Radius (R):

Angle between Diagonals (α):

Angle between Diagonals (β):

Visual Representation

How to Use the Rectangle Calculator

This calculator helps you find various properties of a rectangle, such as its area, perimeter, and diagonal length, based on different sets of known values.

Select Calculation Method:
- Use the “Calculate by:” dropdown menu to choose which two properties of the rectangle you already know. Options include:
  - Width and Height
  - Diagonal and Width
  - Diagonal and Height
  - Area and Width
  - Area and Height
  - Perimeter and Width
  - Perimeter and Height
Enter Known Values:
- Once you select a method, two input fields will appear, labeled according to your choice (e.g., “Width (w)”, “Height (h)”).
- Enter the numerical values for these known properties into their respective fields.
Enter Units (Optional):
- You can specify the units of your measurements (e.g., cm, m, inches, feet) in the “Units” field.
- This is for display purposes only; the calculations are performed based on the numerical values. The results will be displayed with the appropriate units (e.g., area in units²).
Calculate: Click the “Calculate” button.
Review the Results: The calculator will display:
- Width (w) and Height (h)
- Area (A) = w × h
- Perimeter (P) = 2 × (w + h)
- Diagonal (d) = √(w² + h²)
- Circumcircle Radius (R) = d / 2 (The radius of a circle that passes through all four corners of the rectangle)
- Angle between Diagonals (α and β): The two distinct angles (one acute, one obtuse, unless it’s a square) formed at the intersection of the rectangle’s diagonals. These angles always sum to 180°.
Visual Representation: A diagram of the rectangle will be shown, scaled according to the calculated width and height, with its diagonal and dimensions labeled.
Clear: Click the “Clear” button to reset all input fields, results, and the visualization.
Error Messages: If your input is invalid (e.g., non-numeric, negative dimensions, or geometrically impossible values like a diagonal shorter than a side), an error message will appear.

Rectangle Calculator: Your Guide to Four-Sided Fundamentals

What Exactly is a Rectangle? More Than Just a Box!

Ah, the humble rectangle! It’s one of the first shapes we learn as kids, a familiar four-sided figure that pops up everywhere from our phone screens and book pages to doors, windows, and entire city blocks. But what makes a rectangle a rectangle, mathematically speaking? A rectangle is a quadrilateral (a four-sided polygon) where all four interior angles are right angles (90 degrees). This simple definition leads to some very neat and useful properties: opposite sides are equal in length and parallel to each other.

While all squares are rectangles (since a square has four right angles and equal sides), not all rectangles are squares. The key difference is that a rectangle only *requires* opposite sides to be equal, whereas a square demands all four sides be equal. This calculator handles all rectangles, including squares as a special case.

Key Properties Calculated: Unpacking the Numbers

Understanding a rectangle involves more than just its width and height. Here are the core properties this calculator helps you determine:

Width (w) and Height (h): These are the lengths of the two pairs of opposite sides. Sometimes referred to as length and breadth.
Area (A): This is the amount of two-dimensional space a rectangle occupies. The formula is wonderfully simple: Area = Width × Height.
Perimeter (P): This is the total length of the boundary of the rectangle. Imagine walking all the way around it; the distance you cover is the perimeter. Formula: Perimeter = 2 × (Width + Height).
Diagonal (d): A diagonal is a straight line connecting two opposite corners of the rectangle. A rectangle has two diagonals, and they are always equal in length and bisect each other (cut each other in half at their intersection point). The length of a diagonal can be found using the Pythagorean theorem: Diagonal = √(Width² + Height²).
Circumcircle Radius (R): A circumcircle is a circle that passes through all four vertices (corners) of the rectangle. The center of this circle is the point where the diagonals intersect. The radius of this circumcircle is simply half the length of the diagonal: R = Diagonal / 2.
Angles between Diagonals (α, β): When the two diagonals of a rectangle intersect, they form two pairs of vertically opposite angles. Unless the rectangle is a square (where diagonals are perpendicular, forming 90° angles), there will be one acute angle (less than 90°) and one obtuse angle (greater than 90°). These two angles, α and β, will always add up to 180°. This calculator finds both for you.

Why Calculate These Properties? Real-World Relevance

You might be thinking, “Okay, formulas are nice, but when would I actually *use* this?” The applications are vast:

Home Improvement & Construction: Calculating the area of a room for flooring or painting, finding the perimeter for baseboards or fencing, or determining diagonal lengths for ensuring squareness of frames.
Gardening & Landscaping: Planning garden beds, calculating turf needed, or designing patios.
Design & Art: Working with screen resolutions (which are rectangular), canvas sizes, or layout grids.
Manufacturing: Cutting materials, designing packaging, or optimizing space.
Navigation & Surveying: Rectangular plots of land are common, and their properties are essential.
Education: A fundamental tool for students learning geometry and problem-solving.

Solving for the Unknown: The Power of Formulas

The real utility of a rectangle calculator often comes when you don’t know the basic width and height directly, but you have other pieces of information. For example, you might know the area you need and the maximum width you have available, and you need to find the required height. Or you might measure a diagonal and one side of a space to determine the other side.

This calculator is equipped to handle these scenarios by algebraically rearranging the fundamental formulas. For instance:

If you know Area (A) and Width (w), then Height (h) = A / w.
If you know Diagonal (d) and Width (w), then Height (h) = √(d² - w²) (from Pythagoras).
If you know Perimeter (P) and Height (h), then Width (w) = (P/2) - h.

By allowing you to choose what you know, the calculator does the algebraic heavy lifting to find all the other properties.

“Geometry is the art of good reasoning from badly drawn figures.” – Henri Poincaré. This calculator ensures your figures (and calculations) are always good!

A Note on Units

When working with measurements, units are crucial! If you measure your width and height in centimeters, your area will be in square centimeters, and your perimeter and diagonal will also be in centimeters. This calculator allows you to specify a unit for display purposes. While the internal calculations are purely numerical, the output will append your chosen unit (or unit² for area) to make the results meaningful in your context. Always ensure your input values use consistent units for accurate results.

Visualizing Your Rectangle

Sometimes, seeing is believing (or at least, understanding!). This calculator includes a simple visual representation of the calculated rectangle. It draws the shape to scale (within the limits of the display area), showing its width, height, and one of its diagonals. This can help you get a better feel for the proportions and dimensions you’re working with, especially if you’re trying to visualize a space or an object.

Conclusion: Your Go-To Tool for Rectangular Calculations

The rectangle, despite its apparent simplicity, is a shape rich with interesting geometric properties and countless practical applications. Whether you’re a student tackling homework, a DIY enthusiast planning a project, or a professional needing quick dimensional checks, this Rectangle Calculator is designed to provide accurate and comprehensive results swiftly. By handling the formulas and offering multiple ways to input data, it aims to be a versatile and user-friendly tool for all your rectangular needs.