Percentage Mathematical Formulas Explained
A percentage is a dimensionless ratio expressed as a fraction of 100 (from Latin per centum, meaning "by the hundred"). Our calculator encapsulates the four core mathematical relationships required in commerce, statistics, and daily transactions.
1. Percentage of a Number (What is X% of Y?)
Used for calculating sales tax, tips, and proportional shares:
$$\text{Result} = \left(\frac{X}{100}\right) \times Y$$
Example: What is $20\%$ of $\$80$? $\rightarrow (20 \div 100) \times 80 = \$16$.
2. Percentage Share (X is what % of Y?)
Used to determine test scores, market share, and budget allocations:
$$\text{Percentage} = \left(\frac{X}{Y}\right) \times 100\%$$
Example: You scored $45$ out of $50$ on an exam. $\rightarrow (45 \div 50) \times 100\% = 90\%$.
3. Percentage Increase
Used to calculate price inflation, population growth, and revenue expansion:
$$\text{Increase } \% = \left(\frac{\text{New Value} - \text{Old Value}}{|\text{Old Value}|}\right) \times 100\%$$
Example: A stock rose from $\$50$ to $\$65$. $\rightarrow ((65 - 50) \div 50) \times 100\% = 30\%$ increase.
4. Percentage Decrease
Used for store markdowns, depreciation, and weight reduction metrics:
$$\text{Decrease } \% = \left(\frac{\text{Old Value} - \text{New Value}}{|\text{Old Value}|}\right) \times 100\%$$
Example: A laptop price drops from $\$1,000$ to $\$800$. $\rightarrow ((1000 - 800) \div 1000) \times 100\% = 20\%$ decrease.