Polaris altitude and latitude
Compare the north celestial pole’s altitude with Polaris’s upper and lower culminations. Enter the star’s declination for the observing date and your altitude-reading uncertainty.
At latitude 51.5°, the north pole is 51.5° above the north horizon. The entered Polaris declination gives a daily altitude range from 50.764° to 52.236°. Polaris remains above the geometric horizon.
Read this calculation
sin altitude = sin φ sin δ + cos φ cos δ cos H
The north celestial pole sits at an altitude equal to northern latitude. Polaris is offset from it, so the star’s observed altitude varies during a sidereal day. The two culmination values give the geometric range.
The starting declination is the J2000 catalogue coordinate. Precession changes its offset at other dates; replace it with a coordinate for your observing date. Use a level horizon, account for refraction and check the star is above the horizon.