Analyze vertices, perimeter, area, centroid, and normals. Use flexible rows and instant result summaries below. Download reports and inspect polygon geometry with confidence today.
| Vertex | X | Y | Z |
|---|---|---|---|
| V1 | 0 | 0 | 2 |
| V2 | 4 | 0 | 2 |
| V3 | 4 | 3 | 2 |
| V4 | 0 | 3 | 2 |
Example result: perimeter = 14, area = 12, centroid = (2, 1.5, 2).
Distance = √[(x2 - x1)2 + (y2 - y1)2 + (z2 - z1)2]
Perimeter = sum of all edge lengths, including the closing edge from the last vertex back to the first.
The calculator uses Newell’s method to build a polygon normal from ordered vertices. Area = 0.5 × |N|, where N is the Newell normal vector.
Centroid = (sum of x / n, sum of y / n, sum of z / n)
After normalizing the polygon normal, the supporting plane is written as ax + by + cz + d = 0.
List the vertices in boundary order. Use either clockwise or counterclockwise order for consistent area and normal values.
A 3D polygon calculator helps you study a flat shape in space. You enter each vertex with x, y, and z coordinates. The calculator connects those points in the order given. It then computes the edge lengths, full perimeter, polygon area, centroid, plane equation, and unit normal.
This is useful in math classes, modeling tasks, and geometry checks. It reduces manual work. It also helps you confirm whether a group of points behaves like a planar polygon. When the planarity error is small, the input is more reliable for area and plane results.
The order of the vertices is important. A proper order traces the outer boundary of the face. If the points jump across the shape, the polygon may cross itself. That can change the normal direction and distort the area.
For best results, enter the coordinates in clockwise or counterclockwise order. Keep the units consistent. A mixed unit list can produce a correct formula but a useless answer.
Perimeter comes from the 3D distance formula. Each edge length is measured from one vertex to the next. The last point also connects back to the first point. Area is found with Newell’s method. This method builds a normal vector from the ordered vertices. Half of the normal magnitude gives the polygon area for planar data.
The centroid shown here is the average of the entered vertices. It is fast and practical for many coordinate checks. The plane equation is built from the unit normal and one input point. Together, these outputs help you inspect the size, position, and orientation of the polygon.
Use this tool when you need quick shape measurements from coordinate lists. It works well for classroom exercises, CAD preparation, graphics work, and spatial validation. Because the outputs are grouped in one place, you can compare multiple polygons more easily and export the results for review.
A 3D polygon is a flat shape defined by vertices in three-dimensional space. Each point has x, y, and z coordinates. The edges connect in order to form one closed boundary.
You need at least three complete vertices. Two points only form a line. More vertices let you model triangles, quadrilaterals, pentagons, and larger polygon faces.
Yes. The order affects edge connections, area, and normal direction. Enter points around the boundary in clockwise or counterclockwise order for consistent results.
The calculator uses Newell’s method. It builds a polygon normal from ordered vertices. Half of that normal’s magnitude gives the area when the polygon is planar.
Planarity error shows how far the vertices drift from one common plane. A smaller value means the points fit a flat polygon better. A larger value suggests noisy or non-planar input.
This page reports the average of the vertex coordinates. That is useful for many checks. For irregular faces, it is not always the same as the area-weighted center.
Yes. The calculator accepts positive values, negative values, and decimals. Just make sure every used row has all three coordinates filled in.
The CSV button downloads the computed values and edge lengths. The PDF button opens the print flow, where you can save the page as a PDF from your browser.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.