By Marty Simmons, Updated Mar 24, 2022
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The declination of the Sun is the angle between the Sun’s rays and Earth’s equatorial plane. Because the planet’s axis is tilted at 23.44°, this angle varies throughout the year, ranging from –23.44° at the winter solstice to +23.44° at the summer solstice. While the axial tilt slowly changes over millennia, the daily variation can be calculated accurately for any given date.
For example, 14 February is the 44th day of a non‑leap year.
Adding 10 yields 54 in the example.
Divide 360° by the number of days in the year (365 for a common year, 366 for a leap year). The result for a common year is 0.9863° per day.
Multiply the result from Step 2 by the value from Step 3: 54 × 0.9863 = 53.2603.
Take the cosine of the product from Step 4 (cos 53.2603° = 0.5982) and multiply by –23.44° to obtain the solar declination: –14.02°.
Online calculators provide highly accurate declination values for any date. Manual calculation is straightforward and accurate to within a few tenths of a degree, which is more than sufficient for most practical applications.
