What's the difference between "percent of" and "percentage of"?

In general, if you have a number as an adjective, such as five percent of cases go unsolved, 76 percent of them voted in favor, or 50 percent of coin throws land on heads, you use percent of.

If you have roughly the same percentage of men and women, a low percentage chance of failure, or a policy meant to decrease the percentage of drivers without insurance from 25% to 15%, percentage of is more common.

So, in your example, I personally would use frequency as a percentage of the total in a sentence. The other would be perfectly understandable too, and I may favor it (not sure though) as a graph title.

Yes, there are two big differences between "percent" and "percentage".

1. Semantically, percent is a unit of measure (like inches or volts); percentage identifies that which is being measured (like height or voltage). We never say "The inches" or "the volts". But, since this distinction is not taught, intelligent people often use 'The Percent' or 'Percent' in titles of tables and graphs when 'The Percentage' is appropriate.
2. Syntactically there are three big differences:
   • a. 'Percent' is preceded by an amount (i.e., a number); 'percentage' is never preceded by an amount.
   • b. In 'percent of' statements, the part and whole are separated by the main verb (25% of men are runners). In 'percentage of' statements, the part can be located in a relative clause (the percentage of men who run is...) or in the 'of' phrase (Among men, the percentage of runners is...).
   • c. Finally, 'percent of' always introduces the whole or denominator whereas 'percentage of' can introduce either the whole/denominator (the percentage of men who run) or the part/numerator (Among men, the percentage of runners is X%).  See "Difficulties in Describing and Comparing Rates and Percentages". 

To answer your question, it depends on whether and how you include the numerical percent.  You can say, "Smokers are 20% of adults", "Smokers are a small percentage of adults" or "Smokers as a percentage of adults are 20%".

In the percent formula: P=R*B, P is the percentage (amount), R is the percent (%), and B is the base or whole (amount). Also, when you see percent "of" students, the word "of" following the word "percent" means multiply.

To avoid confusion, P was changed to "part". P and R are related in their labels. If R is 3% tax, then P is amount tax (percentage of tax). The word "of" after percentage is just a preposition.

In the above example "frequency as a percentage of the total" is correct, because frequency is an amount.

Beryl Stemen (Math Instructor) Lourdes University