Best conversion from kilometers to degrees distances?

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We have geometries in a Postgis database with SRID WGS84 and we have found lookups directly in degrees to be much faster than in kilometres, because the database can skip the projections I would think.

So, having a reference point in coordinates and a distance threshold in kilometres, is there a somewhat precise way to convert the distance to degrees for the lookup?

Example: Finding all locations within 10 Km of POINT(-3, 40). How do I convert the 10 Km to a degree value?



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