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Most definitely not write your own. As you get more familiar with geographic data you will realize that this particular calculation isn’t at all simple see for example this question for a detailed discussion. However most of the solutions (answers) given in that question only produce approximate results. Partly due to the fact that the earth is not a perfect sphere.
On the other hand if you use Geospatial extensions for mysql (5.7 onwards) or postgresql you can make use of the ST_DWithin function.
ST_DWithin — Returns true if the geometries are within the specified distance of one another. For geometry units are in those of spatial reference and For geography units are in meters and measurement is defaulted to use_spheroid=true (measure around spheroid), for faster check, use_spheroid=false to measure along sphere.
ST_DWithin makes use of spatial indexes which home made solutions will be unable to. WHen GeoDjango is enabled, ST_DWithin becomes available as a filter to django querysets in the form of dwithin
Last but not least, if you write your own code, you will have to write a lot of code to test it too. Whereas dwithin is thoroughly tested.