Percentage Calculator
Work out a percentage of a number, what percent one number is of another, the percentage change between two values, or a value plus or minus a percent, with the formula and every step shown.
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Formula: X% of Y = X ÷ 100 × Y
| Percentage | Value |
|---|---|
| 1% | 0.8 |
| 5% | 4 |
| 10% | 8 |
| 15% | 12 |
| 20% | 16 |
| 25% | 20 |
| 50% | 40 |
| 75% | 60 |
Show the steps
- Turn the percentage into a decimal: 15 ÷ 100 = 0.15.
- Multiply by the number: 0.15 × 80 = 12.
How to calculate a percentage
A percentage is a number out of 100, so every percentage calculation is a multiplication or division by 100. To find X% of Y, divide X by 100 and multiply by Y: 15% of 80 is 0.15 × 80 = 12. To find what percent X is of Y, divide X by Y and multiply by 100: 12 out of 80 is 12 ÷ 80 × 100 = 15%. This percentage calculator does both, plus percentage change, adding or subtracting a percent, and percentage difference, and it shows the formula and each step under the answer.
Percentage increase and decrease
Percentage change compares a new value with an old one: (new − old) ÷ old × 100. A rent that goes from $1,200 to $1,350 rises by 150 ÷ 1,200 × 100 = 12.5%. A share price that falls from $50 to $40 drops by 10 ÷ 50 × 100 = 20%.
The direction matters because the old value is the base. From 80 to 100 is +25%, but from 100 back to 80 is −20%. That is also why a 20% drop followed by a 20% rise does not get you back where you started: $50 → $40 → $48. The calculator shows the reverse change next to every result so you can see the asymmetry.
Adding or subtracting a percentage
To increase a number by a percent, multiply it by 1 plus the percent as a decimal; to decrease it, multiply by 1 minus it. A $64,000 salary with a 4% raise becomes 64,000 × 1.04 = $66,560. A $250 jacket at 30% off costs 250 × 0.70 = $175. Multiplying once is faster than working out the percentage and adding it on, and it makes stacked changes easy: two 10% raises are 1.10 × 1.10 = 1.21, a 21% rise in total, not 20%.
Percentage difference is not percentage change
Use percentage difference when neither number is the starting point, for example two quotes for the same job or two lab measurements. It divides the gap by the average of the two values: |A − B| ÷ ((A + B) ÷ 2) × 100. Quotes of $80 and $100 differ by 20 ÷ 90 × 100 = 22.2%, whichever you list first. As a percentage change the same pair would be +25% or −20% depending on the order, so pick the mode that matches your question.
Common mistakes
- Adding percentage points to percentages. An interest rate that moves from 4% to 5% has risen by 1 percentage point, but by 25% in relative terms.
- Dividing by the wrong base. “What percent of 80 is 12?” divides by 80. “By what percent did 80 grow to 100?” also divides by 80, the old value, never the new one.
- Reversing a percentage by subtracting it. If a price including 20% tax is $120, the price before tax is 120 ÷ 1.20 = $100, not 120 − 20% = $96.
- Percentage change from zero. Growth from 0 has no percentage because the formula divides by zero; report the absolute change instead. When the starting value is negative, the change is measured against its absolute value, so −50 to −25 counts as an increase of 50%.
Frequently asked questions
How do I calculate a percentage of a number?
Divide the percentage by 100 and multiply by the number. 15% of 80 is 0.15 × 80 = 12.
How do I find what percent one number is of another?
Divide the part by the whole and multiply by 100. 12 out of 80 is 12 ÷ 80 × 100 = 15%.
How do I calculate percentage increase or decrease?
Subtract the old value from the new one, divide by the old value and multiply by 100. From 80 to 100 is (100 − 80) ÷ 80 × 100 = +25%; from 100 back to 80 is −20%.
What is the difference between percentage change and percentage difference?
Percentage change measures growth from an old value to a new one and divides by the old value. Percentage difference compares two values with no before and after and divides by their average, so 80 and 100 differ by 22.2% in either order.
How do I add a percentage to a number?
Multiply by 1 plus the percentage as a decimal. 80 plus 15% is 80 × 1.15 = 92; 80 minus 15% is 80 × 0.85 = 68.
Why can't I calculate a percentage change from zero?
The formula divides by the starting value, and dividing by zero has no answer. Going from 0 to 50 is an increase of 50 units, but not any finite percentage.