A = ½|Σ(xᵢyᵢ₊₁ − xᵢ₊₁yᵢ)|。
A = ½|Σ(xᵢyᵢ₊₁ − xᵢ₊₁yᵢ)|。
| Item | Formula / Note | Source / Standard |
|---|---|---|
| Closed-polygon area | A = 0.5 · | sum (x_i · y_(i+1) - x_(i+1) · y_i) | with the first point repeated at the end | GB 50026-2020, Code for engineering surveying |
| Absolute value and orientation | Clockwise ordering gives a negative value and counter-clockwise positive, hence the absolute value | GB 50026-2020, Code for engineering surveying |
| Coordinate closure | Check coordinate closure before computing the area | GB 50026-2020, Code for engineering surveying |
| Area accuracy | Area accuracy depends on point errors and the number of vertices | GB 50026-2020, Code for engineering surveying |