Volume of Parallelepiped Calculator

Volume of Parallelepiped Formula:

\[ V = S_a \times S_b \times S_c \times \sqrt{1 + (2 \times \cos(\alpha) \times \cos(\beta) \times \cos(\gamma)) - (\cos(\alpha)^2 + \cos(\beta)^2 + \cos(\gamma)^2)} \]

Side A of Parallelepiped:

Side B of Parallelepiped:

Side C of Parallelepiped:

Angle Alpha of Parallelepiped:

Angle Beta of Parallelepiped:

Angle Gamma of Parallelepiped:

Volume of Parallelepiped:

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1. What is the Volume of Parallelepiped?

A parallelepiped is a three-dimensional figure formed by six parallelograms. The volume represents the amount of space enclosed within this geometric shape, calculated based on its side lengths and the angles between them.

2. How Does the Calculator Work?

The calculator uses the volume formula:

\[ V = S_a \times S_b \times S_c \times \sqrt{1 + (2 \times \cos(\alpha) \times \cos(\beta) \times \cos(\gamma)) - (\cos(\alpha)^2 + \cos(\beta)^2 + \cos(\gamma)^2)} \]

Where:

\( S_a \) — Length of side A (meters)
\( S_b \) — Length of side B (meters)
\( S_c \) — Length of side C (meters)
\( \alpha \) — Angle between sides B and C (degrees)
\( \beta \) — Angle between sides A and C (degrees)
\( \gamma \) — Angle between sides A and B (degrees)

Explanation: The formula accounts for the spatial arrangement of the parallelepiped by incorporating the cosine of the angles between adjacent sides.

3. Importance of Volume Calculation

Details: Calculating the volume of a parallelepiped is essential in various fields including architecture, engineering, physics, and computer graphics for determining capacity, displacement, and spatial properties.

4. Using the Calculator

Tips: Enter all three side lengths in meters and the three angles in degrees (between 0° and 180°). All values must be positive and valid for the calculation to proceed.

5. Frequently Asked Questions (FAQ)

Q1: What is a parallelepiped?
A: A parallelepiped is a three-dimensional figure with six faces, each of which is a parallelogram. It's the 3D equivalent of a parallelogram.

Q2: What are the units for volume measurement?
A: The volume is calculated in cubic meters (m³) when side lengths are provided in meters.

Q3: What if I get a negative value under the square root?
A: This indicates invalid input angles that cannot form a valid parallelepiped. Please check that the angles are consistent and valid.

Q4: Can this calculator handle different units?
A: The calculator assumes meters for length inputs. For other units, convert your measurements to meters first.

Q5: What are some real-world applications of parallelepiped volume calculation?
A: This calculation is used in packaging design, container volume estimation, architectural planning, and mechanical engineering for component design.