Polar day and polar night

On 10 May 2026 the Sun rose over Utqiaġvik, Alaska, and did not set again for 84 days.

When the formula breaks

In the sunrise equation, cos H = −tan φ tan δ, a cosine must lie between −1 and 1. Near the poles in summer the right-hand side becomes smaller than −1, and in winter larger than 1. There is no hour angle that works: the Sun never crosses the horizon. In summer that means it circles the sky for 24 hours, the midnight sun or polar day. In winter it means it stays below the horizon all day, the polar night.

The boundary is easy to find. On the June solstice the Sun is overhead at 23.44° N, so the circle of illumination reaches 23.44° beyond the North Pole, down to 90° − 23.44° = 66.56° N on the far side. Everywhere north of that line stays lit all day. That line is the Arctic Circle. The Antarctic Circle at 66.56° S plays the same role six months later. On the December solstice the roles swap: north of the Arctic Circle the Sun does not rise at all.

Longer than you expect

Exactly on the Arctic Circle, a purely geometric Sun would stay up for 24 hours on just one day. Real observers see more. The air bends sunlight, and the top edge of the Sun appears before its centre, so the model (using NOAA's 90.833° rule) gives about a month without sunset at 66.56° N. The midnight sun can even be seen a little south of the Arctic Circle. In the other direction, refraction shortens the polar night, so the dark season is always a little shorter than the bright one at the same latitude.

Utqiaġvik (formerly Barrow), the northernmost town in the United States, lies at about 71.3° N. In 2026 FOX Weather reported that the Sun rose there on 10 May and would not set until 2 August, 84 days. The model's formula gives 83 days at that latitude, close enough given local horizon and weather. In winter the town has about two months of polar night, from mid-November until late January. At the North Pole itself the Sun is up for roughly half a year and down for the other half.

Cold even in constant daylight

Twenty-four hours of sunlight sounds like a heat wave, but polar summers stay cool. The Sun circles low in the sky. At the Arctic Circle on the June solstice the noon Sun is only 90° − |66.56° − 23.44°| = 46.88° high, and at the North Pole it never climbs above 23.44°. Low sunlight is spread thin, much of it is reflected by snow and ice, and some of the energy goes into melting rather than warming. Even so, the long days matter: plants in the Arctic grow fast during the short summer.