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Diagonal Calculator Pro

Calculate 3D cuboid space diagonals, 2D rectangle diagonals, and TV screen dimensions with step-by-step solutions.

🎮 3D Interactive 360° Box ⚡ Real-time Results 📐 6 Calculation Modes 📺 TV Screen Sizing 📄 PDF Engineering Reports 📱 Mobile Optimized

3D Cuboid Space Diagonal

Calculate the 3D space diagonal passing through the interior center of a rectangular prism / room / box.

Touch & Drag to Rotate in 3D (360°)

Detailed Step-by-Step Solution

✓ 3D Space Proof
1. Space Formula: d = √(l² + w² + h²)
2. Substitution: d = √(8² + 6² + 4²)
3. Arithmetic: d = √(64 + 36 + 16) = √116
4. Output: d ≈ 10.7703 cm

Diagonal of a Rectangle

A rectangle has two equal diagonals that always bisect each other. Select your parameters and enter measurements below.

Aspect Ratio Presets:

Detailed Step-by-Step Solution

✓ Verified
1. Formula: d = √(l² + w²)
2. Substitution: d = √(8² + 6²)
3. Arithmetic: d = √(64 + 36) = √100
4. Output: d = 10 cm

TV & Screen Display Size Calculator

Compute exact width, height, and display area from any screen diagonal size in inches.

Popular Screen Sizes:
in

Detailed Step-by-Step Solution

📺 Display Optics
1. Trig Ratio: θ = arctan(9 / 16) ≈ 29.357°
2. Width Formula: W = D · cos(θ) = 55 · cos(29.357°)
3. Height Formula: H = D · sin(θ) = 55 · sin(29.357°)
4. Dimensions: 47.9" W × 27.0" H (121.8 × 68.5 cm)

How to Use Diagonal Calculator Pro

Get accurate rectangle and 3D geometry values in seconds

1

Select Parameters

Choose known values: sides, area, perimeter, or diagonal angle.

2

Enter Values

Type your measurements and select matching units (mm, cm, m, in, ft).

3

Instant Results

Diagonal, perimeter, circumcircle and area update in real-time.

4

Copy & Export

Copy all computed outputs or download a PDF engineering report.

How to Find the Diagonal of a Rectangle?

To calculate the diagonal (d) of a rectangle, use the Pythagorean theorem. A rectangle diagonal splits the shape into two right triangles where the diagonal is the hypotenuse.

d = √(l² + w²)

Where l is the rectangle length and w is the rectangle width.

All Measurement Formulas

Depending on what values you know, the exact formulas used by Diagonal Calculator Pro are:

Known Parameters Formula for Diagonal (d)
3D Space Diagonal (l, w, h)d = √(l² + w² + h²)
Length (l) & Width (w)d = √(l² + w²)
Length (l) & Area (A)w = A / l  ⟶  d = √(l² + w²)
Length (l) & Perimeter (P)w = P/2 - l  ⟶  d = √(l² + w²)
Length (l) & Angle α (°)w = l · tan(α/2)  ⟶  d = √(l² + w²)
Width (w) & Area (A)l = A / w  ⟶  d = √(l² + w²)
Width (w) & Perimeter (P)l = P/2 - w  ⟶  d = √(l² + w²)

Practical Calculation Example

If a rectangle has a length of 4 cm and a width of 3 cm:

d = √(4² + 3²) = √(16 + 9) = √25 = 5 cm

Frequently Asked Questions

Clear answers to common questions about rectangle and 3D diagonals

How do you find the 3D space diagonal of a box or room?
Use the 3D extension of Pythagoras theorem: d = √(l² + w² + h²). The base diagonal is first found by √(l² + w²), and combining it with height gives the full interior space diagonal.
What is the formula for the diagonal of a rectangle?
The standard formula is d = √(l² + w²), where l is the length and w is the width, derived from the Pythagorean theorem.
Are both diagonals of a rectangle equal in length?
Yes. Every Euclidean rectangle has two diagonals of identical length that bisect each other at the center point.
Does a rectangle diagonal bisect the corner angles?
No. In a general rectangle, diagonals divide the 90° corner into two unequal angles. They only bisect at 45° if the rectangle is a square.
What is the circumcircle radius of a rectangle?
The circumcircle passes through all 4 corners of the rectangle. Its radius equals half the diagonal: r = d / 2.
How can I find the diagonal if only the area and one side are given?
Divide the area by the given side to obtain the other side (w = A / l), then use d = √(l² + w²). Our calculator solves this automatically.
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