Percentage Calculator — % Of, % Change & % Difference
Calculate any percentage in three modes: find what percent of a number is, calculate the percent change between two values, or find what percentage one number is of another.
How to Calculate Percentages — Complete Guide
A percentage is a way of expressing a number as a fraction of 100. The word comes from the Latin per centum — "per hundred." Understanding the three core percentage calculations covers the vast majority of real-world scenarios.
Mode 1: Finding a percentage of a number
This is the most common percentage calculation. "What is 15% of 80?" Multiply the number by the percentage divided by 100: 80 × (15/100) = 80 × 0.15 = 12. Practical uses: calculating tips (18% of $64 bill), VAT (20% of £250), discounts (30% off $120), tax withholding.
Mode 2: Percentage change
Used to compare two values and express the difference as a percentage. Formula: ((New − Old) / |Old|) × 100. A positive result is an increase; negative is a decrease. Example: a stock goes from $50 to $73 — that's ((73−50)/50) × 100 = 46% gain. Practical uses: year-over-year growth, price changes, test score improvement, weight change tracking.
Mode 3: X is what percent of Y
Used to express a part as a percentage of a whole. Formula: (X/Y) × 100. Example: 45 correct answers out of 60 total: (45/60) × 100 = 75%. Practical uses: exam scores, survey results, market share, completion rates.
Quick Reference: Common Percentage Calculations
| Question | Formula | Example |
|---|---|---|
| What is X% of Y? | Y × (X/100) | 20% of 150 = 30 |
| Add X% to Y | Y × (1 + X/100) | Add 15% to 200 = 230 |
| Subtract X% from Y | Y × (1 − X/100) | Take 25% off 80 = 60 |
| % change from A to B | ((B−A)/|A|) × 100 | 50 to 75 = +50% |
| X is what % of Y? | (X/Y) × 100 | 30 of 120 = 25% |
| Original price before X% off | Sale price / (1 − X/100) | $75 after 25% off → $100 |
| Original before X% increase | New value / (1 + X/100) | $120 after 20% up → $100 |
Percentage Tricks for Mental Maths
The commutative property: X% of Y = Y% of X
This is the most underused percentage shortcut. 8% of 25 = 25% of 8 = 2. When one of the numbers is a "round" percentage like 25%, 50%, or 10%, this trick makes mental calculation trivial.
Using 10% as a building block
10% of any number = move the decimal point one place left. From there, all other percentages build easily:
- 5% = half of 10%
- 20% = 2 × 10%
- 15% = 10% + 5%
- 25% = divide by 4
- 33% ≈ divide by 3
- 1% = move decimal two places left, then multiply by any whole number
Percentage in Finance and Everyday Life
Percentages underpin almost every financial calculation:
- Interest rates: A 5% APR on a $10,000 loan costs $500/year in interest at simple interest
- Inflation: 3% annual inflation means prices double roughly every 24 years (Rule of 72)
- Investment returns: A 7% annual return doubles money every ~10 years
- Tax brackets: Marginal tax rates are percentages — only income in each bracket is taxed at that rate
- Tipping: 18% of a $45 bill = $45 × 0.18 = $8.10; or: 10% = $4.50, plus 8% ≈ $3.60, total ≈ $8.10
- Sales tax: 8.5% on a $120 purchase = $120 × 0.085 = $10.20 tax, total = $130.20
Percentage Errors People Make
The most common percentage mistake is treating percentage increases and decreases as symmetrical. If a price increases by 50%, it does NOT return to the original price with a 50% decrease. Example: $100 + 50% = $150. $150 − 50% = $75. You need a 33.3% decrease to reverse a 50% increase. This asymmetry matters enormously in investing — a 50% portfolio loss requires a 100% gain just to break even.
A second common error is confusing "percentage points" with "percentages." If an interest rate rises from 4% to 6%, it rose by 2 percentage points, but it increased by 50% (2/4 × 100). Politicians and media often conflate these to make changes sound larger or smaller. Always check whether a stated change is in percentage points (absolute) or percent (relative).
Compounding percentages
When the same percentage applies repeatedly, the effect compounds. A 10% annual growth rate does not mean 100% growth in 10 years — it means 159% growth because each year's growth builds on the previous total: 1.10^10 = 2.594. Conversely, a 10% annual loss for 10 years leaves 65% of the original, not 0%: 0.90^10 = 0.349. The Rule of 72 approximates doubling time: divide 72 by the annual percentage rate to get the years to double (72/7% ≈ 10.3 years).
Percentage in Statistics and Science
In scientific contexts, percentage is used to express concentration (a 5% saline solution), probability (a 30% chance of rain), efficiency (an engine operating at 35% thermal efficiency), and error margins. Relative error and percentage error are calculated as: (|Measured − True| / |True|) × 100. A measurement of 98 when the true value is 100 has a 2% error. In statistics, percentage points are used for proportions in surveys — "approval rose from 42% to 47%" (5 percentage points, but 11.9% relative increase).