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2D & 3D Geometry Suite

Diagonal Calculator

Instant precision diagonal calculations for Rectangles, Squares, Right Triangles (Hypotenuse), Parallelograms, Cuboids, Screens, and Construction Cross-Measurement.

Calculate Now Formula Guide
Diagonal -
Primary Result
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Enter dimensions below to calculate.
Rectangle Dimensions
Diagonal Length
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Perimeter
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Area
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Formula
d = √(l² + w²)
Square Dimensions
Square Diagonal
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Perimeter
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Area
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Formula
d = s × √2
Right Triangle (Hypotenuse) & Squaring Mode
Hypotenuse (c)
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Perimeter
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Area
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Interior Angles
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Note: In formal geometry, triangles have 0 internal diagonals ($n(n-3)/2 = 0$). In construction, carpentry, and trigonometry, the term "triangle diagonal" refers directly to the Hypotenuse ($c = \sqrt{a^2 + b^2}$).
Parallelogram Sides & Angle
Diagonal p (Shorter)
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Diagonal q (Longer)
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Area
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Perimeter
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Rhombus Side & Angle
Diagonal p
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Diagonal q
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Area
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Perimeter
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3D Box / Cuboid Dimensions
3D Space Diagonal
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Face Diag (L-W)
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Face Diag (L-H)
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Face Diag (W-H)
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Polygon Side Count
Total Diagonals
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From Single Vertex
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Polygon Formula
n × (n - 3) ÷ 2
Display Resolution & PPI
Diagonal (Pixels)
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Aspect Ratio
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Diagonal (Inches)
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Diagonal (cm)
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Room Dimensions & Cross Measurement Check
Expected Diagonal
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Difference / Offset
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Squareness Status
Enter measured value

Complete Diagonal Formulas & Measurement Guide

Comprehensive geometric formulas, carpentry rules of thumb, and construction cross-measurement techniques.

Rectangle Diagonal Formula

Connecting two opposite corners using the Pythagorean theorem.

d = √(length² + width²)

Square Diagonal Formula

Equal sides simplified Pythagorean relationship.

d = side × √2

Right Triangle "Diagonal" (Hypotenuse)

Carpentry squaring using the 3-4-5 rule and Pythagorean theorem.

c = √(a² + b²)

3D Cuboid Space Diagonal

Interior longest distance from one corner through center to opposite corner.

d = √(l² + w² + h²)

Polygon Diagonals Formula

Calculates the total number of non-adjacent connecting segments for n sides.

n × (n - 3) ÷ 2

Parallelogram Diagonals (Law of Cosines)

Calculates both diagonals satisfying the parallelogram law p² + q² = 2(a² + b²).

p = √(a² + b² - 2ab·cos θ)

Step-by-Step Worked Examples

Example 1: Rectangle Diagonal

Problem: Find the diagonal of a rectangle with length 16 cm and width 12 cm.

Step 1: Square each side: 16² = 256, 12² = 144

Step 2: Add the squares: 256 + 144 = 400

Step 3: Take the square root: √400 = 20 cm

Example 2: 3-4-5 Foundation Squaring

Problem: Check if a 12 ft by 9 ft patio is square.

Step 1: 12² + 9² = 144 + 81 = 225

Step 2: Expected diagonal = √225 = 15.00 ft

Step 3: Measure corner to corner. If both diagonals equal 15 ft, corners are 90° square.

Example 3: 3D Box Diagonal

Problem: Can a 20-inch poster tube fit inside an 8 × 12 × 14 inch box?

Step 1: 8² + 12² + 14² = 64 + 144 + 196 = 404

Step 2: Space diagonal = √404 ≈ 20.10 inches

Result: Yes, it fits along the 3D space diagonal.

Frequently Asked Questions

How to find the diagonal of a rectangle?

Use the Pythagorean theorem: d = √(length² + width²). Square the length, square the width, add them together, and calculate the square root.

Does a triangle have a diagonal?

In pure geometry, a triangle has 0 diagonals because all 3 vertices are adjacent. However, in construction, engineering, and carpentry, the term "triangle diagonal" is universally used for the Hypotenuse (c = √(a² + b²)).

How to square a room using diagonal cross measurement?

Measure corner A to corner D, and corner B to corner C. If the two measurements are identical and match √(length² + width²), the structure is perfectly square.

What is the difference between face diagonal and space diagonal?

A face diagonal runs across the 2D surface of one side. A space diagonal passes through the 3D interior from one corner to the opposite corner (d = √(l² + w² + h²)).