How to Calculate the Sun's Declination

How to Calculate the Sun's Declination
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The declination of the Sun is the angle between the light rays from the Sun and the Earth's equator. Since the Earth is tilted on its axis and rotates every year, the angle of declination changes throughout the year. Every year the solar declination goes from -23.44 degrees to +23.44 degrees in line with the Earth's seasons. Although the tilt of the Earth's axis changes slowly over thousands of years, on smaller timescales it seems perfectly consistent, and the solar declination can be calculated based on what day of the year it is.

    Determine how many days have passed since January 1st. For example, the number of days between January 1st and February 14th is 44.

    Add ten to the number of days passed. Write this number down. Following the example, adding 10 to 44 gives 54.

    Divide 360 by the number of days in the year. Every year has 365 days except leap years. Write this number down. From the example, 360 divided by 365 = 0.9863.

    Multiply the number from Step 2 (the approximate number of days that have passed since the winter solstice) by the amount from Step 3 (the degree of rotation per day). Write down the result. From the example, 54 times .9863 equals 53.2603.

    Find the cosine of the result from Step 4. Multiply it by -23.44, the tilt of the Earth's axis in degrees. The result is the solar declination in degrees for that day of the year. From the example, the cosine of 53.2603 is 0.5982; multiply it by -23.44 to get -14.02 degrees.

    Things You'll Need

    • Calculator with trigonometry functions
    • Pencil
    • Paper


    • Solar declination calculators are available online and offer information on the declination for almost any date using very high accuracy formulas.

      This calculation is relatively simple and is accurate to within tenths of a degree. Small variations in the Earth's orbit and rotation cause predictable changes in the solar declination that require more complicated methods to solve. Outside of astronomy, tenths of a degree are more than sufficient for measurements.

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