A hydrometer is calibrated at one temperature and used at whatever temperature the sample happens to be. Liquid expands as it warms, so a warm sample is less dense than the same liquid cold, and the instrument sinks further than it should. The correction is the number of degrees you add back. It is small on a sample a few degrees off and large on wort straight out of the kettle, and it matters most when your two readings were taken at different temperatures, because then the error does not cancel: it lands squarely in the strength.
Where 20°C comes from
It is not a brewing convention, it is the legal one. HMRC's alcoholic products technical guide defines alcoholic strength as the percentage of alcohol by volume measured at 20°C, and the laboratory method it sets out takes the sample by measure at 20°C and reads the distillate's density at 20°C. Most hydrometers sold in this country are etched for 20°C for the same reason. If yours says something else: some older instruments are 15.5°C: the correction is against that figure, not against 20.
How much it actually moves the answer
A sample read a few degrees above calibration is typically a degree or so light; wort read at 30°C against a 20°C instrument is more like two or three. Two or three degrees on the original gravity of an ordinary beer is roughly a third of a percent of alcohol, which is larger than the difference between every ABV method in use. It is also entirely avoidable: stand the trial jar in cold water for ten minutes, or add the card's figure and move on.
Where the correction goes in the arithmetic
Correct each reading first, then subtract. The ABV calculator on this site has a box for each correction in degrees of gravity, and they default to zero because most brewers cool the sample. Put your instrument's own card figure in (the card that came with the hydrometer is calibrated for that hydrometer) rather than a generic table, and if your card gives a specific-gravity offset like 0.002, that is two degrees. Correct both readings or neither; correcting only one is worse than correcting neither, because it invents a difference that was not there.
The one place the correction cannot rescue you
None of this makes a home reading a laboratory measurement. HMRC's guide offers the factor method to a producer with no or minimal laboratory facilities and reserves the distillation method for where the strength has to stand up. A corrected home reading is right for planning a recipe, for knowing whether fermentation has finished and for a bottle you drink yourself. It is not the number that goes on a label.
Questions people ask about hydrometer temperature correction
My hydrometer did not come with a card. Now what?
Read the sample at the temperature etched on the instrument. Ten minutes standing the trial jar in a jug of cold water is quicker than any table and removes the question entirely, and it is what most brewers end up doing anyway.
Does the correction apply to a refractometer too?
Differently. A refractometer has its own automatic temperature compensation for the instrument, but wort straight off the boil will still read oddly because the drop cools on the prism. Give it fifteen seconds to settle before you read it.
Do I correct the final reading as well?
Yes, and for the same reason: the strength comes from the difference between two readings, so an uncorrected one at either end goes straight into the answer. If both samples were at the same temperature the corrections cancel, but it costs nothing to enter both.
Is a hydrometer calculator doing anything more than this?
On this site, yes: it takes both corrected readings, works the strength by HMRC's factor method rather than the usual 131.25 shortcut, and shows the apparent attenuation alongside. The correction itself is just addition; the value is in what happens after it.