Math lovers often find inspiration in the ways in which simple equations underlie even the most seemingly random phenomena. Language lovers, on the other hand, might be surprised to learn that word frequencies can be neatly modeled on a logarithmic scale. Welcome to Zipf’s law!
Zipf’s Law states that the frequency of a word is inversely proportional to its rank in a frequency table. The most frequent word (which in English is the) appears twice as often as the second most frequent word (of), three times as often as the subsequent word, and so on until you arrive at the least frequent word in the entire lexicon.
On the Zipf Scale of 1-7, a value of 1-3 indicates low-frequency words, while 4-7 encompasses high-frequency words. Each increment of this logarithmic scale represents a tenfold decrease in frequency; a word with a Zipf value of 2 might appear once per 10 million words, which means words with value of 1 might appear once per 100 million words. Clearly, this categorization method delivers more refinement than the 3 Tier paradigm.
So which ranks of words should students know for the SAT or ACT? Consider these 20 words considered to have a Zipf frequency value around 2:
- abjure
- abrogate
- abscond
- abstemious
- accede
- accolade
- accretion
- acumen
- adumbrate
- aegis
- afflatus
- aggrandize
- alacrity
- allocution
- amanuensis
- amorphous
- anachronism
- anathema
- antediluvian
- antipathy
Every single one except adumbrate, afflatus, and amanuensis falls squarely into my pool of testable words. In fact, as of April 2025, Roots2Words has defined 30% of the list and will eventually cover all of them.
How, you might wonder, can anyone learn words that might only appear once in a million? As always, the answer is to read every day and supplement with the right targeted resources:
- Read at least 15 minutes a day (I never tire of making this recommendation)
- Take active steps to learn unfamiliar words
- Understand how to use word roots (which would help decode 19 of the 20 listed words)
- Seek out high quality curated lists
College entrance exams use word recognition as a measurable indicator for reading prowess, so don’t discount the testing value of a powerful personal vocabulary. Zipf scale 1 words may be too rare for the SAT & ACT, but mastering low frequency scale 2 and 3 words will lead to more points as well as enhanced reading, understanding, and communication skills. In other words, mastering these words will be propitious (Zipf scale 2) for your future!
Mike Bergin