Who invented the intelligence quotient (IQ) and how is it calculated?

Alfred Binet is best known as the creator of the first workable intelligence scale. Published in 1905230 and revised in 1908 and again in 1911,231 Binet's 'test' revolutionized psychology's approach to the measurement of higher mental processes. Between 1890 and 1905, Binet laid the groundwork for this famous achievement232 in a series of experimental studies in the psychology of individual differences. In the course of this work, he came to recognize that any successful measure of intelligence must focus on higher mental functions such as judgment and reasoning rather than on the lower sensorimotor processes (e.g., visual or auditory acuity) that had been the focus of earlier attempts to construct an intelligence measure.
http://www.thoemmes.com/psych/binet.htm

Alfred Binet (1857-1911) developed the Binet-Simon (later renamed Stanford-Binet) test to measure mental age. Lewis William Stern (1871-1938) developed the idea of dividing the mental age by the chronological. (I suspect his is the name you're looking for)
Lewis Madison Terman (1877-1956) was the one to codify the test and incorporate Stern's scale, now know as I.Q. This work was done at Stanford U., thus the rename.

The abbreviation "IQ" was coined by the psychologist William Stern for the German term Intelligenz-quotient, his term for a scoring method for intelligence tests he advocated in a 1912 book. When current IQ tests are developed, the median raw score of the norming sample is defined as IQ 100 and scores each standard deviation (SD) up or down are defined as 15 IQ points greater or less, although this was not always so historically. By this definition, approximately 95 percent of the population scores an IQ between 70 and 130, which is within two standard deviations of the mean.

https://en.wikipedia.org/wiki/Intelligence_quotient