The altitude doesn't depend much on whether the night is clear.If you live in the northern hemisphere, the altitude of Polaris above the horizon will APPROXIMATELY be equal to your latitude. If you live in the southern hemisphere, Polaris will be BELOW the horizon, as many degrees as you are south of the equator.
If there were a way to see the south celestial pole, and it was 40 degrees above the horizon, then you would be somewhere along the line of 40 degrees south latitude. Unfortunately, there is no star at or near the south celestial pole, so there is no way for you to see the south celestial pole and observe its elevation.
At the Tropic of Capricorn (approximately 23.5 degrees south latitude), Polaris, the North Star, is not visible and is located below the horizon. Polaris can only be seen in the Northern Hemisphere and its altitude above the horizon increases the further north you go.
37 degrees north latitude
The angle of Polaris above the horizon is equal to the latitude of the observer. This means that at the North Pole (90 degrees latitude), Polaris would be directly overhead (90 degrees above the horizon), and at the Equator (0 degrees latitude), Polaris would be on the horizon (0 degrees above the horizon).