Living in the hilly Ozarks, I'm thinking of getting my road bike geared down a bit. Someone recently told me that adding one tooth to a rear sprocket is equal to subtracting 3 teeth from a front sprocket. First time I've heard that. Is he correct?

Neither right nor wrong, but more wrong than right. It depends on the size of the sprockets.

For comparison purposes it's simple division. The front chainring divided by the rear sprocket is the gear ratio, so if you had a 28T granny and a 28t rear sprockets, adding or subtracting 1 tooth form either is very similar. At the opposite end if you had 52/13 or 4:1, 48/12 is the same 4:1 ratio.

So as you see, you can't blindly apply some simple rule of thumb. Get a hand calculator and compare ratios. If you want a quick rule of thumb for the effect a 1 tooth change divide the change by the number of teeth there originally, ie. adding 1 tooth to a 25t sprocket is 1/25 or a 4% change, while adding 1 to to a 50t chainring is a 2% change.

BTW- if you haven't noticed yet, shrinking a chainring is the same effect as enlarging a rear sprocket, so keep the direction of change in mind.

As suggested above, there are various ways to change your gears. You can go bigger in the back, which may require a different rear derailleur. You can go smaller in the front by getting a compact double crankset, or a triple crankset. Or all the options if you want really low gears ! The best choice is based on what you have now, and how much lower you want to go..... just a notch, or a several notches ?

Theoretically you could get smaller chainrings, but double cranksets usually come with the smallest chainring available for that model already installed.

Do a Google search on "bicycle gear calculator" Find one you like and play with it to get a feel for what effect various choices of sprockets and chainrings have. This one https://www.kstoerz.com/gearcalc/compare/ lets you compare two drivetrains so that you can, for example, compare your present setup with a proposed different one and see, graphically, the differences.

https://www.jbarrm.com/cycal/cycal.html

As rules of thumb go that one is particularly inaccurate. Hope that didn't come from your LBS! Even if you had the largest small chainring, a 39, 3 teeth would still be 8% give or take and smaller chain rings would produce an even larger change in gearing. Let's say your largest cog in the rear was 25. A 1 tooth change is only 4% with larger cogs resulting in an even smaller gearing change.

Conclusion: the "rule" is off by 2:1 even for the most favorable and least likely configuration.

Neat application. I tried inputting 55/11 and it goes off the chart though.

https://docs.google.com/spreadsheet/...Ew0eHhERGJ1cGc

I made this spreadsheet long ago. Maybe it will help.

I know 10t does not exist. That was put on there just for fun. As you can see, the smaller a cog is, the greater difference it makes to change it by only one tooth.

I have lived in the hilly Ozarks, and this is the gearing still on my Peugeot from those days:

Front - TA triple - 30-46-50

Rear - Suntour Perfect - 14-17-24-28-38 (but 14-17-22-28-38 fills in a gap the 24T does not, but I have not made the swap yet)

Changers - Huret Duopar Eco, actuated with Suntour index bar-end shifters (it works!)

Yeah! Click shifting with a Duopar!!

That kind of gearing will serve you well on almost any Ozark hill. In my case, I have moved to the flatter desert country of southeast New Mexico, and am considering a much smaller rear cog.