Subsolar point is the position on the Earth’s surface where the Sun is directly overhead at noon. It varies on a daily basis and follows a regular pattern.

Noon Sun Angle = 90 - arc distance

The "arc distance" is the number of degrees of latitude between the location in question and the declination of the Sun (the vertical rays of the noon Sun).

If the vertical rays of the Sun and the latitude in question are in opposite hemispheres, add both latitudes together to determine the arc distance. If both are in the same hemisphere, subtract the smaller from the larger latitude to determine the arc distance. If the vertical rays of the Sun are striking the equator, then subtract the latitude in question from 90 to determine the noon Sun angle.

For example, on June 21st, the declination of the Sun is 23.5ºN. The latitude of San Francisco is 38ºN.

Since San Francisco and the declination of the Sun are in the same hemisphere, we subtract to determine the arc distance: 38º - 23.5º = 14.5º. We then use formula to calculate the noon Sun angle:

noon Sun angle = 90º - 14.5º = 75.5º

So, on June 21st, the noon Sun is 75.5º above the horizon in San Francisco.

To calculate the solar altitude on December 21st in San Francisco, first determine the arc distance. On December 21st the declination of the Sun is 23.5ºS. Since San Francisco and the declination of the Sun are in opposite hemispheres, we add to determine the arc distance: 23.5º + 38º = 61.5º.

Then, the noon Sun angle = 90º - 61.5º = 28.5º.

So, on December 21st, the noon Sun angle is 28.5º above the horizon in San Francisco.

To calculate the solar altitude on September 22nd or March 20th in San Francisco, first determine the arc distance. The vertical rays of the noon Sun strike the equator. From 38° to the equator there are 38°.

Then, the noon Sun angle = 90º - 38º = 52º.

So, on September 22nd / March 20th, the noon Sun angle is 52º above the horizon in San Francisco.