How do I convert kilometres to degrees in Geodjango/GEOS?

1 deg lat is approx 110.567 km at the equator to 111.699 km at the poles.

This link might be of interest to you. The conversion is based on the circumference of the earth divide by 360 degrees.

1 deg long is also approx 111km at the equator and -> 0 as you go to the poles.

The answer may depend upon location on earth. Near the equator, 1km is going to equal roughly 0.008 degrees (1 km / 40,000 km * 360 degrees) of latitude and longitude, but near the poles, 1km is going to equal roughly 0.008 degrees latitude, but could be many many degrees longitude. (If you're 1km away from the pole, 1km travel 'west' would bring you roughly 57 degrees of longitude west.)

But, if the API just wants degrees along a great circle as the measurement, perhaps it'd be sufficient to use (n km / 40,000 km * 360 degrees). At least, 40,000km is "good enough for me" :) more accurate numbers are available.