Percentage problems show up in three distinct flavors, and confusing them is the most common source of percentage math mistakes — each one answers a genuinely different question, even though they all involve the same basic building blocks.
The three core percentage questions are: finding a percentage of a number (what is 20% of 80?), finding what percentage one number is of another (20 is what percent of 80?), and finding the percentage change between two numbers (what's the percent change from 20 to 80?). Each requires a slightly different formula, even though all three are built from the same underlying relationship between a part and a whole.
The Three Formulas
Percentage of a number: Result = (Percent ÷ 100) × Whole
What percent one number is of another: Percent = (Part ÷ Whole) × 100
Percentage change: Percent Change = ((New Value − Old Value) ÷ Old Value) × 100
A Worked Example
20% of 80: (20 ÷ 100) × 80 = 16.
20 is what percent of 80: (20 ÷ 80) × 100 = 25%.
Percent change from 20 to 80: ((80 − 20) ÷ 20) × 100 = 300% increase.
Notice these three questions, using the exact same two numbers, produce three completely different answers — which is exactly why picking the right formula for the question actually being asked matters.
Common Mistakes to Avoid
- Using the wrong formula for the question being asked: identify which of the three question types you're solving before picking a formula, not after.
- Forgetting percent change can exceed 100%: unlike "percent of," percent change has no upper bound — a value can more than double, tripling would be a 200% increase, and so on.
- Mixing up the order of subtraction in percent change: always subtract old from new (not the reverse), and keep the old value as the denominator.
- Not accounting for the sign in percent change: a negative result means a decrease — this sign is meaningful and shouldn't be dropped.
Bottom Line
Percentage math is just three formulas applied to the right question. Use a Percentage Calculator to instantly solve any of the three percentage question types without manually picking through the formulas each time.