Distância Ponto-Plano
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
ponto-plano
About this calculator
The distance between a point and a plane is a fundamental concept in geometry and is calculated using the formula |ax+by+cz+d|/√(a²+b²+c²). This formula is based on the equation of the plane, which is ax + by + cz + d = 0.
The distance is calculated as the magnitude of the vector normal to the plane, projected onto the vector that links the point to the plane. This means that the distance is a measure of the perpendicularity between the point and the plane.
The distance point-plane formula is used in various fields, such as physics, engineering and geography, to calculate distances and measure the proximity between objects and surfaces.
It's worth noting that the distance point-plane is calculated based on the equation of the plane, therefore, a coordinate system and the plane's equations are necessary.
Frequently asked questions
Do I need to know the equation of the plane to calculate the distance point-plane?
Yes, the equation of the plane is necessary to calculate the distance point-plane. The plane's equation must be provided in the form ax + by + cz + d = 0.
Can I calculate the distance point-plane if the plane is parallel to the x-axis?
Yes, it is possible to calculate the distance point-plane, even if the plane is parallel to the x-axis. Simply substitute a = 0 in the plane's equation and calculate the distance as |bx+cy+d|/√(b²+c²).
Is the distance point-plane always positive?
Yes, the distance point-plane is always positive, as it is the magnitude of the vector normal to the plane, projected onto the vector that links the point to the plane.
Can I use the distance point-plane calculator to calculate distances in different coordinate systems?
Yes, the distance point-plane calculator can be used to calculate distances in different coordinate systems, as long as the plane's equation is provided in the correct form.