Volume of Parallelepiped Calculator

How to find the volume of a parallelepiped? The Volume of Parallelepiped Calculator can make it easy for you to calculate the volume of this three-dimensional figure. Just enter the length, width and height into the calculator and it will display volume.

Volume of Parallelepiped Calculator

Enter any 3 values to calculate the missing variable













How to calculate Volume of Parallelepiped

What is the Volume of a Parallelepiped?

A parallelepiped is a six-faced figure, also called a polyhedron, where each face is a parallelogram. You can find its volume using vector methods, specifically with the scalar triple product of three vectors.

How to Use the Calculator

To use the calculator, follow these steps:

  1. Enter the length of vector A (length): This is the first side of the parallelepiped.
  2. Enter the length of vector B (width): This is the second side of the parallelepiped.
  3. Enter the length of vector C (height): This is the third side of the parallelepiped.
  4. Enter the angle between vectors A and B (angleAB): This is the angle between the first two vectors.
  5. Enter the angle between vectors B and C (angleBC): This is the angle between the second and third vectors.

Formula to Calculate the Volume of a Parallelepiped

The formula to calculate the volume of a parallelepiped is:

Volume=a(b×c)\text{Volume} = |a \cdot (b \times c)|

Here’s a breakdown of the variables used:

Variable Description
aa

 

Vector A
bb

 

Vector B
cc

 

Vector C
\cdot

 

Dot product
×\times

 

Cross product

Example Calculation

Lets understand how the calculator works, let’s go through an example.

1. Basic Calculation

Input Value
Vector A (length) 3 units
Vector B (width) 4 units
Vector C (height) 5 units
Angle between A and B (angleAB) 60 degrees
Angle between B and C (angleBC) 90 degrees

Calculation Steps:

Calculate the cross product of vectors B and C:

b×cb \times c

Calculate the dot product of vector A with the result from step 1:

a(b×c)a \cdot (b \times c)

Take the absolute value of the result to get the volume:

Volume=a(b×c)\text{Volume} = |a \cdot (b \times c)|

2. Advanced Calculation

Input Value
Vector A (length) 3 units
Vector B (width) 4 units
Vector C (height) 5 units
Angle between A and B (angleAB) 60 degrees
Angle between B and C (angleBC) 90 degrees

FAQs

What is a parallelepiped?

A parallelepiped is a 3D shape with six faces, and each face is a parallelogram.

How accurate is the calculator?

The calculator gives accurate results if the input values are correct.

Can I use this calculator for any parallelepiped?

Yes, you can use this calculator for any parallelepiped as long as you have the necessary inputs.

Final Words

I hope you found our Volume of Parallelepiped Calculator, a useful and accurate tool to find the volume of a parallelepiped. It simplify the calculation process, providing quick result to users. Please, let us know your experience and feedback.

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