What are dovetails and why would I want to measure them? Dovetails are types of joints used to connect two pieces (such as wood or metal) together for a (usually) tighter fit. Often they are used where the two pieces must slide relative to one another in only one of the 3 axes (x, y, and z). For example, you might see a dovetail joint used on a vise so the movable jaw can only move either towards or away from the fixed jaw, but in no other direction along any other axis. In some machinery when it is expected to be put into heavy use, small spacers (called gibs) are often placed inside the dovetail, the purpose being to allow the joint to be tightened (by adjusting the gibs) periodically as the parts wear. Of course, the reason you would want to measure dovetails would be preparatory to cutting them.
Dovetails modeled in FreeCAD: stl.stl
But why would I need a calculator to make some measurments? Well, you could certainly measure them without this calculator, but where great precision is needed they can be difficult to directly measure accurately enough. For example, if a machinist is making an accessory for his metal lathe that will extend an existing dovetail, he would need some very accurate measurements of the existing dovetail in order to fashion a piece that would mate with it properly. The primary difficulty is in getting the measuring device into the corners. No matter how tiny the measuring tip of the instrument, it will still never quite get into the corner all the way. (Note the circles in the images above, and how they don't reach completely into the corners.) It's far easier to get really good measurements of the red lines in the images above than it is to do the same with the white lines. By using dowels (or other similarly shaped objects) the dovetails can be measured with great accuracy, provided we know with great accuracy the diameter of the dowels and the angles of the dovetails, along with a little bit of trigonometry. This calculator handles all the trig for you.
In the top image you see a female dovetail, the bottom is the male. The white lines and the blue lines color code the matching surfaces. The 2 circles represent the steel dowels used to aid in the measurements. The dowels are not a part of the joint when the pieces are put together. The green line represents the diameter of the dowel. I say dowels, but these can be any rod-shaped objects of any diameter reasonably close enough to match the scale as shown in the images. The yellow line represents the height of the dovetail. It should be the same for both pieces, but if it's different, use the male part's height. (The Y parts of the tricky ones, but you should be able to get decent measurements for the T parts, both male and female, which can be used as a crosscheck for the values calculated with this calculator. If the T values the calculator gives you aren't very close to the ones you're directly measuring, then something isn't right somewhere, so don't just accept these numbers blindly.)
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