KEVOS® MAKEOS · Geometry
Regular Polygon and Hexagon Sizes
What are the across-flats, across-corners, side and area of this regular polygon?
Convert between side length, across-flats and across-corners sizes of a regular polygon such as a hexagon or square, with area and angles.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Number of sides | sides | 6 for a hexagon, 4 for a square, 8 for an octagon. |
| Known dimension | choice | Which dimension the drawing or standard specifies. |
| Size of the known dimension | mm | The specified dimension in millimetres. |
Method and formulas
- Across flats F = s ÷ tan(π/n); across corners C = s ÷ sin(π/n), where s is the side and n the number of sides.
- Area = n × s² ÷ (4 tan(π/n)); interior angle = 180° × (n − 2) ÷ n.
- Example: a hexagon 24 mm across flats is 27.713 mm across corners with 13.856 mm sides and an area of 498.83 mm².
Limitations
- Sharp corners are assumed; chamfered or rounded corners reduce the across-corners size and area.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Find the bar size that will yield a hexagon or square across flats
- Check spanner flats and corner clearance
- Lay out polygon pockets
Who it is for
- Design engineers
- Toolmakers
- Estimators
What you get
- Across flats
- Across corners
- Side length
- Area
- Interior angle
- Perimeter
Interpreting the result
- Round bar stock must be at least the across-corners size to machine a full polygon.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 76, 81–82. Topic reference; no source tables or recommended settings are reproduced.
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