Percentage Calculator
Result = (X ÷ 100) × Y
How Percentage Calculations Work
A percentage expresses a proportion out of one hundred. The word comes from the Latin per centum, meaning "by the hundred." When you see 25%, you are looking at the fraction 25/100, which simplifies to 1/4. Percentages appear everywhere in daily life — sales discounts, tax rates, exam scores, tip calculations, and financial growth reports all rely on the same core ideas.
The most common task is finding a percentage of a value. The formula is straightforward: result = (percentage ÷ 100) × value. For example, to find 20% of 150, you compute (20 ÷ 100) × 150 = 0.20 × 150 = 30. You can think of the percentage as a decimal multiplier: move the decimal point two places left (20 becomes 0.20) and multiply.
The second common question is reverse: given a part and a whole, what percent is the part? Here the formula is: percentage = (part ÷ whole) × 100. If you scored 45 points out of 60, your percentage is (45 ÷ 60) × 100 = 75%. Always divide the part by the whole — not the other way around — and multiply by 100 to convert the decimal into a percent.
Percent change measures how much a value increased or decreased relative to its starting point. The formula is: percent change = ((new − old) ÷ |old|) × 100. A price rising from $80 to $100 represents a 25% increase because (100 − 80) ÷ 80 × 100 = 25. A drop from $100 to $75 is a 25% decrease. Note that a 50% increase followed by a 50% decrease does not return you to the original value — percentages are relative to different bases.
Quick mental shortcuts help in everyday situations. To find 10% of any number, move the decimal one place left. To find 5%, take half of 10%. To find 15%, add 10% and 5%. For compound scenarios like successive discounts (20% off, then an additional 10% off), apply each discount sequentially to the new price rather than adding the percentages together. This calculator handles all three modes so you can verify homework, check sale prices, or analyze data without memorizing formulas.
Examples
| Example | Result |
|---|---|
| 20% of 150 | 30 |
| 15% of 80 | 12 |
| 25 is what % of 200 | 12.5% |
| 50 is what % of 125 | 40% |
| Percent change from 100 to 150 | 50% |
| Percent change from 80 to 60 | -25% |
| 10% of 500 | 50 |
| 75% of 40 | 30 |
Frequently asked questions
Multiply the number by 0.20, or divide it by 5. For example, 20% of 150 = 150 × 0.20 = 30.
A change from 10% to 15% is a 5 percentage-point increase, but a 50% relative increase (because 5 ÷ 10 × 100 = 50%). Percentage points measure absolute difference; percent change measures relative difference.
Subtract the original value from the new value, divide by the original value, and multiply by 100. Formula: ((new − old) ÷ old) × 100.