Perpendicular Line Calculator

About this calculator

Two lines are perpendicular when their slopes are negative reciprocals of each other — if a given line has slope m, any line perpendicular to it has slope −1/m, a direct result of the geometric fact that perpendicular lines meet at a 90-degree angle. Once that perpendicular slope is known, plugging in a specific point through the point-slope form yields the full equation of the perpendicular line, including its y-intercept.

This relationship is a core tool in coordinate geometry, used to construct perpendicular bisectors of segments, find the shortest distance from a point to a line, determine altitudes of triangles, and check whether shapes have right angles — skills that carry directly into CAD drafting, computer graphics, physics (like resolving forces into perpendicular components), and standardized math tests.

This calculator takes a given slope and a point the perpendicular line must pass through, then returns the perpendicular slope and the full equation of that line.