How to work out "X% of Y" by hand
- Turn the percentage into a decimal — Divide the percentage by 100. So 20% becomes 20 ÷ 100 = 0.2. The word "percent" literally means "per hundred," so this step just rewrites the percentage as a plain number you can multiply with.
- Multiply by the whole amount — Multiply that decimal by Y. For 20% of 150, you calculate 0.2 × 150 = 30. That product is your answer.
- Sanity-check against landmarks — Use easy reference points to confirm the result looks right. 10% of any number is just that number with the decimal point moved one place left (10% of 150 = 15), and 50% is half. Since 20% is double 10%, 20% of 150 should be about 30 — which matches.
What this calculator does
Most percentage problems are really one of three questions in disguise. First, "what is X% of Y?" — for example, how much is a 15% tip on an 80 dollar meal. Second, "X is what percent of Y?" — for example, you scored 45 out of 180 and want to know the grade as a percentage. Third, "what is the percentage increase or decrease?" — for example, a price moved from one value to another and you want to know by how much it changed.
This tool answers all three. You type in the numbers you have, and it returns the percentage, the part, or the change. The sections below show how each calculation works so you can do the quick ones in your head and trust the rest.
Percentage change, and the mistake almost everyone makes
To find a percentage change, subtract the old value from the new value, divide by the old value, then multiply by 100. Going from 200 to 220 is (220 − 200) ÷ 200 × 100 = 10%, an increase. If the result is negative, it is a decrease. The key detail is that you always divide by the starting (old) value, not the new one.
The common trap: a 20% rise followed by a 20% fall does not bring you back to where you started. Start at 100, add 20% to reach 120, then take 20% off 120 — that removes 24, not 20, leaving you at 96. Each percentage is taken from a different base, so the two moves don't cancel out. This is why a stock that drops 50% has to gain 100% just to break even.
Everyday uses
Percentages show up constantly in daily life. A tip is "X% of the bill," a sale tag is a percentage decrease off the original price, and sales tax or VAT is a percentage added on top. Test scores and grades are usually "this many points is what percent of the total," exactly the second question above.
These are general educational examples, not financial or tax advice — real tax rates, rounding rules, and discount terms vary by place and situation, so check the specific figures that apply to you. Used as a quick check, though, the same three formulas cover the vast majority of percentage math you'll meet.
The three percentage formulas
X% of Y = (X ÷ 100) × Y · X is (X ÷ Y × 100)% of Y · change% = (new − old) ÷ old × 100
X% of Y = (X ÷ 100) × Y — turn the percentage into a decimal, then multiply by the whole.
X is (X ÷ Y × 100)% of Y — divide the part by the whole, then multiply by 100 to express it as a percentage.
change% = (new − old) ÷ old × 100 — a positive result is an increase, a negative result a decrease; always divide by the old (starting) value.
| Question | Answer |
|---|---|
| 20% of 150 | 30 |
| 15% of 80 | 12 |
| What % is 45 of 180? | 25% |
| Increase 200 by 10% | 220 |
| Decrease 50 by 30% | 35 |