Percentage Calculator
Find a percentage of any number
Four different questions get called "percentage", and this calculator answers all of them. Pick a mode: a percent of a number, the percent change between two values, what percent one number is of another, or working backwards from a percentage to the original. Below: the formula for each, a worked example, and the percentage traps that catch people out.
The four percentage questions
Almost every percentage problem is one of four shapes, and learning how to calculate percentage figures reliably is mostly a matter of noticing which one you have. The same tool serves as a percentage change calculator, a percent-of tool, a reverse solver, and a way to find what percent of another number something is — but the arithmetic differs in each case, and so does the number you divide by.
| Mode | Question | Formula | Example |
|---|---|---|---|
| Percent of | What is 20% of 150? | value × pct ÷ 100 | = 30 |
| Percent change | 5,000 grew to 6,500. By how much? | (new − old) ÷ old × 100 | = 30% |
| What percent of | 18 out of 24 is what percent? | part ÷ whole × 100 | = 75% |
| Reverse | 45 is 30% of what number? | value × 100 ÷ pct | = 150 |
The one people reach for a calculator to check is percent change, because the base matters and it is easy to divide by the wrong number. The rule is that you always divide by where you started, never where you ended up.
Percentage change and why it is not symmetric
This is the single most useful thing on this page. A percentage increase and the decrease that undoes it are not the same number.
100 rises by 50% to 150. To get back from 150 to 100 is a 33.3% decrease, not 50%. The base changed.
| Increase | Multiplier | Decrease needed to undo it |
|---|---|---|
| +10% | 1.10 | −9.1% |
| +25% | 1.25 | −20% |
| +50% | 1.50 | −33.3% |
| +100% | 2.00 | −50% |
| −50% | 0.50 | +100% |
This is why a stock that falls 50% needs to double just to break even, and why "prices rose 20% then fell 20%" leaves you 4% down rather than back where you started. The calculator's multiplier output makes this visible: chain multipliers rather than adding percentages.
Worked example: a value that grew from 5,000 to 6,500
Set the mode to Percent change, enter 5,000 as the starting value and 6,500 as the ending value:
| Output | Working | Result |
|---|---|---|
| Percent increase | (6,500 − 5,000) ÷ 5,000 × 100 | 30% |
| Change in value | 6,500 − 5,000 | 1,500 |
| Multiplier | 6,500 ÷ 5,000 | 1.3 |
Dividing by 6,500 instead of 5,000 would give 23.1%, which is the answer to a different question — what percent of the new figure the change represents. If you are measuring the return on money you invested rather than a plain change between two numbers, the ROI calculator handles gains, costs and holding periods properly.
Percentage points are not percentages
If an interest rate goes from 5% to 6%, that is a rise of one percentage point — but a 20% increase in the rate itself. Both statements are true and they describe the same event with numbers 20 times apart.
Whenever the thing being measured is itself a percentage, say which you mean. Reporting a change in an interest rate, an unemployment rate or a conversion rate as "up 20%" when you mean one point is the most common numerical mistake in business writing, and it usually flatters whoever wrote it.
Percentages in everyday use
- Discounts. 30% off then 20% off is not 50% off. It is 0.7 × 0.8 = 0.56, so 44% off. The discount calculator stacks them for you.
- Tax added on. Removing tax is a reverse-percentage problem: a $108 total at 8% tax came from $100, not $99.36.
- Tips. A quick 20% is 10% doubled: move the decimal one place, then double it.
- Markup versus margin. A 50% markup on cost is a 33.3% margin on price. They are different bases and shops routinely quote whichever sounds better.
- Compounding. Repeated percentage growth multiplies, so 7% a year for ten years is 1.0710 = 1.97, not 70%.
Common percentage mistakes
- Dividing by the new value instead of the original when finding percent change.
- Adding percentages that have different bases, such as stacked discounts or sequential growth rates.
- Confusing percentage points with percent whenever the quantity is itself a rate.
- Assuming a rise and fall of the same percent cancel out. They never do.
- Averaging percentages without weighting them by the size of what they describe.
How this percentage calculator works out its numbers
Four independent formulas, selected by the mode field. Results round to two decimals, and the multiplier to four.
- Percent of: value × pct ÷ 100, plus the value increased and decreased by that amount.
- Percent change: (new − old) ÷ |old| × 100. The absolute value on the denominator keeps the sign meaningful when the starting value is negative. Returns nothing when the starting value is zero, because percent change from zero is undefined rather than infinite.
- What percent of: part ÷ whole × 100, with the remaining share alongside. Returns nothing when the whole is zero.
- Reverse: value × 100 ÷ pct. Returns nothing when the percentage is zero.
- The multiplier output (new ÷ old) exists so repeated percentage changes can be chained by multiplication, which is the correct way to combine them. Adding percentages with different bases is the error this is meant to prevent.
Reviewed September 2026.
Figures reviewed . Every worked example on this page is checked against the calculator above.
Percentage Calculator: frequently asked questions
How do I calculate a percentage of a number?
Multiply the number by the percentage and divide by 100. For 15% of 80: 80 × 15 ÷ 100 = 12. Use the Percent of mode above, which also shows the value increased and decreased by that percent.
How do I calculate percentage change?
Subtract the old value from the new one, divide by the old value, then multiply by 100. From 5,000 to 6,500 that is 1,500 ÷ 5,000 × 100 = 30%. Always divide by where you started, not where you finished.
How do I find what percent one number is of another?
Divide the part by the whole and multiply by 100. 18 out of 24 is 18 ÷ 24 = 0.75, or 75%. That is the What percent of mode.
How do I work backwards from a percentage?
Multiply the known value by 100 and divide by the percentage. If 45 is 30% of a number, then 45 × 100 ÷ 30 = 150. Use the Reverse mode for this.
Why doesn't a 50% increase cancel out a 50% decrease?
Because the base changes. Rising 50% from 100 gives 150, and falling 50% from 150 gives 75, not 100. Undoing a 50% rise takes a 33.3% fall.
What is the difference between percent and percentage points?
If a rate moves from 5% to 6% that is one percentage point, but a 20% increase in the rate itself. The distinction only matters when the thing being measured is already a percentage, which is exactly when people get it wrong.
How do I calculate a percentage increase?
Use percent change with the smaller number as the starting value. Alternatively multiply by the growth multiplier: a 30% increase means multiplying by 1.30, which is how you should chain several increases together.
How do stacked discounts work?
They multiply rather than add. 30% off then a further 20% off leaves 0.70 × 0.80 = 0.56 of the price, so 44% off in total, not 50%.