Angle Between Line and Plane Calculator
Find the acute angle between a 3D line and a plane from a direction vector or two points on the line and the plane equation coefficients.
D does not change the angle, but it can identify whether a parallel line lies in the plane.
Angle between a line and a plane
English search intent for line-plane angle is a 3D vector problem. The calculator uses the line direction vector and the plane normal vector, then returns the smaller angle between the line and the plane.
theta is the line-plane angle, s is the line direction, and n is the plane normal.
Parallel, perpendicular, and oblique cases
- 0° means the line is parallel to the plane or lies in it.
- 90° means the line is perpendicular to the plane.
- An angle between 0° and 90° means the line meets the plane obliquely.
- D does not change the angle, but it can help test whether a parallel line lies in the plane when a point is known.
Examples
| Line direction | Plane | Angle |
|---|---|---|
| (1, 1, 1) | about 35.264° | |
| (1, 0, 0) | 0° | |
| (0, 0, 1) | 90° |
Frequently Asked Questions
Sources and References
- Angle between a line and planePlanetMath
- Angle between a Plane and a Line Calculator123Calculus
- Online calculator. Angle between line and planeOnlineMSchool
- Angles between flatsWikipedia
Calculations are based on the listed reference sources. Links open in a new tab.
Related Tools
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Calculate the smaller angle between two planes from their normal vectors or standard plane equations, with degree/radian output and relationship labels.
Calculate the perpendicular distance from a 3D point to a plane, with signed distance, orthogonal projection, and plane built from coefficients or three points.
Calculate the shortest distance from a point to a 3D line using a point and direction vector or two points on the line, with projection and closest point.