"Topping up" usually means adding plain water to bring a batch up to a target volume — either because pre-boil or fermenter volume came in short of plan, or deliberately, to stretch a batch slightly. Either way, once fermentation is done, that water dilutes the alcohol that's already there, directly and proportionally.
The arithmetic
Take 18 L of finished beer sitting at 5.3% ABV and stretch it to 19.8 L with plain water, and the strength settles at roughly 4.8% ABV (18/19.8 ≈ 0.91, and 5.3% x 0.91 ≈ 4.8%) — a straightforward concentration calculation, since the total alcohol present hasn't changed, only the volume it's spread across. Check the underlying volume math here — the dilution calculator works in gravity points rather than ABV directly, but the same volume ratio applies to both.
Why this is different from topping up wort before fermentation
Topping up wort before pitching yeast dilutes the sugar that hasn't fermented yet — the final ABV shifts because there's less fermentable extract per litre for the yeast to convert, an indirect effect that plays out over the course of fermentation. Topping up finished beer dilutes alcohol that's already made, directly and immediately — no fermentation step in between, just straightforward volume dilution of a fixed quantity of alcohol. Both use the same gravity-points arithmetic mechanically, but what's actually being diluted, and when the effect shows up, differs.
When topping up is the right move, and when it isn't
Topping up a fermenter that came up short of its target volume — a common brew-day outcome from boil-off running higher than planned, or less sparge water collected than intended — is a completely standard fix, and doing it before fermentation (topping up wort, not finished beer) is generally the better time to do it if you have the choice, since it lets the yeast work on the corrected, properly-diluted wort from the start rather than diluting a fully fermented result afterward. Topping up after fermentation is more often a deliberate strength or volume adjustment — bringing an over-strength batch down to a style-appropriate ABV, similar to what's covered on how to dilute a too-strong wort, just applied after fermentation rather than before it.
What doesn't change
Topping up with water — at any stage — only ever adds water, so it only ever lowers gravity and (after fermentation) ABV, never raises either. If your batch actually came in weaker than intended and you're trying to raise its strength, water is the wrong tool entirely — see my OG came in too low — how do I fix it for the blending-based fix that direction actually requires.