Three percentage calculations in one tool: X% of Y, X is what % of Y, and percent change. Choose a mode, enter two numbers, and see the result with a bar chart visualization.
Which mode do you need?
| Question type | Formula | Example |
|---|---|---|
| What is a% of b? | result = (a÷100) × b | 20% of 150 = 30 |
| a is what % of b? | percent = (a÷b) × 100% | 25 is 12.5% of 200 |
| Percent change a → b | change = ((b−a)÷a) × 100% | 80 → 100 = +25% |
| Increase by a% | new = b × (1 + a÷100) | $50 + 8% tax = $54 |
| Decrease by a% | new = b × (1 − a÷100) | $80 − 25% off = $60 |
For a% of b: a is the percent, b is the base. For a is what % of b: a is the part, b is the whole. For percent change: a is the original value, b is the new value.
How to use
Pick a mode from the dropdown, enter the two values, and click Calculate. The graph shows a bar visualization — a single bar with the percentage portion shaded for the first two modes, or two side-by-side bars (original vs new) for percent change.
Worked examples
Click any example to load it into the calculator above.
Mode: What is a% of b?. (20÷100) × 150 = 0.2 × 150 = 30. The bar chart shows 20% of the total filled.
Mode: a is what % of b?. (25 ÷ 200) × 100 = 12.5%. The bar shows where 25 falls inside a total of 200.
Mode: Percent change. (100−80)÷80 × 100 = 20÷80 × 100 = +25%. Two side-by-side bars compare the values; the second is taller and green.
Mode: Percent change. (75−100)÷100 × 100 = −25%. A 25% decrease. The second bar is shorter and red, indicating a drop.
Common uses
- Sales tax, tips, and discounts ($50 + 8% tax, $80 − 25% off)
- Grade calculations (you got 38 out of 50 — what percentage?)
- Statistics: turning raw counts into percentages
- Year-over-year growth or decline in business reports
- Stock or investment returns over time
- Recipe scaling (increase ingredients by 50% to feed more people)
- Population, inflation, or other growth-rate comparisons
What “percent” really means
Per cent = per hundred
- The word “percent” literally means “per hundred” (Latin per centum). So 25% is just another way to write 25 out of 100, or the fraction 25÷100 = 0.25.
- To convert a percent to a decimal, divide by 100 (move the decimal point two places left). 75% → 0.75. 5% → 0.05.
- To convert a decimal to a percent, multiply by 100 (move two places right). 0.6 → 60%. 1.5 → 150%.
- To find a% of b, multiply the decimal form by the base: a% of b = (a÷100) × b.
- To find what percent a is of b, divide a by b, then multiply by 100 to convert the ratio to a percent: (a÷b) × 100.
- Percent change measures growth relative to the original value: ((new − original) ÷ original) × 100. Positive = increase, negative = decrease.
FAQ
Why can’t I compute percent change from zero?
The formula divides by the original value. If original = 0, you’d be dividing by zero, which is undefined. You can’t express “going from nothing to something” as a percent change; you’d have to use other measures (like the absolute amount).
What’s the difference between percent and percentage points?
If a rate goes from 5% to 7%, that’s a 2 percentage point increase but a 40% percent increase (because 2 is 40% of 5). Important distinction for interest rates, polls, and statistics where both measures get used.
Can percentages be more than 100?
Yes. 200% of 50 is 100 (twice the base). A percent change of +150% means the new value is 2.5× the original. Percentages don’t cap at 100 — only fractions of a whole pie naturally stay between 0% and 100%.
How do I add or remove a percentage from a number?
Add a%: multiply by (1 + a÷100). $100 + 8% tax = 100 × 1.08 = $108. Remove a%: multiply by (1 − a÷100). $80 with 25% off = 80 × 0.75 = $60.
If I increase by 10% then decrease by 10%, do I get back to the original?
No — you end up below the original. $100 + 10% = $110. $110 − 10% = $99. The 10% decrease is taken from a larger base, so the absolute change is bigger. This trips up a lot of people.
What about negative numbers?
Percentages work fine with negative values, but percent change can give unintuitive signs. If a value goes from −5 to 5, the change is (5−(−5))÷(−5) × 100 = −200% — the negative sign comes from the negative denominator, not the direction of movement.