Calculate a percentage of a number, find a percentage, measure change or difference, and increase or decrease values with clear formulas.
A percentage expresses a value as a share of 100. The right formula depends on whether you are finding a portion, comparing values, measuring change, or adjusting a number.
Decide which value is the percentage, which is the part, and which is the reference or whole.
Percentage change needs an original value. Percentage difference treats both values equally and uses their average magnitude.
Dividing a percentage by 100 creates its decimal multiplier. For example, 15% becomes 0.15.
Keep the full value during calculation and round only the displayed answer to avoid unnecessary error.
result = (percentage ÷ 100) × valuepercentage = (part ÷ whole) × 100change = ((new − original) ÷ |original|) × 100adjusted = starting × (1 ± percentage ÷ 100)Percentage difference is symmetric: switching A and B does not change the result.
difference = |A − B| ÷ ((|A| + |B|) ÷ 2) × 100These examples show how each formula is applied.
| Question | Substitution | Answer |
|---|---|---|
| What is 20% of 150? | 20 ÷ 100 × 150 | 30 |
| 30 is what percent of 150? | 30 ÷ 150 × 100 | 20% |
| Increase from 100 to 125 | (125 − 100) ÷ 100 × 100 | 25% |
| Decrease 200 by 15% | 200 × (1 − 15 ÷ 100) | 170 |
| Difference between 80 and 100 | 20 ÷ 90 × 100 | 22.22% |
Divide the percentage by 100, then multiply that decimal by the number. For example, 20% of 150 is 0.2 × 150, which equals 30.
Divide the first number by the comparison number and multiply by 100. The comparison number cannot be zero.
Percentage change compares a new value with an original reference value, so direction matters. Percentage difference compares two values symmetrically and has no original value.
Yes. An increase can exceed 100% when the increase is larger than the magnitude of the original value.
Yes where the formula remains defined. The calculator uses the absolute magnitude of the original value for percentage change and absolute magnitudes in percentage difference.
Those formulas divide by the original or comparison value. Division by zero is undefined, so the calculator asks for a non-zero value.