How to Calculate the Angular Diameter of the Sun

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Our sun is enormous compared to the Earth, measuring 109 times the diameter of the planet. When the great distance between the sun and Earth is factored in, however, the sun appears small in the sky. This phenomenon is known as the angular diameter. Astronomers use a set formula to calculate the relative sizes of celestial objects. The size and distance of objects is directly related; while the sun is 400 times larger than the moon, it is also 400 times farther away, making each object appear to be the same size in the sky -- and making solar eclipses possible.

    Multiply the distance between the sun and the observer by 2. For example, to find the angular diameter of the sun as it appears on Earth, multiply 93 million miles by 2 to get 186 million.

    Divide 865,000 -- the actual diameter of the sun in miles -- by the result from the previous step. The result is 0.00465.

    Calculate the arctangent of the result from the previous step. On a scientific calculator, the arctangent function may be listed as either "tan-1" or "atan." The arctangent of 0.00465 is 0.26642.

    Multiply the arctangent by 2. This result, 0.533 degrees, is the angular diameter of the sun as it appears on Earth.


    • The distance across your pinkie finger held at arm's length is a rough approximation of a degree in the sky.

      Using this formula from Mercury, the closest planet to the sun at 36 million miles, gives a result of about 1.4 degrees -- almost three times as large as the sun appears on Earth.


About the Author

Mike Guilmette has written, designed and edited for newspapers in Michigan, North Carolina, Indiana and Ohio. He has worked with the "South Bend Tribune" and "The Daily Advance," and has also edited works of fiction and news websites. Guilmette received a B.S. and B.A. from Lake Superior State University, specializing in recreation management and computer maintenance and repair.

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