Measuring in cents is "clean" because it converts ratios to differences.
If you start with low A at 27.5 hz and go up an octave at a time, you get
Each A is double the frequency of the previous A.
The human ear hears each octave as being the same "size" as the previous octave. If we arbitrarily assign to low A the value of 0 cents, then we have
What mathematical device converts ratios to differences in this manner? Logarithms (ooh). To convert a ratio to cents, you take the base-2 logarithm of the ratio, and multiply by 1200.
You probably don't have base-2 logarithms on your calculator, but you probably do have base-10 logarithms. So you'd have to find the base-10 log of the ratio, then divide by the base-10 log of 2, then multiply by 1200.
In Excel, it's even easier, because you can specify the base of the log. If, in cell A1, you type
and, in cell B1, you type
then bingo -- you get your 386 cents.
Change the ratio in cell A1, and the cents value in cell B1 changes with it. In this way you can easily convert any "just" (or other) ratio to cents.