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

Volume 6

Formula: V = |a · (b × c)|

Step-by-step with your numbers:

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

Did we solve your problem today?

A parallelepiped's volume equals the absolute value of the scalar triple product of its three edge vectors.

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).