Calculate percentages, percentage change, and percentage difference
A percentage is a way to express a number as a fraction of 100. It is often denoted using the percent sign '%'. Percentages are used to express how large or small one quantity is relative to another quantity. The first quantity usually represents a part of, or a change in, the second quantity.
Percentage = (Value / Total Value) × 100
| Calculation | Expression | Result |
|---|---|---|
| What is 20% of 150? | 20% of 150 | 30 |
| 15 is what % of 60? | 15 / 60 × 100 | 25% |
| Percentage change | From 80 to 100 | +25% |
| Percentage difference | Between 40 and 60 | 40% |
| Add 15% to 200 | 200 + 15% | 230 |
Percentage change measures how much a value has increased or decreased relative to the original value, showing direction (positive or negative). Percentage difference measures the absolute difference between two values relative to their average, always expressed as a positive number regardless of which value is larger.
Divide the first number by the second number, then multiply by 100. For example, to find what percent 25 is of 200: (25 ÷ 200) × 100 = 12.5%
Multiply the number by the percentage and divide by 100. For example, to find 15% of 80: (15 × 80) ÷ 100 = 12. Alternatively, convert the percentage to a decimal (15% = 0.15) and multiply: 0.15 × 80 = 12
Use the formula: ((New Value - Original Value) / Original Value) × 100. A positive result indicates an increase, while a negative result indicates a decrease. For example, if a price went from $50 to $65: ((65 - 50) / 50) × 100 = 30% increase
The basic percentage formula is: Percentage = (Part / Whole) × 100. This can be rearranged to find the part (Part = Percentage × Whole / 100) or the whole (Whole = Part / (Percentage / 100)).
Percentages, fractions, and decimals are different ways to express the same value. To convert: Percentage to decimal: divide by 100 (25% = 0.25). Decimal to percentage: multiply by 100 (0.25 = 25%). Percentage to fraction: put over 100 and simplify (25% = 25/100 = 1/4).