By Kevin Beck
Updated Mar 24, 2022
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At solar noon the sun rarely reaches a true zenith—only at the equator. Even then, the highest point above the horizon changes throughout the year, depending on your latitude and the date.
Your latitude ranges from 0° at the equator to 90° at the poles. In the United States most locations lie between 25° N and 45° N. Each degree of latitude is roughly 69.8 miles (112 km). If you’re unsure of your exact latitude, the NASA Latitude/Longitude Finder can help you locate it. For example, Boston, Massachusetts sits at 42.36° N.
During the equinoxes—about March 22/23 and September 22/23—the day and night are equal, and the sun’s noon altitude is simply:
altitude = 90° – L
where L is your latitude. In Boston this gives 90° – 42.36° = 47.64°, just over halfway to the zenith.
Because Earth is tilted 23.5°, the sun’s noon altitude peaks at the summer solstice (≈June 22) and dips lowest at the winter solstice (≈December 22). The formulas are:
Summer solstice: altitude = 90° – L + 23.5°
Winter solstice: altitude = 90° – L – 23.5°
For Boston: 90° – 42.36° + 23.5° = 71.14° (summer); 90° – 42.36° – 23.5° = 24.1° (winter).
The sun’s declination (D) varies daily between +23.5° and –23.5° and represents the tilt’s effect for that date. The general formula is:
altitude = 90° – L + D
To find D for a specific day, use the NOAA Solar Calculator or the Kiesan Calculator. If you prefer a quick estimate, note that the declination moves roughly linearly between the solstices. For example, in early May in Miami (L ≈ 25° N), D is about +11.5°. The expected noon altitude is then 90° – 25° + 11.5° ≈ 76.5°.
