Rectangle Calculator

Calculate area, perimeter, diagonal, and semi-perimeter of a rectangle with step-by-step solutions.

Enter Dimensions

Result

Area
--
square units
Length--
Width--
Area--
Perimeter--
Diagonal--
Semi-perimeter--

Step-by-Step Solution

A = l x w

Rectangle Formulas

A rectangle is a quadrilateral with four right angles. Its opposite sides are equal and parallel. Here are all the key formulas for rectangle calculations:

Area

The space enclosed within the rectangle.

A = length x width

Perimeter

The total distance around the rectangle.

P = 2(length + width)

Diagonal

The line connecting opposite corners.

d = sqrt(l^2 + w^2)

Semi-perimeter

Half the perimeter, useful in many formulas.

s = (l + w)

Properties of a Rectangle

  • All four angles are 90 degrees (right angles).
  • Opposite sides are equal and parallel.
  • The diagonals are equal in length and bisect each other.
  • A square is a special case of a rectangle where length equals width.
  • The area is always positive for non-degenerate rectangles.

Practical Applications

Rectangle calculations are used in construction (room dimensions, flooring), landscaping (garden beds, fencing), real estate (lot measurements), screen dimensions, paper sizes, and countless other everyday situations. Understanding these formulas is essential for practical problem-solving.

Relationship Between Formulas

The diagonal of a rectangle is derived from the Pythagorean theorem, since the diagonal forms the hypotenuse of a right triangle with the length and width as legs. The perimeter gives the total boundary length, while the semi-perimeter (half the perimeter) is frequently used in more advanced geometric calculations.