Point to Plane Distance Calculator
Calculate the perpendicular distance from a 3D point to a plane, with signed distance, orthogonal projection, and plane built from coefficients or three points.
Distance from a point to a plane
Search intent for point-to-plane distance is direct 3D analytic geometry: enter a point and a plane, then get the shortest perpendicular distance and the foot of the perpendicular.
d is the perpendicular distance from point (x0, y0, z0) to plane Ax + By + Cz + D = 0.
Signed distance and projection
- Ordinary distance is always nonnegative.
- Signed distance keeps the side of the plane relative to the chosen normal direction.
- The projection point is the closest point on the plane.
- If the plane is entered by three points, the calculator first builds its equation.
Examples
| Point | Plane | Distance |
|---|---|---|
| (0, 0, 3) | 3 | |
| (1, 2, 3) | x + y + z - | 0 |
| (0, 0, 0) | x + y + z - | about 0.5774 |
Frequently Asked Questions
Sources and References
- Distance from Point to Plane CalculatorOmni Calculator
- Point-Plane DistanceWolfram MathWorld
- Distance from Point to Plane CalculatorMiniWebtool
- Distance from a point to a planeWikipedia
Calculations are based on the listed reference sources. Links open in a new tab.
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