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The angle between vectors comes from cos θ = (u·v)/(|u||v|). Enter two 2D or 3D vectors to get θ in degrees with the dot product and both magnitudes shown.
2D/3D vector angle from dot product and magnitudes, fully worked.
θ = arccos((u·v) / (|u|·|v|))
| Symbol | Meaning |
|---|---|
| θ | Angle in degrees (0–180°) |
u=(1,0), v=(0,1): dot = 0 → θ = 90° (perpendicular). u=(1,1), v=(1,0): θ = 45°.
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Alignment: 0° = same direction, 90° = perpendicular (independent), 180° = opposite.
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Content updated: September 2026