📊 Percentage Calculator
Calculate percentage of a number, percentage changes, proportions, and percentage differences with step-by-step mathematical explanations.
Understanding Percentage Calculations
A percentage (derived from Latin per centum, meaning "by the hundred") is a number or ratio expressed as a fraction of 100. Percentages are essential across personal finance, stock market investments, academic grading, tipping, sales discounts, and data analytics.
The 4 Core Percentage Formulas
1. How to Find the Percentage of a Number (What is P% of X?)
Formula: Result = (P ÷ 100) × X
Example: What is 15% of $80?
Result = (15 ÷ 100) × 80 = 0.15 × 80 = $12.00
2. How to Find Percentage Proportion (X is What % of Y?)
Formula: Percentage = (X ÷ Y) × 100
Example: You scored 45 points out of 60 on a test. What is your grade percentage?
Percentage = (45 ÷ 60) × 100 = 0.75 × 100 = 75%
3. How to Calculate Percentage Increase or Decrease (% Change)
Formula: % Change = ((New Value − Old Value) ÷ |Old Value|) × 100
If the result is positive, it represents a percentage increase. If negative, it represents a percentage decrease.
Example: A product price changed from $50 to $70.
% Increase = ((70 − 50) ÷ 50) × 100 = (20 ÷ 50) × 100 = +40% increase
4. How to Calculate Percentage Difference
Percentage difference is used when comparing two values of the same type without a chronological "before" and "after" relationship.
Formula: % Difference = (|V1 − V2| ÷ ((V1 + V2) ÷ 2)) × 100
Common Percentage to Fraction & Decimal Conversions
| Percentage | Fraction | Decimal | Mental Math Shortcut |
|---|---|---|---|
| 10% | 1/10 | 0.10 | Move decimal 1 place to left |
| 20% | 1/5 | 0.20 | Divide by 5 (or 10% × 2) |
| 25% | 1/4 | 0.25 | Divide by 4 (half of half) |
| 33.33% | 1/3 | 0.333 | Divide by 3 |
| 50% | 1/2 | 0.50 | Divide by 2 |
| 75% | 3/4 | 0.75 | Divide by 4, then multiply by 3 |
Frequently Asked Questions
In Excel or Google Sheets, divide the part by the total (e.g., =A1/B1), then click the % (Percent Style) button in the toolbar to automatically format the cell as a percentage.
A percentage point is the simple arithmetic difference between two percentages (e.g., an interest rate rising from 5% to 6% is a 1 percentage point increase). Percentage change measures relative growth: going from 5% to 6% is a (1 ÷ 5) × 100 = 20% relative increase.
Yes! x% of y = y% of x. Because multiplication is commutative, (x × y) ÷ 100 is identical in both directions. Calculating 8% of 50 in your head might seem tough, but calculating 50% of 8 is instantly 4!