degree vs magnitude

degree

noun
  • The amount that an entity possesses a certain property; relative intensity, extent. 

  • The curvature of a circular arc, expressed as the angle subtended by a fixed length of arc or chord. 

  • A ‘step’ in genealogical descent. 

  • A unit of measurement of latitude and longitude which together identify a location on the Earth's surface. 

  • The dimensionality of a field extension. 

  • Any of the three stages (positive, comparative, superlative) in the comparison of an adjective or an adverb. 

  • The sum of the exponents of a term; the order of a polynomial. 

  • A stage of proficiency or qualification in a course of study, now especially an award bestowed by a university or, in some countries, a college, as a certification of academic achievement. (In the United States, can include secondary schools.) 

  • The number of logical connectives in a formula. 

  • A unit of measurement of temperature on any of several scales, such as Celsius or Fahrenheit. 

  • A stage of rank or privilege; social standing. 

  • The number of edges that a vertex takes part in; a valency. 

  • A step on a set of stairs; the rung of a ladder. 

  • A unit of measurement of angle equal to ¹⁄₃₆₀ of a circle's circumference. 

  • An individual step, or stage, in any process or scale of values. 

magnitude

noun
  • The absolute or relative size, extent or importance of something. 

  • A measure of the energy released by an earthquake (e.g. on the Richter scale). 

  • A number, assigned to something, such that it may be compared to others numerically 

  • An order of magnitude. 

  • Of a vector, the norm, most commonly, the two-norm. 

  • The apparent brightness of a star, with lower magnitudes being brighter; apparent magnitude 

  • A ratio of intensity expressed as a logarithm. 

How often have the words degree and magnitude occurred in a corpus of books? (source: Google Ngram Viewer )