Calculate the shortest distance between two parallel planes in 3D space.
Plane Equation (Ax + By + Cz + D = 0)
3D Geometry
P₁: 2x + -1y + 2z + 4 = 0
P₂: 2x + -1y + 2z + 10 = 0
Gap Analysis
2
Distance (d)
Normal Vector(2, -1, 2)
Common Denom.3.00
Planes StatusParallel
About this calculator
Measuring 3D Planes
The distance between two parallel planes is the smallest distance from any point on one plane to the other. Two planes are parallel if their normal vectors (A, B, C) are proportional. This calculator assumes you have normalized the normal vectors to be the same for both equations.
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Pro Tips
Planes must be parallel for a constant distance to exist.
Identified by identical or proportional A, B, and C coefficients.
The result is a scalar representing physical separation.
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Fun Facts
"In general relativity, distances between curved surfaces (manifolds) require much more complex tensor calculus."
"Modern architectural software uses plane-to-plane distance to detect 'clashes' in plumbing and electrical layouts."
"The shortest path is always along the normal vector connecting the two planes."
