Percentage Calculator (3-in-1)
Calculate what is X% of Y, percentage increase/decrease, and X is what percent of Y.
Percentage Calculator — interactive calculator, computed instantly in your browser.
The Comprehensive Guide to Percentage Calculations & Rate of Change
Understanding Part, Whole, and Rate Relationships
Key Formula: $\text{Part} = \text{Rate} \times \text{Whole}$, $\text{Rate} = \frac{\text{Part}}{\text{Whole}}$, and $\text{Whole} = \frac{\text{Part}}{\text{Rate}}$.
The word percentage originates from the Latin per centum, meaning "by the hundred." It represents a dimensionless ratio or fraction where the denominator is always fixed at 100.
1. Percentage Increase and Decrease Formula
To compute relative change between an initial baseline value ($V_1$) and a subsequent final value ($V_2$):
If the resulting value is positive, it represents a percentage increase; if negative, it denotes a percentage decrease.
2. Common Real-World Percentage Calculations
| Scenario | Formula Applied | Example Calculation |
|---|---|---|
| Sales Discount | $\text{Final} = \text{Price} \times (1 - d)$ | $20% off $80: $80 \times 0.80 = \$64.00$ |
| Sales Tax / Mark-up | $\text{Total} = \text{Subtotal} \times (1 + t)$ | $8% tax on $50: $50 \times 1.08 = \$54.00$ |
| Restaurant Tip | $\text{Tip} = \text{Bill} \times \text{Tip Rate}$ | $18% tip on $65: $65 \times 0.18 = \$11.70$ |
🔗 Percentage & Proportional Analytics
Percentage mathematics is essential across personal finance, scientific data, and commercial sales. Browse our full ➗ Math & Statistics Hub for all quantitative solvers.
Calculate commercial discounts or convert fractions to decimals using the recommended tools below.
Frequently Asked Questions (Percentage Calculator)
Because the base changes. Starting at $100, a 50% increase yields $150. A subsequent 50% decrease applies to the new larger base ($150), reducing it by $75 down to $75 (a net 25% loss).
Percentage points refer to the direct arithmetic difference between two percentage values (e.g., rising from 4% to 6% is a 2 percentage point increase). Percent change measures relative change: (6 - 4)/4 = a 50% relative increase.
Divide the final tax-inclusive price by (1 + Tax Rate). For a $110 total with 10% tax: $110 / 1.10 = $100 original price.