Let's begin with the fact that you wouldn't be using a calculator with unknown variables in it. You would do your own math, with values that you know. If you want to do this properly then you can't be accepting black box calculations from others. You need to understand the curvature calculation to be able to do it yourself. But let's say you do that. Depending on your mathematical ability it could take a while, but it's not really that hard.
Let's say you're able to view a 1 foot sphere on the same level as you (and there's a whole raft of assumptions in the idea of "same level" as well) from 100km away. That observation would probably not fit with a globe earth of the radius that we typically expect the earth to be, and so that could be seen as evidence that the globe earth hypothesis is false.
Realistically, it would be more likely that there was some form of experimental error in the observation or the calculation and so you'd check those things first. Whenever you get an odd result, you always check for how you've screwed it up first. 9/10 times your earth-shattering discovery turns out to be some sort of error. But plausibly if you got through all that you could make an observation in such a way as to disprove the globe earth hypothesis, yes.
At least below a certain radius of globe, anyway. Which is all you're ever going to be able to do, how do you tell the difference between a flat surface and the surface of a 10 million light year sphere? But this is getting a bit into the weeds, we're trying to compare the hypotheses of a flat plane versus a sphere of about 6-7000km radius.
So good, we've got that. That seems practical in the real world. What's your observation to disprove a flat earth? What observation could you make that you wouldn't expect to if the earth were flat?