Convex Polygon Intersection and IoU Calculator
Clip two convex polygons and calculate intersection, union and IoU with a shared-scale outline diagram.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Normalize each strict convex boundary and apply successive oriented half-plane clipping, then measure the resulting polygon.
Union area=area A+area B−intersection; IoU=intersection/union
Worked example
Two 4 by 3 rectangles at [0,4]×[0,3] and [2,6]×[1,4] overlap in a 2 by 2 rectangle. Intersection is 4, union 20 and IoU 0.2 in the corresponding area units.
Assumptions and input details
3–30 vertices per strictly convex non-self-intersecting polygon in either boundary winding, with no collinear corners. Coordinates have magnitude at most 1e6 before unit scaling. Touching edges/points have zero area. Floating-point clipping is not a robust exact GIS topology engine; concavity, holes, multipolygons and geographical curvature are excluded. Distinct from the existing axis-aligned rectangle overlap calculation.
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
Choose from 23 length definitions, including explicitly labelled regional measures. Area conversions square the length factor; geometric volumes cube it.
Regional measures are not interchangeable merely because their names look similar. This is a documented selection, not a claim to include every historical unit.
NIST measurement tables · Japanese traditional units · Mainland China and Hong Kong unit distinctions
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
Calculate area, perimeter and area centroid from 3–50 ordered vertices of a simple polygon. Inspect an equal-scale outline and a table of edges.
Offset a convex polygon boundary outward or inward by a signed distance and inspect miter coordinates, area and a boundary diagram.
Calculate intersection area, union area and coverage fractions for two axis-aligned rectangles.
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