％ Percentage Calculator: Percent of a Number, Increase, Decrease & Change
By ToolNimba Editorial Team · Updated 2026-06-19
Percentages turn up everywhere, discounts, tips, tax, exam scores, interest and statistics. This calculator covers the three questions people ask most: what is X% of Y, X is what percent of Y, and what is the percentage change from one value to another. Type your numbers and the answer updates as you go, with the working shown so you can learn the method, not just the result.
What is the Percentage Calculator?
A percentage is just a fraction with a fixed denominator of 100. The word comes from the Latin per centum, "per hundred", so 25% literally means 25 out of every 100, or the fraction 25/100, or the decimal 0.25. That single idea is the key to every percentage calculation: once you can move between a percent, a fraction and a decimal, the rest is ordinary multiplication and division. To turn a percent into a decimal you divide by 100 (move the decimal point two places left); to turn a decimal back into a percent you multiply by 100.
Most real questions reduce to one of three shapes. Finding a part asks "what is 20% of 150?" and is solved by turning the percent into a decimal and multiplying: 0.20 × 150 = 30. Finding the rate asks "30 is what percent of 150?" and reverses that: divide the part by the whole and multiply by 100. Finding the change compares a before and an after value, the new minus the old, divided by the old, times 100, and tells you how much something grew or shrank in relative terms. Almost every percentage question you meet in shopping, school or work is one of these three in disguise.
There is a fourth shape that trips people up: the reverse percentage, where you know the final amount and the rate but need the original. If a jacket costs $63 after a 30% discount, you are paying 70% of the original, so the original is 63 ÷ 0.70 = $90. The same logic recovers a pre-tax price: a $108 total that already includes 8% tax came from 108 ÷ 1.08 = $100. The rule is always to divide by the multiplier (1 minus the discount, or 1 plus the tax), never to add the same percent back.
Percentage change and percentage difference sound alike but answer different questions. Change has a clear direction, an old value and a new value, so you divide by the old value and the sign tells you up or down. Difference compares two values where neither is obviously the "starting point", so you divide the gap by the average of the two, and the result is always positive. Reporting a price move as a difference when you mean a change, or vice versa, is one of the most common sources of misleading statistics.
The reason percentages are worth a dedicated tool is that they are deceptively easy to get slightly wrong. Mixing up which number is the "whole", chaining a discount and a tax in the wrong order, confusing percentage points with percent, or assuming an increase and a decrease of the same size cancel out are all common traps. This calculator shows the working, not just the final number, which is the fastest way to catch those mistakes before they cost you money or marks, and to learn the method so you can do the easy ones in your head.
When to use it
- Working out a sale price: a 30% discount on an $80 jacket means you pay 70% of $80 = $56.
- Tipping at a restaurant: an 18% tip on a $45 bill is 0.18 × 45 = $8.10.
- Adding sales tax or VAT: an 8% tax on a $250 purchase adds 0.08 × 250 = $20, for a $270 total.
- Turning an exam score into a grade: 57 correct out of 75 questions is (57 ÷ 75) × 100 = 76%.
- Recovering an original price: working back from a $63 sale price after 30% off to the $90 list price using a reverse percentage.
- Reading statistics and reports: comparing this year to last year as a percentage change rather than a raw difference, and knowing when to use percentage points instead.
How to use the Percentage Calculator
- Pick the calculation you need using the tabs (percent of a number, what percent, or percentage change).
- Enter your two numbers in the boxes; the answer updates as you type.
- Read the result and the step-by-step working shown beneath it.
- For a reverse percentage, divide the final amount by the multiplier (1 minus the discount, or 1 plus the tax).
Formula & method
Worked examples
A $120 pair of shoes is marked 25% off. What do you pay?
- Discount = 25% of 120 = 0.25 × 120 = 30
- Price paid = 120 − 30 = 90
- Shortcut: paying 75% → 0.75 × 120 = 90
Result: You pay $90 (a $30 saving).
You scored 57 out of 75 on a test. What percentage is that?
- Divide the part by the whole: 57 ÷ 75 = 0.76
- Multiply by 100: 0.76 × 100 = 76
Result: 76%.
Monthly revenue rose from $80,000 to $100,000. What is the percentage change?
- Difference = 100,000 − 80,000 = 20,000
- Divide by the old value: 20,000 ÷ 80,000 = 0.25
- Multiply by 100: 0.25 × 100 = 25
Result: A 25% increase.
A coat costs $63 after a 30% discount. What was the original price?
- After 30% off you pay 100% − 30% = 70% of the original
- So the original = final ÷ 0.70 = 63 ÷ 0.70
- 63 ÷ 0.70 = 90
Result: The original price was $90.
What is the percentage difference between 80 and 100?
- Gap = |100 − 80| = 20
- Average = (80 + 100) ÷ 2 = 90
- Divide and multiply by 100: (20 ÷ 90) × 100 = 22.22
Result: About 22.2% (note this differs from the 25% change, which divides by the starting value).
