Racira CAD

Area Calculator (polygon)

Polygon vertices

V1
V2
V3

The polygon is closed automatically — the last vertex connects back to the first. A triangle with vertices at (0,0), (30,0) and (0,40) must return an area of 600.

Result

Area600.000 mm²
Perimeter120.000 mm
Winding (shoelace sign)CCW
Vertices3

Area = ½ × |Σ(xᵢ·yᵢ₊₁ − xᵢ₊₁·yᵢ)|. The winding is the sign of the raw sum — positive is counter-clockwise in the standard CAD convention. A degenerate (zero-area) vertex order reports "Degenerate".

What is Area Calculator (polygon)

Area Calculator (polygon) computes the enclosed area of any closed polygon from its vertex coordinates using the shoelace formula: area equals half the absolute value of the sum over every edge of x-sub-i times y-sub-i-plus-1 minus x-sub-i-plus-1 times y-sub-i. You type the X and Y coordinates of each corner, the polygon is closed automatically back to the first vertex, and the tool returns the area, the perimeter, the winding direction and the vertex count.
The winding direction is the sign of the raw shoelace sum before the absolute value: a positive sum means the vertices were entered counter-clockwise, which is the standard CAD convention, and a negative sum means clockwise. The unit selector covers millimetres, centimetres, metres, inches and feet and only changes how the area is labelled — a 600 square millimetre answer simply becomes the same number in whatever unit you picked, squared. The polygon can be convex or concave; the formula handles both without special cases.

How to Use Area Calculator (polygon)

  1. Step 1: Pick the Unit — millimetres, centimetres, metres, inches or feet. All vertex coordinates are interpreted in that unit.
  2. Step 2: Enter the X and Y coordinates of each polygon corner in the vertex list. The default example is the triangle (0,0), (30,0), (0,40).
  3. Step 3: Press + Add vertex for every corner beyond the starting three, and − Remove to take one back off if you added too many.
  4. Step 4: Read the Result panel: Area, Perimeter, Winding and Vertices. The winding tells you whether your vertex order is clockwise or counter-clockwise.
  5. Step 5: Sanity-check a known case: the default triangle must return an area of 600 and a perimeter of 120, and a rectangle with corners (0,0), (100,0), (100,50), (0,50) must return 5000.
Vertex order matters only for the winding sign, never for the area or perimeter. Entering the same four corners clockwise gives the identical area with a CW reading, so you never have to re-type a shape because you walked it the wrong way round.

Why Use Area Calculator (polygon)

Irregular outlines are everywhere in fabrication — laser-cut profiles, gaskets, site ponds, concrete slabs with notches — and none of them answer to a rectangle formula. The shoelace method is the same arithmetic a CAD system uses to report a closed region's area, so the number this tool returns matches the model rather than an approximation from counting grid squares or splitting the shape into trapezoids by hand.
The perimeter and winding outputs make the tool useful beyond the area itself. The perimeter feeds edge-rolling, trim and weld-length quantities, and the winding direction matters when you are checking the vertex order of a boundary you exported from another program — most CAM and GIS workflows require counter-clockwise ordering for outer boundaries. Because everything runs locally in the browser, you can check a quantity without exporting the model or licensing another package.

Privacy & Security

This tool runs entirely in your browser — no data ever leaves your device. There is no server round-trip, no upload, no logging, and no account required. Your input is processed locally using client-side JavaScript and is never stored, transmitted, or accessible to anyone else. When you close the tab, everything disappears.

Frequently Asked Questions

Do I need to repeat the first vertex at the end of the list?

No. The polygon is closed automatically — the last vertex connects back to the first, exactly as it does in the perimeter tool. A triangle needs three vertices, not four. Repeating the first vertex creates a zero-length closing edge, which leaves the area unchanged but makes the vertex count misleading.

Why does the default triangle return 600?

The shoelace sum for (0,0), (30,0), (0,40) is 0 times 0 minus 30 times 0, plus 30 times 40 minus 0 times 0, plus 0 times 0 minus 0 times 40, which works out to 1200. Half of that is 600, and because the sum is positive the winding reads CCW. This is the classic right-triangle check: the same shape as a 30 by 40 rectangle split on its diagonal, which has half the rectangle's 2400 square units.

Does the order of the vertices change the area?

No — only the winding sign flips. Entering the same boundary clockwise produces the same area and perimeter with a CW reading. If your winding comes out opposite to what your drawing convention expects, the vertices are simply entered in the reverse order, and the numbers you care about have not changed.

Does the formula work for concave polygons?

Yes. The shoelace formula sums signed edge contributions, so a notch subtracts exactly the region it encloses — concave and convex shapes both give the true enclosed area with no special handling. This is the same reason the perimeter behaves independently: a deep notch removes area but keeps its full boundary length.

What units is the area reported in?

The area is the square of the selected unit — millimetres squared, metres squared, inches squared and so on. If you need to compare quantities measured in different units, convert the coordinates first using the CAD Unit Converter, then run the area check, because squaring makes unit errors twice as costly: a 25.4 factor becomes a 645 factor in the area.