c. 1200, "a step, a stair," also "a position in a hierarchy," and "a stage of progress, a single movement toward an end," from Old French degré (12c.) "a step (of a stair), pace, degree (of relationship), academic degree; rank, status, position," which is said to be from Vulgar Latin *degradus "a step," from Latin de- "down" (see de-) + gradus "a step; a step climbed;" figuratively "a step toward something, a degree of something rising by stages" (from PIE root *ghredh- "to walk, go").

A word of wide use in Middle English; in 14c. it also meant "way, manner; condition, state, standing." Most extended senses in Middle English are from the notion of a hierarchy of steps. Genealogical sense of "a certain remove in the line of blood" is from mid-14c.; educational sense of "an academic rank conferred by diploma" is from late 14c. By degrees "gradually, by stages" is from late 14c.

Other transferred senses are from the notion of "one of a number of subdivisions of something extended in space or time," hence "intensive quality, measure, extent." The meaning "1/360th of a circle" is from late 14c. (The division of the circle into 360 degrees was known in Babylon and Egypt; the number is perhaps from the daily motion of the sun through the zodiac in the course of a year.) From 1540s as "a measure of heat;" the specific use as a unit of temperature on a thermometer is by 1727. In reference to crime, by 1670s as "one of certain distinctions of culpability;" in U.S. use by 1821 as "one of the phases of the same kind of crime."

"intense interrogation by police," 1900, probably a reference to Third Degree of master mason in Freemasonry (1772), the conferring of which included an interrogation ceremony. Third degree as a measure of severity of burns (most severe) is attested from 1866, from French (1832); in American English, as a definition of the seriousness of a particular type of crime (the least serious type) it is recorded from 1865.

Proto-Indo-European root meaning "to walk, go." 

It might form all or part of: aggress; aggression; aggressive; centigrade; congress; degrade; degree; degression; digress; digression; egress; gradation; grade; gradual; graduate; grallatorial; gravigrade; ingredient; ingress; plantigrade; progress; progression; regress; regression; retrograde; retrogress; tardigrade; transgress; transgression.

It might also be the source of: Latin gradus "a step, a pace, gait," figuratively "a step toward something, a degree of something rising by stages;" gradi "to walk, step, go;" Lithuanian gridiju, gridyti "to go, wander;" Old Church Slavonic gredo "to come;" Old Irish in-greinn "he pursues."

early 15c., in alchemy, "a tempering, a refining of something to a certain degree; measurement according to the four degrees of a quality," from graduate (n.). General sense of "a dividing into degrees" is from 1590s; meaning "action of receiving or giving an academic degree" is from early 15c.; in reference to the ceremony where a degree is given, from 1818.

early 15c., "one who holds a degree" (originally with man; as a stand-alone noun from mid-15c.), from Medieval Latin graduatus, past participle of graduari "to take a degree," from Latin gradus "a step; a step climbed (on a ladder or stair);" figuratively "a step toward something, a degree of something rising by stages" (from PIE root *ghredh- "to walk, go"). As an adjective, from late 15c.

Old English læst, earlier læsest "smallest, lowest in power or position" (superlative of little (adj.)), from Proto-Germanic superlative *laisista-, from PIE root *leis- (2) "small" (see less). Qualifying phrase at least "not to say more than is certainly true" is Middle English æt læstan, from the notion of "at the lowest degree." As a noun, "smallest admissible quantity or degree," from early 12c.; as an adverb, Old English læst "in the least degree."

"to some degree (usually smaller or lesser), some degree or amount of, somewhat," Middle English som-del, obsolete in Modern English or reverting to two words, but very common in Old English as sume dæle "some portion; somewhat," probably adverbial use of a noun phrase, from some + deal (n.1).

1889 as an abbreviation of British Thermal Unit (1862), a commercial unit of electrical energy (the amount of heat required to raise the temperature of one pound of water by one degree Fahrenheit); the French Thermal Unit is the amount of heat required to raise 1 kilogram of water 1 degree centigrade. Also from 1889 as an abbreviation of Board of Trade Unit, in electicity "1,000 watt hours."

1620s, "university degree of a bachelor," from Modern Latin baccalaureatus, from baccalaureus "student with the first degree," an alteration of Medieval Latin baccalarius "one who has attained the lowest degree in a university, an advanced student lecturing under his master's supervision but not yet having personal licence."

The Medieval Latin word is of uncertain origin; it likely has been altered by folk etymology or word-play, as if from bacca lauri "laurel berry" (laurels being awarded for academic success). Perhaps it is ultimately from Latin baculum "staff" (see bacillus), which the young student might carry. Or it might be a re-Latinization of bachelor in its academic sense.

In modern U.S. usage, baccalaureate usually is a shortening of baccalaureate sermon (1864), a religious farewell address to a graduating class at an American college. This is from the word's adjectival sense of "pertaining to the university degree of bachelor."

late 15c., "to dye, color slightly, imbue with some shade or degree of color," from Latin tingere "to dye, color" (see tincture). The figurative sense of "affect or qualify slightly in mind or feeling" is from 1670s, on the notion of "modify by intermixture or infusion." Related: Tinged; tingeing; tingible; tingent. The noun, "slight or moderate degree of coloration," is attested by 1752.