Ray-Plane Intersection Calculator

About this calculator

In 3D graphics and geometry, a ray is expressed parametrically as O + t·D, an origin point O extended along a direction D by a scalar t, while a plane is defined by the implicit equation n·X = d, where n is the plane's normal vector and d is a constant offset. Substituting the ray into the plane equation and solving gives t = (d − n·O) / (n·D); plugging that t back into O + t·D yields the exact hit point.

This is the core computation behind ray tracing renderers, CAD collision and clipping tests, and physics-engine raycasts. When n·D is zero the ray is parallel to the plane and never intersects it (or lies within it), and a negative t means the intersection lies behind the ray's origin rather than in front of it — both cases this calculator flags explicitly.