Rectangle Calculator
Calculate the area, perimeter, and diagonal of a rectangle. Enter any two known values to get complete dimensions.
How to Use This Rectangle Calculator
Whether you are laying out a foundation for a house, calculating the screen size of a new monitor, or just double-checking geometry homework, dealing with rectangles is a daily necessity.
If you only know the area and one side, or just the perimeter and the diagonal, simply select your known variables from the dropdown menu. The calculator will automatically reverse-engineer the math, provide the missing dimensions.
Core Rectangle Formulas
You need three primary equations. A standard rectangle has two distinct side lengths: length (often denoted as a) and width (denoted as b).
Essential Equations
- Area (A):
A = a × b - Perimeter (P):
P = 2a + 2borP = 2(a + b) - Diagonal (p or q):
p = √(a² + b²)(Derived from the Pythagorean theorem)
Fundamental Properties of a Rectangle
To understand why these formulas work, it helps to know the strict geometric rules that define this shape. A rectangle is a specific type of quadrilateral (a four-sided polygon) that possesses the following traits:
- Four Right Angles: Every internal corner measures exactly 90 degrees.
- Equal and Parallel Opposite Sides: The top and bottom sides are identical in length, as are the left and right sides.
- Equal Diagonals: If you draw a line from the top-left corner to the bottom-right, it will be the exact same length as a line drawn from the top-right to the bottom-left.
- Bisecting Diagonals: The point where the two diagonals cross is the exact center of the shape, cutting each line perfectly in half.
Calculation Examples
Scenario 1: Buying Fencing and Sod for a Yard Imagine your backyard is 15 meters long and 10 meters wide.
- To figure out how much sod you need to cover the ground, you calculate the Area: 15 × 10 = 150 square meters.
- To figure out how much fencing you need to enclose it, you calculate the Perimeter: 2(15) + 2(10) = 50 meters of fence.
Scenario 2: Verifying TV Screen Sizes Televisions and monitors are sold by their diagonal measurement. If you buy a “65-inch TV” with a standard 16:9 aspect ratio, the screen isn’t 65 inches wide. Using the diagonal formula in reverse, we can determine the actual width is roughly 56.7 inches and the height is 31.9 inches.
FAQs
Q1. Is a square a rectangle?
A: Yes. A square is a special, highly specific type of rectangle where all four sides are equal. It meets all the criteria: four 90-degree angles and parallel opposite sides. However, a rectangle is not necessarily a square.
Q2. How do I find the dimensions if I only know the area and perimeter?
A: This is one of the trickiest calculations to do by hand because it requires solving a quadratic equation. You have to set up a system of equations: a × b = Area and 2a + 2b = Perimeter. You can save time by selecting the “Find side” options in the dropdown of the calculator above, which runs the quadratic formula automatically.
Q3. What happens if my diagonal is shorter than my side length?
A: Geometrically, this is impossible. The diagonal of a rectangle forms the hypotenuse of a right triangle with the two sides. According to the laws of geometry, the hypotenuse must always be the longest side. If you enter a diagonal shorter than a side into the tool, it will flag an error.
Sources: CalculatorSoup, Omni Calculator, Inch Calculator, Pi Day, GraphCalc, Analyze Math, Vedantu, nCalculators.