How to calculate percentages
Percentages show up everywhere — sale tags, test scores, tip lines, nutrition labels. There are really only three operations you need to know, and once you see how they all connect to the same underlying idea, none of them are hard.
The one idea behind all of them: "of means multiply"
The word "percent" means "per hundred" — 35% is shorthand for 35 per 100, or 0.35 as a decimal. To convert any percent to a decimal, divide by 100 (just shift the decimal point two places left). That decimal is the number you multiply with.
The phrase "of means multiply" is the key that unlocks every percentage problem. When you read "35% of 200," translate it directly: 0.35 × 200. That's it.
Operation 1 — Find X% of a number
Formula: result = (percent ÷ 100) × number
Example: What is 35% of 80?
0.35 × 80 = 28
Real-world use: a jacket costs $80 and is 35% off. The discount is $28, so you pay $80 − $28 = $52.
Example 2: You want to leave an 18% tip on a $45 restaurant bill.
0.18 × 45 = 8.10
The tip is $8.10. Total: $45 + $8.10 = $53.10.
Operation 2 — Express one number as a percent of another
Formula: percent = (part ÷ whole) × 100
Example: You scored 42 out of 60 on a quiz. What percent did you get?
(42 ÷ 60) × 100 = 0.7 × 100 = 70%
Example 2: A store sold 15 of 40 items it stocked. What percent sold through?
(15 ÷ 40) × 100 = 0.375 × 100 = 37.5%
The direction matters: the "part" goes on top, the "whole" goes on the bottom. If you get a number bigger than 100%, it means the part is larger than the whole — which can be correct (e.g., growth comparisons) but is a sign to double-check which is the base.
Operation 3 — Calculate percent change
Formula: percent change = ((new − old) ÷ old) × 100
A positive result means an increase; a negative result means a decrease.
Example: A grocery item cost $2.40 last month and costs $2.76 this month. By what percent did it increase?
((2.76 − 2.40) ÷ 2.40) × 100 = (0.36 ÷ 2.40) × 100 = 0.15 × 100 = 15%
Example 2: Your gym membership was $55/month and dropped to $44/month. What is the percent decrease?
((44 − 55) ÷ 55) × 100 = (−11 ÷ 55) × 100 = −0.20 × 100 = −20%
The price fell by 20%.
Mental-math shortcuts
You do not always have a calculator handy. These shortcuts work surprisingly often:
10% trick — the anchor
To find 10% of any number, move the decimal point one place to the left.
- 10% of 340 = 34
- 10% of 8.50 = 0.85
From that anchor, you can scale to almost any common percent:
- 20% = double 10%
- 5% = half of 10%
- 15% = 10% + 5% (i.e., 10% plus half of 10%)
- 25% = divide by 4 (or 10% + 10% + 5%)
- 1% = move decimal two places left; then multiply to reach 3%, 7%, etc.
Example: 15% tip on $60.
10% of 60 = 6. Half of that = 3. Add them: $9.
Example: 35% of 200.
10% = 20. Three of those = 60. 5% = 10. Total: 60 + 10 = 70.
Flip the problem when that's easier
Because multiplication is commutative, X% of Y = Y% of X. So "4% of 75" is the same as "75% of 4." The second form is often much simpler: 75% of 4 = 3.
Common mistakes
- Forgetting to convert. Using 35 instead of 0.35 gives a result 100 times too large. Always divide by 100 first, or keep the decimal form in mind.
- Reversing part and whole. In the "X as a percent of Y" formula, the base (the "whole" you're comparing to) goes in the denominator. Swapping them gives a completely different — and wrong — answer.
- Using the wrong base for percent change. Percent change is always measured relative to the starting value, not the ending value. If you accidentally divide by the new number instead of the old one, you'll get a different percent.
- Adding percents directly. A 20% increase followed by a 20% decrease does not return you to the starting point. After a 20% increase on 100 you have 120; a 20% decrease on 120 gives 96, not 100. Percents always compound on their current base.