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Angle between Skew Lines Calculator

Online skew-lines angle: enter two direction vectors and take the acute/right angle after translating to intersect, range (0°,90°].

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cosφ=|u·v|/(|u||v|)
Direction u
x
y
z
Direction v
x
y
z

📖 Tutorial | Skew Lines

1. Definition
Translate the lines to intersect and take the acute/right angle: cosφ=|u·v|/(|u||v|), the absolute value ensuring an acute angle.
2. Formula & Notation
u,vDirection vectors
3. Properties & Laws
  • cosφ=|u·v|/(|u||v|);
  • Range (0°,90°];
  • Parallel 0°, perpendicular 90°;
  • Any parallel direction works.
4. Steps
  1. Enter two directions;
  2. Click "Angle";
  3. Or click "Load Example".
5. Worked Examples
Example: (1,0,0),(1,1,0): cos=√2/2, φ=45°.
6. Common Pitfalls
Use absolute value;
Zero vectors invalid;
Skew lines do not meet; angle uses translation.

❓ FAQ | Skew Lines

Range?
(0,90°].
Absolute?
Acute.
Parallel?
0°.
Perpendicular?
90°.
Direction?
Any parallel.
Meet?
Translation only.