How Percentages Work

Three sentences, three formulas

“What is 15% of 240?” means divide 15 by 100 and multiply by 240: 36. “36 is what percent of 240?” means 36 ÷ 240 × 100: 15%. “36 is 15% of what?” means 36 ÷ 0.15: 240. The percentage calculator is three modes because swapping those sentences by hand is how people get 0.15 or 5,400.

Enter 15 for 15%, not 0.15. The tool divides by 100. A zero total in “what percent of” has no answer.

Of versus off

20% of 50 is 10. 20% off 50 is 50 − 10 = 40. Sale signs mean the second sentence. The first mode of the calculator returns 10. Subtract if you want the price you pay, or use the discount calculator when the story is a marked-down price.

Scores and shares

18 of 25 is (18 ÷ 25) × 100 = 72%. That is a share of a whole, not a change. Turnout, tax as a share of a bill, and “what part of the budget” are the same mode.

When the whole moved

A price from 50 to 60 is a 20% increase: (60 − 50) ÷ 50 × 100. That is not “60 is what percent of 50” (which is 120%). Use percentage change when both numbers are totals at two times. Mixing the two is the usual error in “my rent went up 20%” stories that actually compared the new rent with a different base.