Diagonal of a Rectangle Calculator
Calculate rectangle diagonal length using dimensions, area, or perimeter with step-by-step solutions
Calculate Rectangle Diagonal
The longer side of the rectangle
The shorter side of the rectangle
Rectangle Diagonal Results
Example Calculation
Standard Rectangle Example
Rectangle: TV screen dimensions
Length: 40 inches
Width: 22.5 inches
Application: Finding diagonal screen size
Calculation Steps
d = √(l² + w²)
d = √(40² + 22.5²)
d = √(1600 + 506.25)
d = √2106.25
d = 45.9 inches
Rectangle Properties
Four Right Angles
Each corner is exactly 90°
Parallel Sides
Opposite sides are equal and parallel
Equal Diagonals
Both diagonals have same length
Circumscribable
Can fit inside a circle
Formula Reference
Basic Diagonal
d = √(l² + w²)
From Area & Perimeter
d = ½√(P² - 8A)
Circumradius
r = d/2
Diagonal Angle
α = 2×arctan(w/l)
Understanding Rectangle Diagonals
What is a Rectangle Diagonal?
A rectangle diagonal is a straight line connecting two opposite corners (vertices) of a rectangle. Every rectangle has two diagonals, and they are always equal in length and bisect each other at the center of the rectangle.
Why Calculate the Diagonal?
- •Determine screen sizes for TVs and monitors
- •Calculate material needs for construction
- •Find maximum object size that fits diagonally
- •Solve geometry and trigonometry problems
Mathematical Foundation
d = √(l² + w²)
(Pythagorean Theorem)
The diagonal formula is derived from the Pythagorean theorem. When you draw a diagonal in a rectangle, it creates two right triangles, where the diagonal is the hypotenuse and the length and width are the legs.
Alternative Formulas
From area and perimeter: d = ½√(P² - 8A)
From angle α: d = w/sin(α/2) = l/cos(α/2)
From circumradius: d = 2r
Real-World Applications
- • Television and monitor sizing
- • Picture frame diagonal measurements
- • Construction and carpentry
- • Packaging and shipping calculations
- • Sports field and court design
Special Cases
- • Square: d = a√2 (where a = side)
- • Golden rectangle: ratio = φ ≈ 1.618
- • Unit rectangle: l = 1, w = 1, d = √2
- • 3-4-5 rectangle: d = 5 units
Related Concepts
- • Pythagorean theorem
- • Right triangle properties
- • Circumcircle geometry
- • Coordinate geometry
- • Vector mathematics