How can I know the number of teeths I need to go uphill? I have a singlespeed with a flipflop hub to change to fixed gear. In my freewheel sprocket I have 16 teeth and in the ring chain 46 teeth.

For me this is almost always the perfect combination for touring where I live.

But sometimes I want to go up a mountain (15-17% ) and I,m not strong enough to keep pedaling. I,d like to have the fixie side as backup for those occasions with more teeth.

I don't have any local shop to try gear ratios so I have t guess and buy.

Is there any method to guess how many more teeth do I need considering what I already have? I can go around 15km/h in a 7%hill.
I don't think you can do it unless you are planning on carrying a few chain links to splice in whenever you flip your wheel. In any case, with the relatively large 46 tooth chain ring I think you'd need at least 36 teeth on the back to get up a 15% grade. Which would require a chain with 10 more links