View Full Version : Converting round to hexagon or square

Allan Waterfall
11-29-2004, 05:44 AM
Can anyone help with a formula that will give me the OD. reqd .to be able to mill an across the flats hexagon or square of any given size.

ie..... What will be the largest hexagon or square from any given size of round bar.

I've looked on Marv Klotzs site but cannot see a formula for this.


Ian B
11-29-2004, 06:54 AM

For a square, multiply the bar's diameter by 0.7071 (ie. square root of 2)

For a hexagon, multiply the bar's diameter by 0.8660



Ian B
11-29-2004, 07:24 AM

To work it out for any regular even faced polygon, take the angle between a flat and a radius from the end of the flat, and find it's sine.

ie. for a square, the angle between a radius and the end of a flat is 45 degrees; sin 45deg = 0.7071


Allan Waterfall
11-29-2004, 08:09 AM
Thanks Ian,that was just what I was looking for.


11-29-2004, 08:55 AM

There's a chart in the Machinery's Handbook in case you don't want to do the math...Goes up to 4 1/2". It's on page 169 of the 18th edition. Squares and hexes only, though.

Andy Pullen

Forrest Addy
11-29-2004, 09:14 AM
Ian, I thought the proper function was cosine.

D = size across desired flats divided by the cosine of the angle 360/n where n = number of sides.

Working the other direction: size across flats = diameter times the cosine of the angle 360/n

11-29-2004, 10:44 AM
I use a program called Machinists Friend. It works great.


11-29-2004, 12:03 PM

There's no explicit formula for this on my page. You could easily work it out
with my CSEG (Circular SEGment) program, although that's probably more work
than simply drawing it and doing a bit of simple trig.

The formula you want is:

D = daf/cos(360/N)


D = required (cylindrical) stock diameter

daf = distance across flats

N = (even) number of polygon faces

You may want to examine the TENON program, which will calculate the depth of
cut you need to form each polygon face.

Regards, Marv

Home Shop Freeware - Tools for People Who Build Things

11-29-2004, 12:18 PM
This might help...


Allan Waterfall
11-29-2004, 01:59 PM
Thanks to everyone who replied,I can now make the appropriate hexagons.
Not having done any trig. for more than 45 yrs I have forgotten how to work things like that out.


11-29-2004, 03:20 PM
Allan, it`s time to dust off the old log tables http://bbs.homeshopmachinist.net//biggrin.gif http://bbs.homeshopmachinist.net//biggrin.gif
Seasons greetings, Ken