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Angle between Line and Plane Calculator

Online line-plane angle: enter the line direction and plane normal to find the angle, range [0°,90°].

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sinθ=|v·n|/(|v||n|)
Direction v
x
y
z
Normal n
x
y
z

📖 Tutorial | Line-Plane

1. Definition
The angle between a line and its projection, complementary to the normal angle, so sinθ=|v·n|/(|v||n|).
2. Formula & Notation
v,nVectors
3. Properties & Laws
  • sinθ=|v·n|/(|v||n|);
  • Range [0°,90°];
  • Parallel 0°;
  • Perpendicular 90°.
4. Steps
  1. Enter v and n;
  2. Click "Angle";
  3. Or click "Load Example".
5. Worked Examples
Example: v=n=(0,0,1): sin=1, θ=90°.
6. Common Pitfalls
Use sin, not cos;
n is the normal;
Absolute value.

❓ FAQ | Line-Plane

Range?
[0,90°].
Why sin?
Complement.
Parallel?
0°.
Perpendicular?
90°.
n?
Normal.
Projection?
Orthogonal.