How to draw a hexagon by across-flats (nut head)
Hex nut heads and flanges are usually specified by their across-flats size (AF) — the distance between two parallel faces. An M10 nut, for example, usually takes a 17 mm spanner, meaning 17 mm across flats. To draw a hexagon correctly you first convert AF to a radius or to corner coordinates. This guide explains the geometry, shows accurate ways to draw it in DXCAD2D, and gives a spanner-size table.
The geometry of a regular hexagon
A regular hexagon has three key values with fixed relationships.
| To find | Formula | Approx. |
|---|---|---|
| Radius R (centre → corner) | R = AF ÷ √3 | 0.5774 × AF |
| Across corners AC | AC = 2R = 2·AF ÷ √3 | 1.1547 × AF |
| Side length s | s = R = AF ÷ √3 | 0.5774 × AF |
| Across flats AF (from AC) | AF = AC × (√3 ÷ 2) | 0.866 × AC |
Method 1: construction circle, then trace the corners
If the program can snap to points, this is the quickest way.
- Work out R = AF ÷ √3 (or AF × 0.5774), press C and draw a construction circle at the centre with radius R.
- Press P for a polyline and click six points around the circle, one per corner, then close back to the first.
- Delete the construction circle when done.
This is easy, but accuracy depends on snapping. For an exact position, use the coordinate method below.
Method 2: corner coordinates (most accurate)
Put the hexagon centre at (0,0) with the top and bottom as horizontal faces (the faces the spanner grips). The six corners are at these coordinates, where R = AF ÷ √3.
| Corner | X | Y |
|---|---|---|
| 1 | +R | 0 |
| 2 | +R/2 = +0.2887·AF | +0.5·AF |
| 3 | −R/2 = −0.2887·AF | +0.5·AF |
| 4 | −R | 0 |
| 5 | −R/2 | −0.5·AF |
| 6 | +R/2 | −0.5·AF |
Example: an M10 nut head, AF = 17 mm → R = 17 ÷ √3 = 9.815 mm. The six corner coordinates (mm) are
(9.815, 0) (4.907, 8.5) (−4.907, 8.5) (−9.815, 0) (−4.907, −8.5) (4.907, −8.5)
In DXCAD2D press P for a polyline, type each coordinate and press Enter, six points in all, then close back to the first — an exact 17 mm across-flats hexagon.
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Open DXCAD2D OnlineSpanner sizes of metric nuts (reference)
| Thread | Across flats (mm) | Thread | Across flats (mm) |
|---|---|---|---|
| M5 | 8 | M14 | 22 |
| M6 | 10 | M16 | 24 |
| M8 | 13 | M18 | 27 |
| M10 | 17 | M20 | 30 |
| M12 | 19 | M24 | 36 |
Frequently asked questions
What spanner size does an M10 nut take
Usually a 17 mm spanner (17 mm across flats), though some standards use 16 mm. When drawing from a real part, measure it with a caliper first.
What does across-flats mean
It is the distance between the two parallel flat faces of a hex nut or hexagon flange — the value the spanner size is based on.
How do I draw a hexagon from the across-flats size
Convert it to a radius first: R = AF ÷ √3 ≈ 0.577 × AF. Then draw a construction circle of radius R and trace the corners, or type the six corner coordinates for an exact result.
How much longer is across-corners than across-flats
Always about 15.5% longer, because AC = 1.1547 × AF (so a 17 mm across-flats hexagon is 19.6 mm across corners).
Summary
The key to drawing a hexagon is to convert the across-flats size to a radius first: R = AF ÷ √3 ≈ 0.5774 × AF. Then draw with a construction circle and trace the corners, or use the six coordinates for maximum accuracy. Across-corners is always 15.5% longer than across-flats — and remember that real spanner sizes vary by standard, so measure the actual part when drawing to it.