Angle Between Two Lines Calculator
Determine the precise angle between intersecting lines or vectors using Slope or Coordinate Geometry.
The Math Behind It
The angle θ (0° ≤ θ ≤ 180°) represents the inclination between two linear entities.
Method 1: Slopes
Best for algebra and 2D graphs. Uses the tangent difference formula:
Method 2: Vectors
Best for physics and 3D geometry. Uses the Dot Product rule:
Quick Interpretations
- ||0° (Parallel)
Lines run in the same direction and never intersect.
- ⊥90° (Perpendicular)
Lines intersect at a perfect right angle. (Slopes multiply to -1).
- ∠< 90° (Acute)
A sharp intersection angle.
Enter values to compute the angle
Real-World Scenarios
Game Development
Used in collision detection. If the angle between a character's velocity vector and a wall's normal vector is < 90°, the character is moving towards the wall.
Architecture
Essential for calculating roof pitches. Architects measure the angle between two roof planes to determine proper drainage and structural support beams.
Aviation
Pilots calculate the angle between their current heading vector and the wind vector to correct for drift and maintain a straight course.
Frequently Asked Questions
Why are there two possible angles?
Two intersecting lines actually create two pairs of angles: an acute pair (e.g., 30°) and an obtuse pair (e.g., 150°). This calculator typically returns the acute angle (0-90°) by convention.
What if the lines don't intersect?
In 3D space, non-intersecting lines are called skew lines. However, you can still calculate the angle between their direction vectors by translating them to a common origin.