ToolnozaThree questions, three modes
“What is X% of Y?” returns an amount. “X is what percent of Y?” returns a share. “Percentage change from X to Y” compares a new value with an original value. Pick the question before entering numbers.
Find a percentage of an amount
20% of 150 is 20 ÷ 100 × 150 = 30. For a 20% discount on a price of 150, the discount is 30 and the remaining price is 120. The percentage result alone is not the discounted price.
Find a share
If 30 items out of 150 pass an inspection, the share is 30 ÷ 150 × 100 = 20%. The total belongs in the denominator. Reversing the values gives a different answer.
Calculate a change
From 80 to 100, change = (100 − 80) ÷ 80 × 100 = 25%. Returning from 100 to 80 is a 20% decrease, not 25%, because the starting value changes.
Percentage points and zero
A rate rising from 10% to 12% gains 2 percentage points, but increases by 20% relative to the old rate. A percentage change from zero is undefined under this formula. Describe the absolute increase instead of reporting an infinite growth rate.