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Calculate percentages in 3 modes: X% of Y, X is what % of Y, and % change between two values. The formula is shown alongside every answer.
Enter values to calculate
Percentages represent fractions expressed as parts per hundred (from the Latin per centum). They are ubiquitous in financial budgeting, tax calculations, statistical data analysis, and retail discounting. Understanding the mathematical relationship between the base, the rate, and the percentage enables accurate problem-solving.
What is $P%$ of $X$? $$\text{Result} = X \times \left(\frac{P}{100}\right)$$
$Y$ is what percentage of $X$? $$P = \left(\frac{Y}{X}\right) \times 100$$
Percentage Increase or Decrease from $X_1$ to $X_2$: $$\Delta% = \left(\frac{X_2 - X_1}{X_1}\right) \times 100$$
| Calculation Scenario | Base Value ($X$) | New Value ($Y$) | Formula Applied | Output Result |
|---|---|---|---|---|
| 20% Tip on a £65 bill | £65.00 | - | $65 \times (20 / 100)$ | £13.00 tip (Total: £78.00) |
| Score 42 out of 50 on an exam | 50 | 42 | $(42 / 50) \times 100$ | 84.0% score |
| Price changes from £120 to £90 | £120 | £90 | $((90 - 120) / 120) \times 100$ | -25.0% (25% discount) |
| Salary increases from £50k to £55k | £50,000 | £55,000 | $((55000 - 50000) / 50000) \times 100$ | +10.0% increase |
A common mistake in financial analysis is treating sequential percentage changes additively:
JavaScript
// Calculate percentage change
function getPercentageChange(originalValue, newValue) {
if (originalValue === 0) return 0;
const change = ((newValue - originalValue) / originalValue) * 100;
return Number(change.toFixed(2));
}
// Calculate percentage of value
function getPercentageOf(percentage, total) {
return Number(((percentage / 100) * total).toFixed(2));
}
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