Lathe leveling - will this work?

In general, leveling is a short-cut to get you really close to true alignment, you still gotta prove it via taking some test cuts. So, start with the bench or cabinet or whatever, then the bedways, get it as close to level with what you have, then adjust the bed at the tailstock end based on actual turning to minimize the taper, like John mentioned above. There are plenty of 'how to' descriptions out there on the net, once you get past the leveling part of things. Admittedly you are starting out with a disadvantage given the resolution of your level, but if you don't have a more accurate one, you gotta use what you got. Harder to do and takes longer, but do the best you can.
 
I have an iGaging digital level which also reads to .05º. However, in testing that I have done, it is not repeatable to better than .3º. The test is this: my mill bed is leveled with a .0005"/10" machinists level. An 18" ground steel bar is placed on the bed and the level placed on that and zeroed. Shims are placed on on or the other end and the level read. A .045" shim shows a reading of .20º when placed under the left side and .00º when placed under the right side. The angle should be arcsin .04/18 or .127º. Various other angles yield similar results.

On the other hand, this angle is equivalent to 1/32" per ft and is easily detectable with a good carpenter's or mason's level.

The digital level is useful for setting work angles that don't require the precision of a sine bar setup. (And I hang picture with the free digital level ap on my phone.)
 
My floor is unfortunately very uneven and I’ve noticed that the machine was not properly tight around the frame etc. I have now sorted that and replaced some bolts even. I have also noticed a taper across a fairly short distance so I just want to rule out leveling and go from there.
You dont need a level..
Check the taper 12" apart and take it form there..
Is the lathe new or old?

 
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If you want to buy a level buy a cheap one like this on Ebay: I looked on SA Ebay. I agree with BenChee and Eeler and the others. Use the 3 collar test
it is on a big lathe but the principal is the same.

cheap level.
 
Bench lathes generally have a 3 point mounting and do not need accurate leveling, small lathes with metal legs or stands under them can be aligned by the two collar method; here, accurate leveling is not necessary, only proper alignment to eliminate taper in the workpiece.

Very correct Ben. It is a false premise that a late has to be level. Picture if you will a lathe in the workshop on a ship It's bolted to a heavy steel frame that is in turn bolted or sometimes welded to the ships structure. Now every time the ship rolls or pitches that lathe is going through the exact same motions. Yet the Engineers / machinists on board regularly make and repair precision parts under these conditions. I did it for most of my working life.

What is important that lathe bed us straight and true, no twists or bends no hogging or sagging. The ultimate test is turning a test piece. It can be a great mistake to just bolt a machine down to a base whether it be steel, timber or concrete. It is often necessary to use shims or jacking screws when bolting down to avoid inducing unwanted stress and bending or twisting moments into the machine.
 
If you add a wide parallel to it to measure across the ways I think a digital level is a great way to start. At .1 degrees it is only a little less accurate then a machinist's level at .005 per foot. (about twice the error).
 
Thanks everyone, managed to get hold of this and watched a YouTube clip on calibrating it (picture is not on the actual lathe). I think it’s safe to say my lathe is now level :)

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