The three percentage formulas
Almost every real-world percentage question reduces to one of three calculations. Knowing which one you need is usually the hard part — the arithmetic itself is simple once you do.
| Question | Formula | Example |
|---|---|---|
| What is X% of Y? | (X ÷ 100) × Y | 20% of 150 = 30 |
| X is what % of Y? | (X ÷ Y) × 100 | 30 is 20% of 150 |
| % change from X to Y | ((Y − X) ÷ X) × 100 | From 150 to 180 is a 20% increase |
Worked examples
- Sales tax: a rate of 17% on a bill of Rs. 2,000 is 17% of 2,000 = Rs. 340 in tax.
- Discount: a Rs. 500 item marked 30 is what percentage of 500? 30 ÷ 500 × 100 = 6%.
- Growth: revenue moving from Rs. 80,000 to Rs. 92,000 is a change of ((92,000 − 80,000) ÷ 80,000) × 100 = 15% increase.
Step-by-step: reading a percentage change result
- Identify which number came first (the "From" value) and which came after (the "To" value).
- Subtract From from To — a positive result means an increase, a negative result means a decrease.
- Divide that difference by the original "From" value, then multiply by 100 to express it as a percentage.
- Watch the direction: a 50% increase from 100 takes you to 150, but a 50% decrease from 150 only takes you back to 75 — percentage increases and decreases aren't symmetric.
Percentage points vs. percentage change
These two phrases get mixed up constantly, especially in news headlines about interest rates or inflation. If a savings rate moves from 4% to 6%, that's a 2 percentage point increase — a simple subtraction of the two percentages. But expressed as a percentage change, it's a 50% increase, because the rate grew by half of its starting value (2 ÷ 4 × 100 = 50%). Both statements are correct; they're just answering different questions. When a change involves rates, always check which framing is being used before comparing numbers.
Common mistakes to avoid
- Averaging percentages directly. If two groups of different sizes each have their own percentage, you can't just average the two percentages to get the combined rate — you need to go back to the underlying counts.
- Applying a percentage increase then the same percentage decrease and expecting to land back at the start. A 20% increase followed by a 20% decrease does not return you to the original number, because the second 20% is calculated on a larger base.
- Confusing "of" with "off." "30% of 200" (=60) is a very different calculation from "30% off 200" (=140, i.e. 200 minus 30% of 200) — read the question carefully before picking which calculator on this page to use.
Where percentages show up in everyday decisions
Beyond tax and discounts, percentages drive most of the comparisons people make when spending or saving money: comparing interest rates between two savings accounts, working out a tip at a restaurant, checking whether a "50% more free" promotion is actually a better deal than a flat discount, or estimating how much a grade needs to improve to raise a course average. Because the underlying formula is always one of the same three calculations above, getting comfortable with which one applies to a given question is usually more useful long-term than memorizing any single example.
Frequently asked questions
Percentage change is a relative measure — going from 50 to 75 is a 50% increase. Percentage points is an absolute difference between two percentages — going from 50% to 75% is a 25 percentage point increase. The two numbers can look similar but mean very different things, especially with rates like interest or tax.
The calculator shows a dash placeholder instead of an error whenever a field is empty, not a number, or would require dividing by zero (for example, asking what percentage X is of 0). Fill in valid numbers in both fields and the result appears immediately.
Use the "percentage change" calculator on this page: enter the original (larger) number as "From" and the new (smaller) number as "To." The tool automatically labels the result as a decrease and shows the percentage by which the value fell.
Yes — the "X% of Y" calculator works for both: enter the bill amount as Y and the tax or tip rate as X to find the tax/tip amount, then add it to the bill yourself for the total.
Results are rounded to two decimal places for readability, which is precise enough for nearly all everyday, business, and academic uses. If you need more decimal precision for a scientific or financial application, calculate with the full unrounded formula directly.