Quick answer: X% of Y = (X ÷ 100) × Y. X as a % of Y = (X ÷ Y) × 100. % change = ((new − old) ÷ old) × 100. So 20% of 150 is 30, 30 out of 120 is 25%, and 80 to 100 is a 25% increase.
The three percentage problems
A percentage is a fraction of 100, so 25% is 0.25. Almost every real question is one of three types, and most mistakes come from picking the wrong one or putting the numbers the wrong way round.
Type 1: What is X% of Y?
result = (percent ÷ 100) × number20% of 150 → 0.20 × 150 = 30This is the discount, tip, tax and commission sum. A handy shortcut: 10% of anything moves the decimal point one place left. 20% is double that, 5% is half, and 15% is 10% plus half of 10%.
Type 2: X is what percent of Y?
percent = (part ÷ whole) × 10030 out of 120 → (30 ÷ 120) × 100 = 25%The number you are measuring goes on top and the total on the bottom. Flip them and 25% becomes 400%. If the part is smaller than the whole, the answer must be under 100%.
Type 3: Percentage increase and decrease
change = ((new − old) ÷ old) × 100Positive = increase, negative = decreaseThe original value is always the denominator. A $20 rise means something very different on a $40 item than on a $4,000 one.
A sale price: $80 reduced to $60
- Change: ((60 − 80) ÷ 80) × 100 = −25%
- Check with type 1: 25% of 80 = 20, and 80 − 20 = 60
Result: 25% off
Why a 20% drop does not undo a 20% rise
Each change is measured against a different starting number. 100 up 20% is 120. Taking 20% off 120 removes 24, not 20, so you land on 96.
| Start | Change | Result | Net vs start |
|---|---|---|---|
| 100 | +20% | 120 | +20% |
| 120 | −20% | 96 | −4% |
| 100 | −50% | 50 | −50% |
| 50 | +50% | 75 | −25% |
A 50% loss needs a 100% gain to recover. That is why a portfolio that halves has to double to break even.
Margin vs markup: same profit, two answers
- Markup is profit as a percentage of cost.
- Margin is profit as a percentage of the selling price.
Buying at 50, selling at 75
- Profit: 75 − 50 = 25
- Markup: 25 ÷ 50 × 100 = 50%
- Margin: 25 ÷ 75 × 100 = 33.3%
Result: 50% markup, 33.3% margin
Someone who wants a 40% margin but applies a 40% markup will under-price everything. A 40% margin needs about a 67% markup. The gross margin calculator works this out for you.
Common mistakes with percentages
- Dividing by the new value. Percentage change always divides by the starting value.
- Adding percentages with different bases. Two 10% discounts are 19% off, not 20%.
- Mixing up percent and percentage points. 4% to 6% is 2 percentage points, but a 50% increase.
- Reversing by subtracting. $60 after 20% off was $60 ÷ 0.80 = $75, not $72.
Frequently asked questions
How do I find a percentage of a number?
Divide the percent by 100 and multiply by the number. 15% of 200 is 0.15 × 200 = 30. This is the calculation behind discounts, tips, tax and commission.
How do I find what percent one number is of another?
Divide the part by the whole and multiply by 100. 30 out of 120 is (30 ÷ 120) × 100 = 25%. The number you are measuring goes on top.
How do I calculate percentage increase or decrease?
Subtract the old value from the new, divide by the old value and multiply by 100. 80 to 100 is ((100 − 80) ÷ 80) × 100 = 25%. A negative result is a decrease.
Why does a 20% drop not cancel a 20% rise?
Each percentage uses a different starting value. 100 up 20% is 120, and 20% of 120 is 24, so the fall lands on 96, not 100.
What is the difference between margin and markup?
Markup measures profit against cost, margin against selling price. Cost 50, price 75 is a 50% markup but a 33.3% margin.
How do I reverse a percentage to find the original price?
Divide rather than subtract. $60 after a 20% discount was $60 ÷ 0.80 = $75. Subtracting 20% from $60 wrongly gives $48.
Related tools
Accuracy note: Every worked example on this page is re-derived from the formulas above. Results are rounded to four decimal places for display. Confirm financial or pricing figures independently before acting on them.
Content Lead, Anchor AI Tools, California, USA. Spotted an error? Email hello@anchoraitools.com and it will be checked and corrected. See our editorial standards.