Length of a Rectangle Calculator
Calculate rectangle length from area, perimeter, or diagonal
Calculate Rectangle Length
The shorter side of the rectangle
Total area of the rectangle
Calculate Length from Area and Width
Example Calculations
Example 1: Area and Width Method
Problem: Find the length of a rectangle with area 24 m² and width 4 m
Solution: Length = Area ÷ Width = 24 ÷ 4 = 6 m
Example 2: Perimeter and Width Method
Problem: Find the length of a rectangle with perimeter 20 m and width 3 m
Solution: Length = (Perimeter ÷ 2) - Width = (20 ÷ 2) - 3 = 10 - 3 = 7 m
Example 3: Diagonal and Width Method
Problem: Find the length of a rectangle with diagonal 5 m and width 3 m
Solution: Length = √(diagonal² - width²) = √(5² - 3²) = √(25 - 9) = √16 = 4 m
Rectangle Formulas
Length from Area
Length = Area ÷ Width
Length from Perimeter
Length = (P ÷ 2) - Width
Length from Diagonal
Length = √(d² - w²)
Basic Properties
Area = Length × Width
Perimeter = 2(L + W)
Diagonal = √(L² + W²)
Quick Tips
Length is conventionally the longer side of a rectangle
For perimeter method: P must be greater than 2 × width
For diagonal method: diagonal must be greater than width
All calculations use the Pythagorean theorem for diagonal
Understanding Rectangle Length Calculations
What is Rectangle Length?
The length of a rectangle is typically the longer of its two sides. However, in some contexts, it may refer to the vertical dimension when the rectangle is positioned upright.
Key Properties
- •Rectangles have four right angles (90°)
- •Opposite sides are equal and parallel
- •Diagonals are equal in length and bisect each other
- •Length and width determine all other properties
Calculation Methods
From Area
When you know the total area and one side dimension
From Perimeter
When you know the distance around the rectangle and one side
From Diagonal
Using the Pythagorean theorem with diagonal and one side
Mathematical Derivations
Area Method
Starting with: Area = Length × Width
Solve for Length: Length = Area ÷ Width
This is basic algebraic rearrangement
Perimeter Method
Starting with: P = 2(Length + Width)
Divide by 2: P/2 = Length + Width
Solve: Length = (P/2) - Width
Diagonal Method
Pythagorean theorem: d² = L² + W²
Rearrange: L² = d² - W²
Take square root: L = √(d² - W²)