Angle Between Two Lines Calculator

About this calculator

Given the slopes of two straight lines, m₁ and m₂, the acute angle θ between them follows from the tangent of the angle between two vectors formula: tan(θ) = |(m₂ − m₁) / (1 + m₁·m₂)|. The absolute value guarantees the result is the acute angle rather than its obtuse supplement, and taking the arctangent of that ratio converts it back into an actual angle, which can then be reported in degrees or radians.

This relationship falls directly out of the fact that a line’s slope equals the tangent of the angle it makes with the horizontal axis, so the difference formula for tangent (tan(A − B)) applied to each line’s angle of inclination reduces to an expression in slopes alone, with no need to compute either angle individually first. Students and engineers use this shortcut in analytic geometry, technical and engineering drawing, and any application involving line intersections — road and rail alignment design, structural framing angles, computer graphics — where the two lines are already known by their slopes rather than by two points each. This calculator takes the two slopes and returns the angle between the lines in both degrees and radians.