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I have a 3 * 7 Shimano set. I would like to change this into either a 1 * 12 or 1 * 11. How much would the conversion approximately cost? I am new to the biking world, so forgive me if I am saying things imprecisely.
I am mostly going to be on the road or gravel trails.
The questions about the price is out of topic here because they are impossible to answer "universally", for the answer to be useful to more than one person, especially when no details about the existing setup are given. So let me instead outline a structure of the costs.
A new 1×11 groupset (cassette, chain, derailleur, shifter, front chainring, possibly front crankset, possibly new rear wheel) costs anywhere from 200 $/€/£ to 2000 and more, depending on what level of performance you want. An existing rear wheel may be sometimes preserved (again, we do not know your setup), but if you go for 1×12, you'll definitely need a new rear hub (essentially, a new wheel).
Smaller stuff, such as new shifting cables/housing, are worth as well, costing you maybe additional 10—30 $/€/£.
If you buy components online, add another 10—100 $/€/£ for postal services. If you buy at a bike shop, add implicit higher margin they have compared to online shops.
Then, there are installation costs. They can vary wildly: from zero if you are ready to learn the skills yourself, can loan specialty tools and have a lot of time to learn required skills, or have a friend that is willing to help you for free, to what price is for 1 or 2 hours of work of professional bicycle mechanic in your area.
Note that for these money, it is often possible to buy a complete new bicycle with entry to medium level of a 1×11 drivetrain. Selling your existing bike would even offset the cost a bit (I doubt that by much).
There are also cheaper wide range 1×10 groupsets (and even 1×9 and 1×8 by Microshift), which maybe are a better choice for upgrading an older bicycle.
Do you want to give only a "modern" spin to your bicycle or is your conversion performance oriented?
In the first case, get ready to spend quite a lot of money (wild guess: 6-700 USD/EUR/GBP ) or a lot of money and time, by doing most of the work yourself (hint: how much do you value your time?) and possibly buying the parts used and having your bike "under construction" for extended amount of time.
An alternative and quick&dirty solution: look for appropriate size (I guess you have an old steel mtb, so the fitting tyres should be 26" and up to 2.2-2.4 inches wide) gravel tyres and possibly a sweeping handlebar, so you will get a different position and look from your old reliable bicycle (to get some inspiration, look for "steel frame adventure bicycle sweep bar" in your favorite internet search engine).
If you are interested in performance, see my first point, but multiply a lot of money for a factor 3 to 5. Becuase either you will look at lighter, expensiver parts (with dubious outcome), or completely a new bicycle.
