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The acute angle where two lines cross, from their slopes (tan formula) or from two direction vectors (dot product). Perpendicular pairs are flagged at exactly 90°.
Crossing angle from slopes or direction vectors; perpendiculars at 90°.
Slopes: tan θ = |(m₂−m₁)/(1+m₁m₂)| · Vectors: cos θ = |u·v|/(|u||v|)
| Symbol | Meaning |
|---|---|
| θ | Acute crossing angle (0–90°) |
Slopes 0 and 1 → 45°. Slopes 2 and −0.5 → exactly 90° (perpendicular).
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This tool reports the acute angle (0–90°); the obtuse supplement is 180° − θ.
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Content updated: September 2026