I need to machine a spindle taper ISO, NT, BT all the same taper 7:24 included angle, here is my question :-

What angle do I program into the lathe?

ATAN(7/24)/2 or ATAN(7/48) ??

   I just had to machine some grinder spindle hubs over the holidays. So I wrote a program (using Arts Gearotic/Auggie/Monkey C code) to help me understand the start and stop points for my lathe

Interested to see if these are correct for you; I used the major OD dimension and a length of a holder I'd found on the net.
24/7 = 12/3.5 = 3.5" per foot

I'd verified my grinder spindle taper dimensions with autocad.
the trick to my programming was to remember the taper is included angle not a right triangle. So the calculations had to take that into account.

I modified a Bridgeport spindle a few years ago with my tool post grinder on a manual lathe, still works great for my needs. Now handles both R8 and Cat30 collets.

Thanks, that is what a German tooling company and I get but some forums and web site say different so I thought I would open it up to this forum to see what results I got.

Your welcome

did find this info that might verify for you:

http://www.practicalmachinist.com/vb/general/what-angle-bt40-taper-272649/

Good luck Have Fun

FROM WIKIPEDIA

The National Machine Tool Builders Association (now called the Association for Manufacturing Technology) defined a steep taper that is commonly used on milling machines. The taper is variously referred to as NMTB, NMT or NT. The taper is 3.500 inches per foot and is also referred to as "7 in 24" or 7/24; the computed angle is 16.5943 degrees.[5] All NMTB tooling has this taper but the tooling comes in different sizes: NMTB-10, 15, 20, 25, 30, 35, 40, 45, 50 and 60. These tapers were apparently also specified in ASA (now ANSI) B5.10-1943.

[ 5 ]The angle of the cone is 2 atan(7/48).

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RICH COMMENT:
So cone angle is 16.5943 deg
About the center line of the cone, one side would be 8.29714 deg.

Make sure when you use your calculator you have it set for degrees and not radians ,or grad.  

And if you use the taper wizard in Mach, double check as I don't remember if it works in both radius and diameter mode and also don't recall what angle you input.
Opps, strike through were  thoughts  relative to  threading a taper.  MODIFIED:1/9/17 BY RICH

RICH