You could do this with a protractor. Originally I thought you'd need to do an upgrade and measure the difference, but I was making it more complicated than it needs to be.

Thankfully, the bar is exactly half a circle, this makes things a bit easier with a standard protractor. I have assumed that the bar is linear, meaning that if the bar is half full, then the Pokémon is at half of it's max CP.

The bar on this example is 110 / 180 or about 60% full.

You can then work out your estimated max level with this formula:

max = CurrentCP / (angle / 180)

Example:
max = 72        / (110 / 180)
max = 72        /  0.61
max = 118

Based on the other answer, it seems that the max CP might change as you level up, so you might need to remeasure.

You could do this with a protractor. Originally I thought you'd need to do an upgrade and measure the difference, but I was making it more complicated than it needs to be.

Thankfully, the bar is exactly half a circle, this makes things a bit easier with a standard protractor. I have assumed that the bar is linear, meaning that if the bar is half full, then the Pokémon is at half of it's max CP.

The bar on this example is 110 / 180 or about 60% full.

You can then work out your estimated max level with this formula:

max = CurrentCP / (angle / 180)

Example:
max = 72        / (110 / 180)
max = 72        /  0.61
max = 118

Based on the other answer, it seems that the max CP might change as you level up, so you might need to remeasure.

But again, a physical one would have to have the same radius as the image/app on your screen.

Nope, with a ruler (or any straight edge for that matter), you can use a smaller protractor. Just put the protractor so that it's middle is in the middle of the bar and place your straight edge as indicated by the white line.