Percentage Calculator
Three ways to work out any percentage — instantly.
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Most percentage questions are really one of three: what is X% of a number, what percent one number is of another, or how much something changed in percentage terms. Pick the mode, type two numbers, and get the answer with the exact formula shown — so you can check the working, not just copy the result.
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How to Calculate a Percentage — The Quick Answer
Almost every percentage question is one of three. Each is a single formula: to find a part, divide the percent by 100 and multiply; to find a percent, divide and multiply by 100; to find a change, divide the difference by the original.
Shortcut
X% of Y = (X ÷ 100) × Y | X is what % of Y = (X ÷ Y) × 100 | change A→B = ((B − A) ÷ A) × 100
Fact-Checking Claims You May Have Seen Online
A 50% rise followed by a 50% fall brings you back to where you started
False
100 up 50% is 150; 150 down 50% is 75 — you end 25% lower. The second percentage is taken from the bigger number, so an equal up-then-down never returns to the start.
Going from 10% to 15% is a 5% increase
It's 5 percentage points
That is a rise of 5 percentage points, but a 50% relative increase, because (15 − 10) ÷ 10 = 0.5. "Percentage points" and "percent" are not the same thing.
To undo a 20% discount, just add 20% back on
False
A price of 120 after 20% off was 150, not 144. Divide by 0.8 to reverse a 20% discount — adding 20% (which gives 144) takes the percentage from the wrong number.
The three questions and their formulas
| Question | Formula | Example |
|---|---|---|
| What is X% of Y? | (X ÷ 100) × Y | 20% of 150 = 30 |
| X is what % of Y? | (X ÷ Y) × 100 | 45 of 180 = 25% |
| Change from A to B? | ((B − A) ÷ A) × 100 | 120 → 150 = +25% |
Quick percentage reference
| Calculation | Result |
|---|---|
| 10% of 50 | 5 |
| 15% of 80 | 12 |
| 20% of 150 | 30 |
| 25% of 200 | 50 |
| 5% of 1,000 | 50 |
| 75% of 60 | 45 |
A quick shortcut: X% of Y always equals Y% of X. So 18% of 50 is the same as 50% of 18 = 9 — and the second version is often far easier to do in your head.
How It Works
The Three Formulas
Every percentage question on this page reduces to one of these
Formula
Part = (Percent ÷ 100) × Whole Percent = (Part ÷ Whole) × 100 Change = ((New − Old) ÷ Old) × 100
Variables
Percentage of a number
Converts the percentage to a decimal (dividing by 100) and multiplies by the whole. 20% of 150 becomes 0.20 × 150 = 30. This is the calculation behind a tip, a discount amount, or a tax line.
One number as a percent of another
Divides the part by the whole and multiplies by 100. 45 out of 180 is 45 ÷ 180 = 0.25 = 25%. This is how you turn a score, a share, or a completion count into a percentage. The whole must not be zero.
Percentage increase or decrease
Takes the difference between the new and old values and divides by the ORIGINAL value, not the new one. 120 to 150 is (150 − 120) ÷ 120 = 25% increase. A positive result is an increase; a negative result is a decrease.
Reversing a percentage (bonus)
To find the original price before an X% discount, divide the final price by (1 − X/100). A price of 120 after 20% off was 120 ÷ 0.8 = 150. Adding 20% back on would wrongly give 144.
Note: Percentages are just fractions out of 100 ('per cent' = 'per hundred'). Converting the percentage to a decimal first — 20% → 0.20 — is the single step that makes every one of these calculations straightforward.
Worked Examples
One for each mode, step by step
What is 20% of 150?
Convert the percent to a decimal: 20 ÷ 100 = 0.20. Multiply by the whole: 0.20 × 150 = 30.
45 is what percent of 180?
Divide the part by the whole: 45 ÷ 180 = 0.25. Multiply by 100: 0.25 × 100 = 25%.
What is the percentage change from 120 to 150?
Difference ÷ original: (150 − 120) ÷ 120 = 30 ÷ 120 = 0.25. Times 100 = a 25% increase.
