Considering changing my wife's bike to belt drive but not sure how to calculate gear inches.

Use the same formula as usual for calculating gear-inches: Ft/Rt * Wd [Number of teeth on chainring divided by number of teeth on rear cog or sprocket multiplied by the outside diameter of the mounted and inflated tire (or a nominal equivalent if you aren't fussy about accuracy).

It all works out the same. For example (with a nominal 27in wheel)...

40t x 20t = 54 gear-inches

20t x 10t = 54 gear-inches

10t x 5t = 54 gear-inches

As for Gates' take on ratios compared to gear-inches, they provide a useful comparison here:

https://www.gatescarbondrive.com/~/media/files/gcd/oemfactoryresources/gatesshimanomanualen.pdf?la=enThere are not direct equivalencies on belt drive to chain drive, but pretty close. For example (again calculated with a nominal 27in outside wheel diameter):

46 x 22 = 56.45

Gates offers the close equivalent: 38 x 18 = 57

50 x 22 = 61.36

Gates offers the close equivalent: 40 x 18 = 60

55 x 22 = 67.5

Gates offers the close equivalent: 44 x 18 = 66

60 x 22 = 73.63

Gates offers the close equivalent: 50 x 18 = 75

You'll note that like gear-inches, the ratios are also only approximately equivalent but still close. For example, a 50 x22 in chain drive gives a ratio of 2.27 (F/R) vs a belt-drive equivalent (40x18 F/R) of 2.22. This is because there are not so many tooth options available in belt drive as in chain drive.

Best,

Dan.