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Parallelepiped Volume Calculator.

Calculate volume from three edges and their pairwise angles.

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Volume: 60

Volume

0.000000

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Use Cases

Geometry and Math Problems

Solve homework or exam problems involving parallelepiped volume, especially when angles are not 90 degrees.

Example: Find the volume of a parallelepiped with edges 5, 6, 7 and angles 60°, 70°, 80°.

Engineering and Physics Calculations

Compute volumes of skewed boxes or unit cells in materials science and crystallography.

Example: Calculate the volume of a triclinic unit cell given lattice parameters.

Frequently Asked Questions

How is the volume of a parallelepiped calculated?
The volume is calculated using the edge lengths (a, b, c) and the angles between them (α, β, γ). The formula is V = a * b * c * sqrt(1 + 2*cos(α)*cos(β)*cos(γ) - cos²(α) - cos²(β) - cos²(γ)). This calculator applies that formula directly.
What units should I use for the edge lengths?
You can use any consistent unit for the edge lengths (e.g., meters, centimeters, inches). The volume will be in cubic units of that same unit. For example, if edges are in meters, the volume is in cubic meters.
Can I use this calculator for a rectangular box?
Yes, for a rectangular box (cuboid), all angles are 90 degrees. Enter the three edge lengths and set α, β, γ to 90°. The calculator will give the volume as a*b*c.

Tips & Common Mistakes

Tips

  • Ensure all angles are entered in degrees, as the calculator expects degree values.
  • Use consistent units for all three edge lengths to get the correct volume unit.
  • For a rectangular box, set all angles to 90° to get the simple product of edges.
  • Double-check that the angles are between the correct edges: α between b and c, β between a and c, γ between a and b.

Common Mistakes to Avoid

  • Entering angles in radians instead of degrees.
  • Using mixed units for edge lengths (e.g., meters and centimeters) without converting.
  • Assuming the volume is simply a*b*c when angles are not 90°, which is incorrect.

Last updated: August 13, 2026