Angle Between Two Lines Calculator

About this calculator

When two straight lines are described by their slopes m1 and m2, the angle between them can be found without ever drawing a diagram, using tan θ = the absolute value of (m1 − m2) divided by (1 + m1·m2). The formula falls directly out of the tangent subtraction identity applied to each line's angle of inclination, and it correctly returns zero for parallel lines (equal slopes) and is undefined for perpendicular lines (where 1 + m1·m2 equals zero).

This calculator takes the two slopes and returns the angle between the lines they represent. It's a standard tool in coordinate geometry and trigonometry courses, and the same relationship is used in fields like surveying, CAD drafting, and engineering drawing whenever the angle between two linear features needs to be derived from their gradients rather than measured directly.