1. What is Space Diagonal of Cuboid?

The space diagonal of a cuboid is the longest straight line that can be drawn from one vertex to the opposite vertex through the three-dimensional space inside the cuboid. It connects two vertices that are not on the same face.

2. How Does the Calculator Work?

The calculator uses the space diagonal formula:

Where:

• \( d \) — Space diagonal
• \( l \) — Length of the cuboid
• \( w \) — Width of the cuboid (calculated from perimeter)
• \( h \) — Height of the cuboid

Width Calculation: Width is derived from the perimeter using the formula \( w = \frac{P - 4l}{4} \), where P is the perimeter of the cuboid.

3. Importance of Space Diagonal Calculation

Details: Calculating the space diagonal is important in various applications including packaging design, construction, 3D modeling, and determining the maximum length of objects that can fit inside containers or boxes.

4. Using the Calculator

Tips: Enter the perimeter, height, and length of the cuboid in consistent units. All values must be positive numbers. The calculator will compute the width from the perimeter and then calculate the space diagonal.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between space diagonal and face diagonal?
A: Space diagonal connects opposite vertices through the 3D space, while face diagonal lies on a single face of the cuboid.

Q2: Can the space diagonal be longer than the sum of all edges?
A: No, the space diagonal is always shorter than the sum of any three edges meeting at a vertex.

Q3: How is width calculated from perimeter?
A: For a cuboid, perimeter P = 4(l + w), so width w = (P/4) - l.

Q4: What units should I use?
A: Use consistent units for all measurements (meters, centimeters, inches, etc.).

Q5: Can this calculator handle decimal values?
A: Yes, the calculator accepts decimal values for more precise calculations.