Volume of Cube given Face Diagonal Calculator

Formula Used:

\[ V = \left( \frac{d_{Face}}{\sqrt{2}} \right)^{3} \]

Volume of Cube:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Volume of Cube given Face Diagonal?

The Volume of Cube given Face Diagonal is the total quantity of three dimensional space enclosed by the surface of a Cube, calculated using the face diagonal measurement.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V = \left( \frac{d_{Face}}{\sqrt{2}} \right)^{3} \]

Where:

\( V \) — Volume of Cube (m³)
\( d_{Face} \) — Face Diagonal of Cube (m)
\( \sqrt{2} \) — Square root of 2 (approximately 1.4142)

Explanation: The formula derives from the relationship between face diagonal and side length of a cube, where side length = face diagonal/√2, and volume = side length³.

3. Importance of Volume Calculation

Details: Calculating volume from face diagonal is useful in geometry, engineering, and construction applications where diagonal measurements are more accessible than direct side measurements.

4. Using the Calculator

Tips: Enter face diagonal measurement in meters. The value must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: Why is √2 used in this formula?
A: In a square face of a cube, the face diagonal relates to the side length by d = s√2, hence s = d/√2.

Q2: What are the units for volume calculation?
A: Volume is in cubic meters (m³) when diagonal is in meters. Ensure consistent units for accurate results.

Q3: Can this formula be used for rectangular prisms?
A: No, this specific formula applies only to perfect cubes where all sides are equal.

Q4: How accurate is this calculation?
A: The calculation is mathematically exact for perfect cubes. Accuracy depends on the precision of the input measurement.

Q5: What if I have space diagonal instead of face diagonal?
A: A different formula would be used: V = (dSpace/√3)³, where dSpace is the space diagonal.