Common percentages of round numbers
| Percent | of 50 | of 100 | of 200 |
|---|---|---|---|
| 5% | 2.5 | 5 | 10 |
| 10% | 5 | 10 | 20 |
| 15% | 7.5 | 15 | 30 |
| 20% | 10 | 20 | 40 |
| 25% | 12.5 | 25 | 50 |
| 50% | 25 | 50 | 100 |
Percent, fraction and decimal equivalents
| Percent | Fraction | Decimal |
|---|---|---|
| 10% | 1/10 | 0.10 |
| 12.5% | 1/8 | 0.125 |
| 20% | 1/5 | 0.20 |
| 25% | 1/4 | 0.25 |
| 33.3% | 1/3 | 0.333 |
| 50% | 1/2 | 0.50 |
| 75% | 3/4 | 0.75 |
| 100% | 1/1 | 1.00 |
Mental-math shortcuts
| To find | Quick method | Example |
|---|---|---|
| 10% | Move the decimal one place left | 10% of 240 = 24 |
| 1% | Move the decimal two places left | 1% of 240 = 2.4 |
| 5% | Take 10% then halve it | 5% of 240 = 12 |
| 20% | Take 10% then double it | 20% of 240 = 48 |
| 15% | Add 10% and 5% | 15% of 240 = 36 |
| X% of Y | Equals Y% of X (swap them) | 8% of 50 = 50% of 8 = 4 |
Common mistakes to avoid
- Assuming a 50% drop then a 50% rise returns to the start. It does not. Start at 100, fall 50% to 50, then rise 50% of 50 (which is 25) and you reach 75, not 100. The percentages act on different bases, so equal-sized up and down moves never cancel out. To undo a 50% drop you need a 100% rise.
- Confusing percentage points with percent. A rate moving from 4% to 6% is a rise of 2 percentage points, but a 50% increase. Reporting it as “up 2%” is wrong.
- Using the wrong number as the “whole”. For percentage change, always divide by the original (old) value, not the new one. Dividing by the new value gives a different, and incorrect, answer.
- Forgetting that stacked discounts do not add. Taking 20% off then a further 10% off is a 28% total discount, not 30%, because the second cut applies to the already-reduced price.
- Adding a percent back to reverse it. To undo a 20% discount you do not add 20%. The discounted price is 80% of the original, so you divide by 0.80, not multiply by 1.20. Adding 20% back lands you below the true original.
- Dividing by the part instead of the whole. To find what percent 30 is of 120, divide the part by the whole (30 ÷ 120 = 25%). Flipping them (120 ÷ 30) gives 400%, which answers a different question entirely.
Glossary
- Percent
- A number expressed as a fraction of 100. 25% means 25 per hundred, i.e. 25/100 or 0.25.
- Percentage point
- The plain arithmetic difference between two percentages. Going from 10% to 15% is a rise of 5 percentage points (but a 50% relative increase).
- Percentage change
- How much a value grew or shrank relative to its starting value: (new − old) ÷ old × 100, expressed as a percent.
- Percentage difference
- How far apart two values are when neither is a clear baseline: the gap divided by their average, times 100. Always positive, and different from percentage change.
- Reverse percentage
- Working back to the original amount from the final amount and the rate. You divide by the multiplier, e.g. final ÷ 0.80 to undo a 20% discount.
- Part and whole
- The part is the amount you are measuring and the whole is the total it is measured against. Percent = (part ÷ whole) × 100.
- Multiplier
- The decimal you multiply by to apply a percentage in one step. A 15% increase uses 1.15; a 15% decrease uses 0.85.
Frequently asked questions
How do I calculate a percentage of a number?
Divide the percentage by 100, then multiply by the number. For example, 20% of 150 is (20 ÷ 100) × 150 = 30.
What is X% of Y?
X% of Y equals (X ÷ 100) × Y. So 30% of 80 is (30 ÷ 100) × 80 = 0.30 × 80 = 24. A quick mental trick: 10% of any number is just that number with the decimal point moved one place left.
How do I find what percentage one number is of another?
Divide the first number by the second, then multiply by 100. For example, 30 out of 120 is (30 ÷ 120) × 100 = 25%.
What is the difference between percentage change and percentage difference?
Percentage change has a clear before and after, so you divide by the original value: from 80 to 100 is a +25% change. Percentage difference compares two values with no “starting point”, so you divide by their average: the difference between 80 and 100 is 20 ÷ 90 × 100 ≈ 22.2%.
How do I convert a percentage to a decimal?
Divide the percentage by 100, which is the same as moving the decimal point two places to the left. So 75% becomes 0.75, 8% becomes 0.08, and 150% becomes 1.5. To go the other way, multiply the decimal by 100.
How do I work out the original price before a discount?
Use a reverse percentage: divide the final price by 1 minus the discount. If you paid $63 after 30% off, you paid 70% of the original, so the original is 63 ÷ 0.70 = $90. Do not add 30% back, as that gives the wrong answer.
How do I add or subtract a percentage from a number in one step?
Multiply by a single factor. To add 15%, multiply by 1.15; to subtract 15%, multiply by 0.85. For example, $200 plus 15% is 200 × 1.15 = $230, and $200 minus 15% is 200 × 0.85 = $170.
What is the difference between a percentage point and a percent?
A percentage point is the plain gap between two percentages, while a percent is relative. If an interest rate rises from 4% to 6%, that is a 2 percentage point increase but a 50% relative increase. Mixing them up is a common reporting error.
Why does a 50% decrease followed by a 50% increase not return to the start?
Because each percentage acts on a different base. Starting at 100, a 50% drop gives 50, then a 50% rise of 50 adds only 25, leaving 75. To fully undo a 50% drop you need a 100% rise.
How do I calculate a percentage in Excel or Google Sheets?
For a percent of a number, type =rate*value, for example =0.2*150. To find what percent one cell is of another, use =part/whole and format the cell as a percentage. For percentage change use =(new-old)/old.
Is this percentage calculator free?
Yes. Every ToolNimba tool is free, needs no sign-up, and runs entirely in your browser, so your numbers never leave your device.