Percentage Calculator
Calculate percentages easily. Find X% of a number, determine what percent one number is of another, or calculate percentage change between two values.
Percentage Calculation Guide
Percentages are used in virtually every aspect of daily life: shopping discounts, tax calculations, interest rates, tips, investment returns, test scores, and more. The word "percent" comes from Latin "per centum," meaning "out of 100." This calculator supports three fundamental percentage operations that cover most real-world scenarios.
Three Core Percentage Formulas
1. X% of Y = Y x X / 100
Example: 15% of $80 = $80 x 15/100 = $12.00
2. X is what % of Y = X / Y x 100
Example: 45 out of 60 = 45/60 x 100 = 75%
3. Percentage Change = (New - Old) / Old x 100
Example: $200 → $250 = (250-200)/200 x 100 = +25%
Percentage vs. Percentage Points
Percentage (%) measures relative change, while percentage points (pp) measure the absolute difference between two percentages. For example, if unemployment rises from 4% to 6%, that is a 2 percentage point increase but a 50% relative increase. When reading news about interest rates, inflation, or poll results, this distinction is critical for accurate interpretation.
Common Percentage Applications
| Scenario | Formula | Example |
|---|---|---|
| Sales tax | Price x (1 + Tax%/100) | $50 + 8.25% tax = $50 x 1.0825 = $54.13 |
| Tip calculation | Bill x Tip%/100 | $65 x 20% = $13.00 tip |
| Discount price | Price x (1 - Disc%/100) | $120 at 30% off = $120 x 0.70 = $84 |
| Investment return | (End - Start) / Start x 100 | $10,000 → $11,500 = 15% return |
| Test score | Correct / Total x 100 | 42/50 = 84% |
| Body fat % | Fat mass / Total mass x 100 | 30 lbs fat / 180 lbs total = 16.7% |
Common Fraction-to-Percentage Conversions
| Fraction | Percentage | Fraction | Percentage |
|---|---|---|---|
| 1/2 | 50% | 1/3 | 33.3% |
| 1/4 | 25% | 3/4 | 75% |
| 1/5 | 20% | 2/5 | 40% |
| 1/8 | 12.5% | 1/10 | 10% |
| 2/3 | 66.7% | 7/8 | 87.5% |
Quick Mental Math Tips
- To find 10%, move the decimal point one place to the left (e.g., 10% of $450 = $45)
- To find 5%, take half of the 10% value (e.g., 5% of $450 = $22.50)
- To find 15%, add 10% + 5% (e.g., 15% of $60 = $6 + $3 = $9)
- To find 20%, double the 10% value (e.g., 20% of $75 = $7.50 x 2 = $15)
- To find 25%, divide by 4 (e.g., 25% of $200 = $50)
- To reverse a sales tax: divide by (1 + tax rate). E.g., $54.13 / 1.0825 = $50 pre-tax
Important Notes
- Stacking discounts is not additive: 20% off + 10% off = 28% total discount, not 30%
- Percentage changes are asymmetrical: a 50% increase followed by a 50% decrease yields 75% of the original, not 100%
- Do not confuse percentage with percentage points when interpreting rates and statistics
- Compound growth (interest on interest) accelerates over time -- use the compound interest formula for investments