That UTM/MGRS even exits seems to be lost on most pitching W3W.
For great circles the metric ratio is close to 40000km/360. A simple trick would be converting to 400gon first¹, but even using 111 Km per degree is a useful approximation.
So 0.01 decimal degree difference in latitude is always 1.11km or roughly 1km.
All you need to remember is your length of 1 degree longitude at given latitude which is the following basic trigonmetric relation:
0.01deg = cos(lat) * 1.11km
Cheap linear approximation will do well here too.
In South to North order: So usually factor down to 0.8 to 0.7 (38 to 48 Miles) if you live anywhere in the continental US. For Europe it's 84km in Rome, 72km in Paris, 69 in London, 67 in Berlin and 56km in Stockholm
And for approximating local distances it's simply those metric deltas with pythagoras, no need for Haversine or even non-spherical earth models here.
The most important relation for anyone who is into earth and the metric system, is that it's 10M meters or 10,000 km from pole to equator per original definition. You dont even need to remember the earth radius, since that's also defined by 4x10,000km/2π historically.
¹It's a shame that the metric revolution stopped short of Gradians, when it comes to full metric convenience here.
https://en.wikipedia.org/wiki/Earth%27s_circumference#Histor...