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Percentages show up everywhere — sale prices, tips, grades, pay rises, and tax. The maths behind them is simple, but it is easy to get tangled when you are doing it in your head at the checkout. This calculator handles the three calculations people use most, so pick the one you need and get the answer in seconds.
How to Use This Percentage Calculator
Start by choosing the calculation that matches your question. “What is X% of Y?” covers discounts, tips, and tax — 20% off a $250 jacket, for example. “X is what % of Y?” answers questions like “50 is what percent of 250?”, which comes up with test scores and survey results. The third mode, percent increase or decrease, compares two numbers over time, such as a salary going from $80,000 to $100,000.
Type in your numbers, press Calculate, and the answer appears with the working shown underneath, so you can see exactly how it was reached. The Clear button wipes the fields for a fresh calculation. If you are working out tax on a purchase, our GST calculator is built for that job specifically.
What Is a Percentage?
A percentage is simply a number out of 100. The word comes from the Latin “per centum”, meaning “by the hundred”, and the % sign is shorthand for “divided by 100”. So 20% means 20 out of every 100, or 0.20 as a decimal. That is why percentages are so handy for comparisons: 20% off means the same thing whether the item cost $25 or $2,500, while a $5 discount would mean something very different on those two prices.
Because percentages are ratios, they compare different-sized things on equal footing. A student scoring 45 out of 50 and another scoring 90 out of 100 both got 90%, though their raw marks look nothing alike. The same idea works for budgets, interest rates, and growth figures — the percent strips away the size of the numbers and leaves the proportion. A percentage can also be more than 100%: that just means the part is bigger than the whole you are comparing it to. If your sales double, they grew by 100%; if they triple, they grew by 200%. Percentages above 100% are normal for growth, markups, and comparisons against a smaller base.
The Three Formulas
1. X% of Y: (X ÷ 100) × Y. So 20% of 250 is 0.20 × 250 = 50.
2. X is what % of Y: (X ÷ Y) × 100. So 50 is (50 ÷ 250) × 100 = 20% of 250.
3. Percent change from A to B: ((B − A) ÷ A) × 100. A positive answer means an increase; a negative one means a decrease.
Worked Examples
A discount: a jacket costs $250 and the store is offering 20% off. Using formula 1: 20% of 250 = 50, so you save $50 and pay $200. This is the percentage calculation shoppers get wrong most often, by subtracting 20 from the price instead of 20 percent of it.
A test score: you scored 50 marks out of a possible 250 on a practice test. Using formula 2: (50 ÷ 250) × 100 = 20%. The same maths works for a tip: a $50 tip on a $250 meal is also 20%.
A pay rise: your salary goes from $80,000 to $100,000. Using formula 3: (100,000 − 80,000) ÷ 80,000 × 100 = 20,000 ÷ 80,000 × 100 = 25%. Your pay rose by 25%. The same $20,000 rise on a $40,000 salary would be 50% — the percent depends on where you started, so percent change and absolute change tell different stories.
Common Percentages at a Glance
| Percent | As a decimal | As a fraction | Of $100 |
|---|---|---|---|
| 5% | 0.05 | 1/20 | $5 |
| 10% | 0.10 | 1/10 | $10 |
| 20% | 0.20 | 1/5 | $20 |
| 25% | 0.25 | 1/4 | $25 |
| 50% | 0.50 | 1/2 | $50 |
| 75% | 0.75 | 3/4 | $75 |
Memorising the easy ones — 10% is a tenth, 25% a quarter, 50% a half — makes mental estimates much faster. For anything else, the calculator above gives the exact figure.
Tips and Common Mistakes
The most common mistake is mixing up “percent of” and “percent change”. If a $100 item rises by 20% and then falls by 20%, it does not return to $100: the rise takes it to $120, and a 20% fall from $120 is $24, leaving $96. Percentages always apply to the current amount, not the original one, unless the problem says otherwise.
Another trap is adding percentages with different bases. A 10% rise followed by another 10% rise is not 20% overall — it is 21%, because the second rise applies to the already-increased amount. This compounding is how interest works, which is why small rates add up over years. And “percentage points” differ from percent: going from 20% to 25% is a rise of 5 percentage points, but a 25% increase in the rate itself. If an interest rate rises from 4% to 6%, that is a rise of 2 percentage points, but a 50% increase in the rate. News reports usually mean percentage points when they say a rate “rose by 2 points”. If health numbers are what you are crunching, our BMI calculator pairs well with this one.
To work a percentage out in your head, start with 10%: move the decimal point one place left, so 10% of 250 is 25. Then build from there — 20% is double 10% (50), 5% is half of 10% (12.50), and 15% is 10% plus 5% (37.50). One more thing to watch: because percent change divides by the starting number, a small base makes the percent look huge. Going from 2 to 4 is a 100% increase, the same as going from 2,000 to 4,000 — the absolute change is very different, but the relative change is identical. Always check the raw numbers alongside the percent.
Percentages sit behind almost every money decision you make. Keep this calculator bookmarked, and the next time a discount, tip, or pay figure comes up, you will have the exact number in seconds.