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How to Determine Solar Altitude Angle

The solar altitude angle, or simply altitude, is the Sun’s angular position above the horizon from the perspective of an observer on the earth. It is an important factor to consider in fields such as solar energy, building energy, and agriculture.

It is easy to know the solar altitude angle for where you are at the present moment. Just go out, look for the Sun, and estimate its angle above the horizon. But how about for any given set of location, date, and time? For example, what is the solar altitude angle for Boston, MA at noon on the winter solstice?

We can figure this out using a little bit geometry. Take a look at the diagram below. We know that the latitude of Boston, MA, is 42° and the Earth’s tilt is 23°. On the winter solstice, the Sun reaches its southernmost point and the Earth’s North Pole tilts away from the Sun. Thus, the angular distance between the observer and the orbital plane is the sum of the latitude and the Earth tilt (42° + 23° = 65°). Assuming the orbital plane is parallel to the sunray, according to the Parallel Lines Theorem, the solar zenith angle (Z) is equal to the angular distance (65°) we just calculated. Then, according to the Complementary Angles Theorem, the solar altitude angle is 90° minus the solar zenith angle (90° - 65° = 25°).

Now, try for yourself to find out the solar altitude angle for Boston, MA, at noon on the summer solstice (June 22) and verify your result using the Energy3D software.

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