I use (tan(new fov ÷ 2) ÷ tan(old fov ÷ 2)) × -1 + 1 = multiplier x old 360cm = new 360cm
example (horizontal fov)
old fov: 115
new fov: 106
old 360: 18 cm
(tan(106 ÷ 2) ÷ tan(115 ÷ 2)) × -1 + 1 = 1.30745902778 x 18 = 23.5342625 cm
So in this example your main fov is 115 with a sensetivity that gives you 18 cm for a 360, when using a fov of 106 that could be zoomed in or a different game you will need to slow down your 360 to 23.53 cm for the same feel. This works for me but it's a hassle so I just use the calculator with 0% coeffecient/monitor distance because it seems to do the same thing as I manually did.
edit: this is faster I guess
((tan(new fov ÷ 2) ÷ tan(old fov ÷ 2)) × -1 + 1) x old 360cm = new
or ((tan(new fov ÷ 2) ÷ tan(old fov ÷ 2)) -1 + 1) old 360cm
idk if you can leave out the x because that's how I learned it in school but that's way too long ago lmao