This is a calculator to help determine the necessary angle to set your compound feed on your metal lathe at in order to achieve the desired ratio of the amount of feed in the x-axis to the amount the cutting tool actually moves in the y-axis towards the work. For example, if you set the compound angle at 30 degrees relative to the ways (which would be 60 degrees relative to the crossfeed y-axis) this would give you a 2:1 ratio. For every 2 thousandths you feed in at the 30 degree angle the cutting tool will move 1 thousandth in the y-axis towards the work. The value in this is you can advance the cutting tool towards the work with greater precision. If you set it at the proper angle for a 10:1 ratio and advance the compound feed one thousandth the cutting tool will only move 1/10 of one thousandth towards the work.
You can either enter the angle (in which case the ratio is computed) or the ratio (in which case the angle is computed). The 10:1 ratio offers great precision, but sometimes there might not be enough room to use that angle if you are working between the centers of the headstock and the tailstock with a long piece of work. If that's the case you can set the most acute angle you can use, and then use this calculator to see what ratio that angle would give you. Alternatively, you can try other ratios, such as 9:1 or 8:1 until you find you that works for you. For example, if you wanted to take 1 thousandth off the work and 8:1 is the best ratio you can use, you'd set the compound angle to the one computed for 8:1 ratio and feed the tool 8 thousandths.
If you want to watch a great youtube video on this process, see this one by mrpete222, who also has a great many other fantastic videos if you're interested in machine shop-related videos.
--Mark Ganson