Calculate the angle of intersection between two straight lines based on their slopes.
Line Equations (y = mx + b)
Line 1: y = 1x + b₁
Line 2: y = -1x + b₂
Intersection Angle
90.00°
Acute Angle (θ)
Obtuse Angle90.00°
Value in Radians1.5708
Perpendicular?Yes
About this calculator
Angles and Slopes
The angle between two lines is determined by their slopes. If the lines are not vertical, the tangent of the angle between them is given by the relative difference in their slopes. This formula finds the angle of intersection in a 2D plane.
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Pro Tips
If 1 + m₁m₂ = 0, the lines are perpendicular (90°).
If m₁ = m₂, the lines are parallel (0°).
The result is usually given as an acute angle (0-90°).
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Fun Facts
"Slopes are also a form of 'gradient' used in machine learning to optimize neural networks."
"The angle between lines is invariant under rotation and translation of the coordinate system."
"In surveying, calculating precisely how lines meet is vital for property boundary definitions."
