This is a razor bevel calculator spreadsheet in OpenOffice native format. Try it with excel, it might work. I dont know cause I domt mess with that Microsoft stuff. But in case it doesn't work for you WinDohs guys, here it is in Microsoft 97 format. Aint that something... Linux can use and even write WinBlows files but WinDOHs can't open a totally open source file format? So much for supposed superiority of secret source big pricetag software. Anyhow here is bevelcalc.xls
The spreadsheet doesn't do you much good if you don't know how to use it. Well, it's not rocket science. The two red cells are user-entered data. Enter the smallest spine thickness you expect to deal with in the first cell, A1. The next measurement is the distance between the upper edge of the spine bevel to the shaving edge. This is the hypotenuse of an imaginary triangle that the spreadsheet will solve to give the bevel angle. Enter that value in cell B1, the second red cell. Click on a cell in the table and your spreadsheet app will calculate all possible values for the range beginning at your entered data, and populate the table with these values, so you can look up a hypotenuse and a spine thickness and find the calculated bevel angle. Further, you can look at nearby values and see what width or thickness you need to get the desired bevel angle. And by the way, cell C1 is the bevel angle for the entered values.
And here is a screenshot of the spreadsheet, opened with LibreOffice in Ubuntu.
Why is the bevel angle important? Well, if it is too acute, i.e. too skinny or too sharp, the edge will topple when you try to hone it. Or maybe the edge will hone up okay but will crumble as soon as you try to use it. If the bevel angle is too obtuse, i.e. too fat or too blunt, the shave will be mediocre or worse. Every razor has its sweet spot depending on your tastes, the steel, and the grind of the razor. Usually the sweet spot is between 16 and 17 degrees. A degree more or less is still usually quite good. Below 14 degrees is usually way too acute and above 19 degrees way too obtuse. YMMV of course. So the bevel angle is important... what can we do about it? After all, everybody talks about the weather, but nobody does anything about it. Well, sometimes you can do something about the bevel angle. When modifying a Gold Dollar, for instance, you have complete control over the bevel angle. Do it like you feel it. When honing, you can deal with an acute bevel with tape on the spine. You can deal with an obtuse bevel by honing deep into the spine. Or just leave it be, but you will have a good idea where certain performance issues might originate, because you know what the bevel angle is, precisely.
For the mathematically inclined or the curious, here is how the bevel angle is calculated. The geometry of the blade can be represented by an isoceles triangle. The base is a line from the upper edge of the spine bevel on one side, to the same spot on the other side. From those two points, the two sides run to the edge, where they meet. An isoceles triangle can be most easily solved by cutting it into two right triangles. One long side becomes the hypotenuse for each right triangle. That is the longest, diagonal, side. Take half of the base and that is the Opposite side from the angle to discover. The third side, the Adjacent side, cannot be measured reliably since it exists only within the steel. But we have two sides, and that is enough to solve for the angle.
The formula to use here is S=O/H, where S is the unknown Sine of the unknown angle, O is the Opposite side, H is the Hypotenuse. The Hypotenuse as you remember can be measured. It is the distance from the shaving edge to the top edge of the spine bevel. O is half the thickness of the spine. So a little division and we get the Sine of the angle. Looking up the angle is easy enough on a scientific calculator. Doubling that angle gives the bevel angle. Lucky for you, the spreadsheet does the math automatically for you. But, that is how it finds the bevel angle, and that is how you can do it, too, if you dont have this really cool spreadsheet at your disposal.
Here is a diagram showing how the triangle relates to the razor.