THE NUMBERS, EXPLAINED
How to use this calculator.
Uses the shoelace formula for a simple polygon. Vertices must follow the boundary; self-intersecting paths are rejected.
Start with your inputs
Enter ordered vertices x,y (one per line). Keep amounts in the units shown on each field. The example is a starting point, not a recommended value.
| Input | Example value |
|---|---|
| Ordered vertices x,y (one per line) | 0,0 4,0 4,3 0,3 |
A worked example
With the example inputs above, area is 12. Change the inputs to explore your own scenario.
| Result | Example answer |
|---|---|
| Area | 12 |
| Perimeter | 14 |
How this is calculated
Area
Join the final vertex back to the first. Area = abs(sum of xᵢ × yᵢ₊₁ − xᵢ₊₁ × yᵢ)/2 (shoelace rule).
Perimeter
Add sqrt((xᵢ₊₁−xᵢ)^2 + (yᵢ₊₁−yᵢ)^2) for every edge, including the closing edge.
Symbols and units
- a
- Ordered vertices x,y (one per line)
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Assumptions and limits
Uses the shoelace formula for a simple polygon. Vertices must follow the boundary; self-intersecting paths are rejected.
Calculations use the values you enter. Blank or invalid inputs show an error instead of silently substituting zero. Results are displayed to useful precision; calculations retain the underlying numeric precision.
Questions about this tool
What does the result tell me?
Area; Perimeter. The result applies to the method and inputs described above. Check the units and assumptions before using it in a decision.
Why might another calculator differ?
Differences in units, rounding, timing or model definitions can produce different answers. Compare the input definitions and the method, rather than only the final number. For this tool: Uses the shoelace formula for a simple polygon. Vertices must follow the boundary; self-intersecting paths are rejected.
Are my inputs stored or sent to AI?
Calculations on this page happen in your browser. The separate AI question finder sends its submitted conversation to OpenAI; these calculator fields are not sent. Favourites and recent tool names are stored locally. A shared link contains the inputs you choose to include.
Further reading
Background reading; this does not imply endorsement or independent review of SumFizz.
Review status
Software example and browser checks are recorded in our quality report. No external expert review is claimed. Created with coding assistance; calculations run as ordinary browser code.
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