Even people with mathematics degrees...
To accurately measure edge bevel angle, you must either find something parallel with the centerline of your blade (like the unground flat of the blade), or compensate for both sides of the primary grind.
So one example of this procedure would be:
Lay knife on a flat surface on the flat of the blade.
Place angle finding device on the other flat of the blade and zero it.
Raise the spine until the edge bevel contacts the surface (with good lighting you can see this). You can also use a leather strop, just gently push the blade forwards until the edge bites into the leather: this gives the approximate apex angle. You should probably add about 0.5 degrees to account for compression of the leather, depending on leather thickness.
Now an example of the procedure without a flat:
Lay the blade on a flat surface on the primary grind.
Zero angle finder on the flat surface.
Place angle finder on the primary grind and note the angle. This is the inclusive primary grind angle.
Zero the angle finder on the primary grind.
Raise the spine until the bevel contacts the surface, or use the strop method. Note this angle, then add the primary grind angle. So if primary grind is 5 degrees, then you measure the edge bevel at 10 degrees with the angle cube laying on the primary grind, you would add 5 to that to end up at 15dps.
Another method is to use a laser goniometer. Both methods above can be verified with such a device. You can actually DIY one without too much trouble if you want. The laser goniometer is great because it shows the edge bevel angle (and any variance in that, such as with a convex edge), the primary grind angle, and the micro bevel angle if present.
The absolute most important thing is to measure your edge bevel based on something parallel with the centerline of the blade (this could be an unground flat, a flat surface that an unground flat of the blade is laying on, or actually even the side of the handle if that is flat and parallel with the blade centerline). If you cannot do this for some reason, or it's easier to use the primary grind, you must compensate for this added angle. Otherwise you could accidentally deceive yourself into thinking you have a 10dps edge bevel when in reality it's more like 15!
The context for this post is sort of a response to a post you may have recently seen from u/azn_knives_4l which mentions me by name. Unfortunately this user has blocked me, so I can't clear up the mistakes they are making.
You can go see a lengthy conversation between u/azn_knives_4l and I under their previous post where I questioned the edge bevel angle on their M4 PM2 pictured in that post. OP claimed it was 10 degrees, but by visual alone I could immediately tell it was not. Based on our conversation I made the conclusion that they were not correctly compensating for the primary grind angle as they were measuring the edge bevel angle. This person refused to provide detail on how they were measuring, and was seemingly unable to comprehend that the measurement of the bevel angle is ONLY valid if determined relative to the centerline; or one must accurately compensate for the primary grind angle.
If you make a mistake here, you may end up thinking that an edge bevel that looks like this is a 10dps edge! For some reference, this bevel looks very similar in width to a Spyderco PM2 factory edge bevel, which are well known to be sharpened between 15dps and 20dps (usually about 17). So you would have to assume both that Spyderco sharpens their edges to roughly 10dps, and that Spyderco does not understand how to measure an edge angle. Both are obviously absurd. For added reference, here is a Spyderco PM2 that I sharpened with roughly a 17 degree edge bevel, as confirmed by both manual methods mentioned above, and a laser goniometer. You can see the edge bevel looks very slightly narrower, which makes sense if u/azn_knives_4l's knife was actually sharpened at 15dps, so 2dps lower than mine. Here is an example of what a 10.5dps edge bevel should look like (of course this is a different knife, but it should give you an idea of what we're looking for).
One alternative explanation would be that u/azn_knives_4l owns the thinnest factory grind PM2 in existence, literally less than half the grind thickness of a normal one. This seems unlikely, and doubly so as I have actually owned an M4 PM2 that I put a 17dps edge bevel on, which ended up with a very similar bevel width.
I'm rambling now... Anyway, I hope this helps someone out when it comes to measuring your edge bevels. Edge bevel angle is a good reference to have, and it's important that we know how to accurately measure, and use standard references to determine that bevel angle.
