Quick guide
How to use this calculator
- Enter three three-dimensional vectors.
- Preserve the requested vector order.
- Read the signed scalar and its non-negative volume magnitude.
Calculation method
Cross two vectors, then take a dot product
The scalar triple product a · (b × c) is the signed volume of the parallelepiped formed by the ordered vectors. Its absolute value is the geometric volume.
Worked example
Standard basis volume
Use the three standard basis vectors in cyclic order.
⟨1,0,0⟩ · (⟨0,1,0⟩ × ⟨0,0,1⟩) = 1
Supported inputs
Precision and limits
Vector size
General vectors may contain 2–8 components; three-dimensional products require exactly three.
Entry precision
Each signed decimal may contain up to 30 digits and 15 decimal places.
Square roots
Squared magnitudes remain exact. Irrational roots and normalized components are explicitly labelled approximations.