Rectangle Calculator

What is a Rectangle?

A rectangle is a quadrilateral (4-sided shape) where every angle is a right angle (90°). The opposite sides are equal in length and parallel to each other.

It is the most common shape in modern construction, from the room you are sitting in to the screen you are reading this on.

The 3 Essential Formulas

To fully define a rectangle, you only need two numbers: Length ($l$) and Width ($w$).

1. Area (A)

This is the amount of space inside the rectangle. Used for flooring, painting, and land plotting.

2. Perimeter (P)

This is the total distance around the outside edge. Used for fencing, baseboards, and framing.

3. Diagonal (d)

The distance from one corner to the opposite corner. This creates a right triangle, so we calculate it using the Pythagorean Theorem ($a^2 + b^2 = c^2$).

The Construction Hack: "Squaring" a Room

If you are laying out a foundation for a shed or deck, how do you know your corners are exactly 90 degrees? You use the Diagonal.

If you have a rectangle with sides of 10 ft and 20 ft, measuring the sides isn't enough (it could be a slanted parallelogram). You must measure the diagonal.

Special Case: The Square

A Square is a special type of rectangle where the Length equals the Width ($l = w$).

• Area: $s^2$ (Side squared)
• Perimeter: $4s$
• Diagonal: $s\sqrt{2}$ (approx $1.414 \times s$)

The "Golden Rectangle" is another special type where the ratio of length to width is approximately 1.618 (The Golden Ratio). It is considered the most visually pleasing shape.

Common Area Units