Math

Volume of a Parallelepiped Calculator

Find the volume from three edge vectors via the scalar triple product.

a x

a y

a z

b x

b y

b z

c x

c y

c z

Calculated Output

Volume 6

Formula: V = |a · (b × c)|

Step-by-Step Breakdown

1. Values used:

2. a x = 1

3. a y = 0

4. a z = 0

5. b x = 0

6. b y = 2

7. b z = 0

8. c x = 0

9. c y = 0

10. c z = 3

11.

12. Volume = 6

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The math behind it

V = |a · (b × c)|. The cross product b × c gives the base area as a vector; dotting with a projects the height.

Edges (1,0,0), (0,2,0), (0,0,3) → volume = 6.

What if the volume is zero?

The three vectors are coplanar (linearly dependent).