公 gōng is a meaning-built compound: 八 (bā, to divide) above 厶 (sī, private, self). The lower element 厶 is the old graph for the private and the enclosing, a closed-off self; the upper 八 is a pair of strokes splaying apart, the picture of splitting or dividing. Read together, the early gloss is famous: to divide away what is private is to arrive at the public. The Shuōwén reads the character exactly this way, with 八 set against 厶 to mean the opposite of the private.

From that one image, dividing the private into the shared, four senses fan out:

1. Public, common, shared. What belongs to everyone rather than to one: 公共 gōnggòng (public), 公园 gōngyuán (park), 公司 gōngsī (company), 办公室 bàngōngshì (office).
2. Fair, impartial, just. Holding to no private side: 公平 gōngpíng (fair), 公正 gōngzhèng (just), where the moral 公 lines up with the upright 正.
3. Official, metric, standard. The publicly agreed measure: 公里 gōnglǐ (kilometer), 公斤 gōngjīn (kilogram), 公历 gōnglì (the common calendar).
4. A duke, an elder male. A title of rank and a term of respect for older men: 公公 gōnggong (grandfather, father-in-law), 老公 lǎogōng (husband, colloquial), and the male of animals, 公鸡 gōngjī (rooster).

The thread through every sense is the move from private to public. The duke held office on behalf of all; the kilometer is a measure all agree on; fairness is judgment with the private self divided away. 公 is the line drawn between what is mine and what is ours, always falling on the side of ours.

The moral sense of 公 is older and deeper than the modern "public transit" one. To act 公 is to set the private self aside and judge by the common standard, which is why 公 pairs so naturally with 正 zhèng (upright). 公正 gōngzhèng, just and impartial, fuses the two: the public standard (公) and the straight line everyone is measured against (正). The classical ideal of the ruler or the judge is exactly this, to hold to the line without bending it toward kin, friend, or personal gain.

Its opposite here is again 私, the private and the partial. Where 私 means favoring one's own, 公 means favoring no one, which is the same as treating all alike. This is the thread that ties the fairness of a referee, the impartiality of a court, and the selflessness praised in the idiom 大公无私 into one idea: the private divided away leaves only the common good.

Two further senses of 公 sit a little off the public-fairness road. The first is the metric one. When China adopted the international system of measures, 公 became the prefix marking the standard, agreed-upon unit, the public measure as against the old local ones: 公里 gōnglǐ (kilometer), 公斤 gōngjīn (kilogram), 公尺 gōngchǐ (meter). The logic still runs through 公: a unit everyone shares.

The second is the oldest of all, 公 as a noble title and a term of respect for older men. As a rank it named a duke, the highest of the classical noble grades. From that respect it softened into kinship and address: 公公 gōnggong (a grandfather or a husband's father), 老公 lǎogōng (the colloquial word for husband), 外公 wàigōng (maternal grandfather). The same character even marks the male of animals: 公鸡 gōngjī (rooster), 公牛 gōngniú (bull).

See the two strokes of 八 at the top splaying apart, a pair of hands prying something open, and beneath them 厶, the closed-off private self. The whole character is that act: dividing the private away to leave the common. Hold that one picture and the senses follow.

Split the private from a garden and it becomes a park (公园); from a business, a company (公司); from a judgment, fairness (公平, 公正); from a measure, the shared unit everyone agrees on (公里, 公斤). Even the duke and the grandfather are the elder who stands for the family or the realm rather than himself. Whenever you meet 公, look for the line between mine and ours, and you will find it falling on the side of ours.