ClarityHow to use this tool
- Enter vertices: x,y per line.
- Select Calculate to view the result.
- Check the method and assumptions below before using the result.
The method, explained
Apply the shoelace sum to successive vertex cross-products, closing the final vertex to the first. Area is half its absolute value; perimeter sums edge lengths.
Using vertices: x,y per line = 0,0 4,0 4,3 0,3, the result is 12. Change these example inputs to match your task; use the method above to check each step.
Understanding your result
Yes. List consecutive boundary vertices, clockwise or counterclockwise. Reversing the order preserves absolute area, but arbitrary reordering changes the edges and shape.
What to keep in mind
Supply a simple non-self-intersecting polygon in boundary order, without holes. Self-intersections are not detected; their algebraic area may be misleading. Use the indicated units consistently. Ideal shapes are assumed; dimensions must describe the same object. Display rounding does not increase measurement precision.
Common questions
Does the vertex order matter?
Yes. List consecutive boundary vertices, clockwise or counterclockwise. Reversing the order preserves absolute area, but arbitrary reordering changes the edges and shape.
How can I check the result?
Apply the shoelace sum to successive vertex cross-products, closing the final vertex to the first. Area is half its absolute value; perimeter sums edge lengths. The worked example uses editable inputs. Calculations run on your device; no external API or account is required.
Methodology maintained by ClarityKit. How these tools are built and checked.