Percentage Calculator
Five everyday percentage questions in one place: find a percent of a number, work out what percent one number is of another, calculate percent change, reverse-solve the whole from a part, or apply a percentage increase or decrease to any value.
Formula
Worked example
What is 20% of 150? Decimal: 20/100 = 0.2; result: 0.2 x 150 = 30. Reverse: 30 is 20% of what? 30 / 0.20 = 150. Percent change 120 to 150: (150-120)/120 x 100 = +25%.
The five percentage questions this calculator solves
Almost every percentage problem falls into one of five patterns. "What is P% of N?" scales a number by a percentage, the basis of discounts, tips and tax. "X is what percent of Y?" converts a ratio into a percentage, used for test scores, budget shares and survey results. "Percent change from X to Y" measures growth or decline relative to the starting value. "X is P% of what?" is the reverse-solve or back-calculation: you know the part and its percentage share, and you want the whole, which is common when working out full prices from deposits or reverse-engineering budgets. "Increase or decrease a value by P%" applies a known rate to project a new value, the key step in price adjustments, salary increases and inflation calculations.
How to calculate a percentage by hand
To find a percent of a number, divide the percent by 100 and multiply: 20% of 150 is 0.20 x 150 = 30. To find what percent one number is of another, divide the part by the whole and multiply by 100: 30 / 150 x 100 = 20%. To find percent change, subtract the original from the new value, divide by the absolute original, and multiply by 100. To reverse-solve the whole, divide the known part by the percentage expressed as a decimal: 30 / 0.20 = 150. To apply a percentage change, multiply by (1 + P/100) for an increase or (1 - P/100) for a decrease.
Percentage change vs percentage points
These two are commonly confused. If a savings rate rises from 4% to 5%, that is a 1 percentage-point rise but a 25% increase in the rate itself. Percentage points describe the arithmetic gap between two percentages. Percentage change describes that gap relative to the starting value. In finance and statistics, the distinction is critical: central bank rate decisions are reported in percentage points, but their effect on borrowers is discussed as a percentage change in repayments.
Chaining percentage changes and common pitfalls
Percentage changes do not add linearly because each applies to a different base. A 50% increase on 100 gives 150, and a 50% decrease on 150 gives 75, not 100. Similarly, a 10% rise followed by a 10% fall gives 100 x 1.10 x 0.90 = 99, a net loss of 1%. When you see a sale that claims "50% off, then an extra 20% off", the real discount is 1 - (0.50 x 0.80) = 60%, not 70%. Use the increase or decrease mode twice in succession to check compounded changes.
Real-world percentage examples
Discounts: a $120 jacket at 25% off costs 120 x 0.75 = $90. Tips: a 20% tip on a $47 dinner is 0.20 x 47 = $9.40. Tax: 8.5% sales tax on $35 adds 0.085 x 35 = $2.98. Wage growth: a salary of $55,000 raised by 4% becomes 55,000 x 1.04 = $57,200. Reverse-solve: if $240 is your 30% deposit, the full price is 240 / 0.30 = $800. Grades: 42 correct answers out of 56 questions is 42 / 56 x 100 = 75%.
Common percentage equivalents
| Fraction | Decimal | Percentage | Common use |
|---|---|---|---|
| 1/100 | 0.01 | 1% | Fine tolerances, basis points |
| 1/10 | 0.10 | 10% | Quick estimates, standard tip |
| 1/8 | 0.125 | 12.5% | Trade discounts |
| 1/5 | 0.20 | 20% | Standard tip, deposit |
| 1/4 | 0.25 | 25% | Quarter off, VAT in some regions |
| 1/3 | 0.333... | 33.3% | One-third reduction |
| 1/2 | 0.50 | 50% | Half off, majority vote |
| 2/3 | 0.667... | 66.7% | Two-thirds majority |
| 3/4 | 0.75 | 75% | Three-quarter off |
Quick reference: fractions, decimals and their percentage equivalents.
Frequently asked questions
How do I find what percent one number is of another?
Divide the first number by the second and multiply by 100. For example, 30 out of 150 is 30 / 150 x 100 = 20%. Use the "X is what percent of Y?" mode to do it instantly.
What is percentage change?
It is the difference between two values expressed as a percentage of the starting value: (new - old) / old x 100. A positive result is an increase, a negative one a decrease.
How do I find the whole when I know a part and its percentage?
Divide the known part by the percentage expressed as a decimal. If $240 is 30% of a total, the total is 240 / 0.30 = $800. Use the "X is P% of what?" mode to calculate this instantly.
How do I apply a percentage increase to a number?
Multiply the original value by (1 + P/100). For a 15% increase on 200, the multiplier is 1.15 and the result is 230. For a decrease, multiply by (1 - P/100) instead. The "Increase / decrease" mode handles both.
Does a 50% increase then a 50% decrease return to the start?
No. Increasing 100 by 50% gives 150, and decreasing 150 by 50% gives 75, not 100. Because each change is measured against a different base, equal-looking percentages do not cancel out.
What is the difference between percentage change and percentage points?
Percentage points are the arithmetic difference between two percentages (from 4% to 5% is 1 percentage point). Percentage change is that same gap relative to the starting value (from 4% to 5% is a 25% increase in the rate). Mixing these up is a common error in journalism and finance.