The traditional rule: farther for physical distance, further for degree or extent — farther down the road, further from the truth. In practice further covers both and is the more common word everywhere, especially in British English. Farther is never wrong for distance, but further is never wrong at all.
The core difference
A traditional split that only runs one way in practice.
- farther — physical distance: farther than I thought.
- further — degree, extent, or distance: further discussion, further down the list.
Why further is the safer choice
Because it covers both senses and always has. Farther is restricted to distance, so using it for degree — "farther research" — is an error, while using further for distance is not. If you only remember one, remember further.
The other senses of further
Further is also a verb meaning to advance something — further your career — and an adjective meaning additional: further details. Farther can do neither, which is another reason the two are not symmetrical.
British usage
Farther is markedly rarer in British English, where further serves almost universally.
Frequently asked questions
Which one is safe for both meanings?
Further. Farther is restricted to physical distance.
Is "farther research" correct?
No — that is degree rather than distance, so it needs further.
Can farther be a verb?
No. Further can — to further your career — which farther cannot do.