Rectangle Formulas

Calculate diagonal length, perimeter, area, and angles of a rectangle.

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What is the Rectangle Formulas?

The Rectangle Formulas Calculator is a versatile geometric tool designed to find all fundamental properties of a rectangle from the lengths of its two distinct sides (Side A and Side B).

By simply entering the length and width of a rectangle, this calculator instantly computes the diagonal length, total perimeter, enclosed area, and the angles of intersection. It is a highly useful tool for construction, architecture, math students, and professionals working with rectangular shapes.

Practical Examples & Reference Guide

Here is a reference table showing how different side inputs translate to the calculated properties of a rectangle:

Side A (Length)Side B (Width)DiagonalPerimeterArea
3451412
512133460
101014.142140100
8151746120

Note: Diagonal values and some derived properties are rounded to 4 decimal places for precision.

In-Depth Technical Guide

The Geometry of a Rectangle

A rectangle is a quadrilateral with four right angles (90 degrees). Unlike a square, a rectangle's adjacent sides can be of different lengths, typically denoted as length ($l$ or Side A) and width ($w$ or Side B). Opposite sides of a rectangle are parallel and equal in length.

Core Formulas

Let $a$ represent Side A (length) and $b$ represent Side B (width) of the rectangle:

  1. Area ($A$): The total 2D space enclosed within the boundary of the rectangle. $$A = a \times b$$

  2. Perimeter ($P$): The total distance around the outside edge of the rectangle. $$P = 2 \times (a + b)$$

  3. Diagonal ($d$): The straight line distance connecting opposite corners. According to the Pythagorean theorem ($a^2 + b^2 = d^2$), it is: $$d = \sqrt{a^2 + b^2}$$

Angles

  • Internal Angle: The angle between any two adjacent sides is exactly 90°.
  • Diagonal Angle: The diagonals of a rectangle bisect each other and form an intersection. The acute angle ($\theta$) between the diagonals can be found using trigonometry: $$\theta = 2 \times \arctan\left(\frac{\min(a,b)}{\max(a,b)}\right)$$ This represents the smaller angle at which the diagonals cross.

Frequently Asked Questions

What is the difference between a square and a rectangle?
All squares are rectangles because they have four 90-degree angles. However, not all rectangles are squares because a rectangle can have adjacent sides of different lengths, whereas a square must have all four sides exactly equal.
How do you find the diagonal of a rectangle?
You can find the diagonal of a rectangle using the Pythagorean theorem. Simply square the length and the width, add them together, and then calculate the square root of that sum.
Why are the internal angles of a rectangle always 90 degrees?
A rectangle is defined geometrically as an equiangular quadrilateral. Since the sum of the interior angles of any quadrilateral is always 360 degrees, dividing that equally among four corners yields exactly 90 degrees per corner.
Do the diagonals of a rectangle cross at a 90-degree angle?
No, the diagonals of a rectangle only intersect at 90 degrees if the rectangle is a square. In a standard rectangle where the length and width are different, the diagonals cross at acute and obtuse angles.