I have seen that string manufacturers publish tables of string gauges and tensions.
For example, this one.
How can I use these to choose a set of strings for my instrument?
The simple answer is to leave it to the experts. Strings are sold in packs, with a sensibly chosen set of gauges, for most common instrument configurations, whether you have a 4 or 5 string bass guitar, a 6 or 12 string guitar, a mandolin, or whatever.
Even if you don't want to buy a full set, you can look at the gauges supplied in a set, and buy an individual string of that gauge.
But standard sets might not meet your needs for various reasons:
So if you do want to work from the tables, here's how.
There are two factors that affect your choice of string:
So, let's find out approximately what tension your current strings have. You can use this as a guideline.
One row in the D'Addario tables describes their plain steel PL010 string:
Item# Unit Weight g' f' e' d' c' b a g PL010 .00002215 22.9 18.2 16.2 12.9 10.2 9.1 7.2 5.7
The '010' in the string's item number refers to its width in 1000ths of an inch; but for shorthand we refer to this string as "a 10". The unit weight is its weight in pounds per inch. The remaining numbers are the tension in pounds, at the pitch shown.
So if your guitar's top E --
e' -- uses this string, then its tension is 16.2 pounds.
(D'Addario has chosen to produce its tables in non-metric measures, alas)
If you feel you want a tighter top E string, then, you might choose a PL013 at 27.4 pounds. If you want a looser top E string, you might choose a PL07 at 7.9 pounds.
As you can see, there is quite a difference in tension - the 13 is three times tauter than the 7.
As a starting point, you're likely to want all your strings to have approximately the same tension, so that the action of fretting a note feels similar on all strings. So, let's say you've decided that you're comfortable with the 16.2 pound tension of your top E string, and you'd like a G string to match.
Look through the tables, until you find a string in the
g column which is close to 16.2.
Item# Unit weight b a g f e d c B NW018 .00006215 25.5 20.2 16.1 12.8 11.4 9.0 7.2 6.4
Note that this part of the chart has lower pitches than the previous example. That's because we've moved on to nickel-wound strings designed for lower pitches. Here, we've found a string that, when tuned to 16.1 pounds of tension, plays a G.
Now you have the flexibility to play with these tensions. Perhaps you'd prefer your bass strings to be slightly looser than the treble strings; just decide on the pitch and tension you want, and choose the string that matches.
Note that your instrument's neck has to endure the sum of all the string tensions. So if you have 6 strings at 16.1 pounds, that's 96.6 pounds your neck has to stand up to. You may have some documentation that indicates the maximum tension your instrument is designed for. If not, sticking to tensions that are similar to standard sets is likely to be safe.
Finally, when you change string gauge, it's likely that other aspects of your instrument will also need adjustment. The bridge intonation may need adjustment. The truss rod will probably need adjustment. These are reasonably advanced jobs. There is a lot to be said for sticking with standard string sets and letting a professional set up your instrument.