1. What is Edge Length of Cube given Face Diagonal?

The edge length of a cube can be calculated from its face diagonal using the geometric relationship between these two measurements. This calculation is fundamental in geometry and 3D modeling.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( l_e \) — Edge Length of Cube (m)
• \( d_{Face} \) — Face Diagonal of Cube (m)

Explanation: The formula derives from the Pythagorean theorem applied to a square face of the cube, where the face diagonal forms the hypotenuse of a right triangle with two edges as legs.

3. Importance of Edge Length Calculation

Details: Calculating edge length from face diagonal is essential in geometry, architecture, engineering, and 3D design where precise cube dimensions are required from diagonal measurements.

4. Using the Calculator

Tips: Enter the face diagonal measurement in meters. The value must be positive and greater than zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: Why is there a square root of 2 in the formula?
A: The square root of 2 comes from the Pythagorean theorem applied to a square, where diagonal = side × √2.

Q2: Can this formula be used for other shapes?
A: This specific formula applies only to cubes and squares. Other shapes have different relationships between edges and diagonals.

Q3: What are the units of measurement?
A: The calculator uses meters, but the formula works with any consistent unit system (cm, mm, inches, etc.).

Q4: How accurate is this calculation?
A: The calculation is mathematically exact, assuming precise input measurements and a perfect cube shape.

Q5: Can I calculate face diagonal from edge length?
A: Yes, the reverse calculation is dFace = le × √2, using the same mathematical relationship.