NumberTally The Four Percentage Formulas
“Percent” means “per hundred” — 20% is 20/100, or 0.20. Every percent problem is one of these four rearrangements:
X% of Y = (X ÷ 100) × Y
X is what % of Y = (X ÷ Y) × 100
% change = (New − Old) ÷ Old × 100
Original = After ÷ (1 + change/100)
The reverse formula is the one people trip over: if a $50 shirt rises 20% to $60, the original is $60 ÷ 1.20 = $50 — not $60 minus 20% ($48). Percentages don’t reverse by subtraction because the base changed.
Percent Change vs Percentage Points
They measure different things. Going from 50% to 60% is a 10 percentage point change, but the percent change is (60 − 50) ÷ 50 × 100 = 20%. Percent change is always relative to the starting value — that’s why a 50% drop needs a 100% gain to recover.
Frequently Asked Questions
How do I find X percent of a number?
Divide the percentage by 100 to get a decimal, then multiply by the number. For example, 20% of 150 is 0.20 × 150 = 30.
How do I figure out what percent one number is of another?
Divide the part by the whole and multiply by 100. For example, 30 is what percent of 150? (30 ÷ 150) × 100 = 20%.
What happens if I divide by zero in a percentage calculation?
Division by zero is undefined in mathematics, so the calculator shows a dash instead of a result. If you see this, check that the ‘whole’ or ‘old value’ field is not zero.
What is the difference between percent change and percentage points?
They measure different things. Going from 50% to 60% is a 10 percentage point change, but the percent change is (60 − 50) ÷ 50 × 100 = 20%. Percent change is always relative to the starting value.
How do discounts work with percentages?
Multiply the original price by (1 − discount). A 25% discount on $80 is $80 × (1 − 0.25) = $80 × 0.75 = $60. The discount itself is $80 × 0.25 = $20.