Percent Calculator
Find percentages, increases, decreases, and percent change.
About the Percent Calculator
Most percentage questions are one of four things: a percentage of a number, an increase, a decrease, or the change between two numbers. This does all four.
How to use it
- Enter the base number.
- Enter the percentage.
- Pick the mode that matches your question.
The formula
Almost every percentage question is one of three, and confusing them is what makes the topic feel harder than it is.
What is X% of Y? → Y × (X ÷ 100)
X is what percent of Y? → (X ÷ Y) × 100
Percent change → (New − Old) ÷ Old × 100
The word 'percent' means 'per hundred', so 25% is simply 0.25. Every one of these formulas is that conversion plus a multiplication or a division.
The third is where the money is lost. Percent change is always measured against the old value, which is why a rise and a fall of the same percentage do not cancel: $100 up 20% is $120, and $120 down 20% is $96. The base changed underneath you.
Worked examples
| Question | Calculation | Answer |
|---|---|---|
| What is 15% of 80? | 80 × 0.15 | 12 |
| 12 is what percent of 80? | 12 ÷ 80 × 100 | 15% |
| 80 rises to 92 — what change? | (92 − 80) ÷ 80 × 100 | +15% |
| 92 falls to 80 — what change? | (80 − 92) ÷ 92 × 100 | −13.04% |
The last two rows are the same two numbers and different answers, and the reason is the denominator. Going up from 80 is measured against 80; coming down from 92 is measured against 92. This is why a stock that falls 50% needs to rise 100% to recover, and why a shop can offer 20% off and still be ahead after marking prices up 25%.
Common mistakes
- Assuming a percentage rise and fall cancel out. They never do. Up 20% then down 20% leaves you at 96% of where you started, because the second percentage is applied to a larger number.
- Confusing percent with percentage points. A rate moving from 4% to 6% has risen two percentage points, which is a 50% increase. Reports blur these constantly, and the difference is often the whole story.
- Adding percentages of different bases. 20% of one number plus 30% of another is not 50% of anything. Percentages are only additive when they share a base.
- Reversing a discount by adding the same percentage. If a price after 20% off is $80, the original was $80 ÷ 0.8 = $100, not $80 × 1.2 = $96. To undo a percentage you divide.
Terms explained
- Percent
- Per hundred. 25% is 25 per 100, or 0.25 as a decimal.
- Percentage point
- The arithmetic gap between two percentages. From 4% to 6% is two percentage points and a 50% increase — both true, and very different.
- Base value
- The number a percentage is measured against. Identifying it correctly settles most percentage problems.
- Percent change
- (New − Old) ÷ Old × 100. Always relative to the starting value.
- Percent difference
- The gap between two values relative to their average. Used when neither is naturally the baseline.
- Basis point
- One hundredth of a percentage point, used in finance. A 25 basis point rise is 0.25%.
Common questions
- How do I calculate a percentage of a number?
- Divide the percentage by 100 and multiply. 15% of 80 is 80 × 0.15 = 12.
- How do I work out percent change?
- Subtract the old value from the new, divide by the old, and multiply by 100. Always divide by the starting value, not the ending one.
- Why do a 20% rise and a 20% fall not cancel?
- Because the second is applied to a bigger number. $100 up 20% is $120; $120 down 20% is $96. The percentage is the same, the base is not.
- What is the difference between percent and percentage points?
- Moving from 4% to 6% is a rise of two percentage points and an increase of 50%. Both describe the same change and imply very different things.
- How do I reverse a discount?
- Divide rather than multiply. An item costing $80 after 20% off was $80 ÷ 0.8 = $100 originally.
- How do I add a percentage on top?
- Multiply by 1 plus the rate. Adding 8% sales tax to $50 is $50 × 1.08 = $54.
- What does a percentage over 100 mean?
- More than the whole. A 150% increase means the value has grown to two and a half times its original size — the increase is 150%, the result is 250% of the start.
- How do I find the original number from a percentage?
- Divide by the decimal form. If 12 is 15% of something, that something is 12 ÷ 0.15 = 80.