A jacket is 120 after 20% off. What was the original price?
Divide by (1 − 0.20): 120 ÷ 0.8 = 150. Check: 150 × 0.20 = 30 off, and 150 − 30 = 120. Correct.
Reference Guide
| unit | value | note |
|---|---|---|
| 20% of 150 | 30 | Part of a whole |
| 45 of 180 | 25% | One number as a percent of another |
| 120 → 150 | +25% | Percentage increase |
| 200 → 150 | −25% | Percentage decrease |
| 120 after −20% | 150 | Reversed discount |
Key Features
💡 Pro Tips
- →X% of Y always equals Y% of X. Stuck on 18% of 50? Flip it: 50% of 18 = 9. The flip is often far easier mentally.
- →To take a percentage off in one step, multiply by (1 − rate): a 30% discount on 80 is 80 × 0.70 = 56. To add a percentage on, multiply by (1 + rate).
- →Percentage change always divides by the ORIGINAL (older) value. Swapping which number is 'original' changes the answer, so decide your starting point first.
- →Watch the difference between 'percent' and 'percentage points'. A rate moving from 4% to 6% is up 2 percentage points, but a 50% relative increase.
- →For percentage change, a negative result simply means a decrease — there is no separate formula for 'decrease'.
Common Mistakes
Dividing percentage change by the new value instead of the original
Percentage change is always measured against where you started. From 120 to 150 you divide the 30 difference by 120 (the original) to get 25%, not by 150. Dividing by the new value is the single most common percentage error.
Assuming an equal percentage up and down cancels out
A 50% rise then a 50% fall does not return to the start: 100 → 150 → 75. Because each percentage is taken from a different base, you end up 25% lower. The same trap applies to gains and losses in investing.
Reversing a discount by adding the percentage back
If a price is 120 after 20% off, the original was 120 ÷ 0.8 = 150, not 120 + 20% = 144. Adding the percentage applies it to the smaller, discounted number instead of the original.
Confusing percent with percentage points
If a figure goes from 10% to 15%, that is a rise of 5 percentage points but a 50% relative increase. Reporting one as the other overstates or understates the change dramatically — especially with interest rates and statistics.
Last updated: October 5, 2026
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Frequently Asked Questions
How do I calculate a percentage of a number?
Divide the percentage by 100 and multiply by the number. For 20% of 150: 20 ÷ 100 = 0.20, then 0.20 × 150 = 30. A mental shortcut is that X% of Y equals Y% of X, so 20% of 150 is the same as 150% of 20.
How do I find what percentage one number is of another?
Divide the part by the whole, then multiply by 100. For 45 out of 180: 45 ÷ 180 = 0.25, and 0.25 × 100 = 25%. The whole can't be zero, because nothing can be a percentage of zero.
How do I calculate percentage increase or decrease?
Subtract the original value from the new value, divide by the original, and multiply by 100. From 120 to 150: (150 − 120) ÷ 120 × 100 = 25% increase. From 200 to 150: (150 − 200) ÷ 200 × 100 = −25%, i.e. a 25% decrease. A negative answer always means a decrease.
What is the difference between percent and percentage points?
A percentage point is the arithmetic gap between two percentages; percent is the relative change between them. If a rate moves from 10% to 15%, that is a 5 percentage-point rise but a 50% increase in relative terms ((15 − 10) ÷ 10). Mixing them up is a common source of misleading statistics.
How do I reverse a percentage — find the original price before a discount?
Divide the final price by (1 minus the discount as a decimal). A jacket costing 120 after 20% off was 120 ÷ 0.8 = 150. Don't add 20% back on — that applies the percentage to the discounted price and gives the wrong answer (144).
Why doesn't a 50% increase followed by a 50% decrease return to the original?
Because each percentage is taken from a different starting number. 100 increased by 50% is 150; 150 decreased by 50% is 75, not 100. The decrease is calculated on the larger value, so you end up 25% below where you started. This is why percentage gains and losses don't simply cancel.