Perimeter of a Rectangle Calculator
Calculate rectangle perimeter using length, width, area, or diagonal measurements
Calculate Rectangle Perimeter
Length of the rectangle (longer side)
Width of the rectangle (shorter side)
Formula Used
Perimeter: P = 2(l + w) = 2l + 2w
Area: A = l × w
Diagonal: d = √(l² + w²)
Calculation Results
Step-by-step calculation:
Input Validation
Example Calculations
Basic Rectangle
Given: Length = 8 cm, Width = 5 cm
Formula: P = 2(l + w)
Calculation: P = 2(8 + 5) = 2 × 13 = 26 cm
Area: A = 8 × 5 = 40 cm²
Diagonal: d = √(8² + 5²) = √89 ≈ 9.43 cm
Length and Area Known
Given: Length = 12 cm, Area = 84 cm²
Find Width: w = A/l = 84/12 = 7 cm
Perimeter: P = 2(12 + 7) = 38 cm
Width and Diagonal Known
Given: Width = 6 cm, Diagonal = 10 cm
Find Length: l = √(d² - w²) = √(100 - 36) = √64 = 8 cm
Perimeter: P = 2(8 + 6) = 28 cm
Rectangle Properties
Four right angles (90°)
Opposite sides are parallel and equal
Two diagonals of equal length
Diagonals bisect each other
Can be circumscribed by a circle
Essential Formulas
Perimeter
P = 2(l + w)
Sum of all sides
Area
A = l × w
Length times width
Diagonal
d = √(l² + w²)
Pythagorean theorem
From Area
P = 2l + 2A/l
When area is known
Calculation Tips
Length is typically the longer side
Diagonal must be longer than any side
Use consistent units for all measurements
Square is a special case of rectangle
Understanding Rectangle Perimeter Calculation
What is a Rectangle?
A rectangle is a quadrilateral with four right angles (90°). The name comes from the Latin "rectangulus," meaning "right angle." Rectangles have opposite sides that are parallel and equal in length. The perimeter is the total distance around the rectangle's boundary.
Key Properties
- •Four sides: Two lengths and two widths
- •Right angles: All internal angles are 90°
- •Parallel sides: Opposite sides are parallel
- •Equal diagonals: Both diagonals have the same length
Calculation Methods
Direct Method
When length and width are known
P = 2(l + w)
Area Method
When one side and area are known
P = 2s + 2A/s
Diagonal Method
When one side and diagonal are known
P = 2s + 2√(d² - s²)
Note: The rectangle calculator assumes length ≥ width by convention, but mathematically both arrangements are valid rectangles.
Mathematical Relationships
Rectangles have several important mathematical relationships that allow us to calculate missing dimensions when some properties are known:
- •Area: A = length × width
- •Diagonal: d = √(l² + w²) (Pythagorean theorem)
- •Circumradius: R = d/2 (radius of circumscribed circle)
Real-World Applications
- •Construction: Room dimensions and flooring
- •Landscaping: Garden borders and fencing
- •Manufacturing: Material calculations and cutting
- •Design: Frame sizing and layout planning