Percentage Calculator

Solve any percentage problem instantly. Compute percentage of values, find percentage increase or decrease, solve proportional ratios, and inspect step-by-step mathematical proofs.

1. What is $X\%$ of $Y$?
What is % of ?
Result
30
Formula: $\frac{15}{100} \times 200 = 30$
2. $X$ is what $\%$ of $Y$?
is what % of ?
Result
25%
Formula: $\frac{45}{180} \times 100\% = 25\%$
3. Percentage Change (from $X$ to $Y$)
From to
Result
+25.0% (Increase)
Formula: $\frac{100 - 80}{80} \times 100\% = +25\%$

The Complete Mathematical Guide to Percentages

The term percent originates from the Latin per centum, meaning "by the hundred." A percentage is simply a dimensionless ratio expressed as a fraction of 100 (symbolized by %).

1. Essential Percentage Formulas in LaTeX

  • Percentage of a Value: $$\text{Amount} = \frac{P}{100} \times \text{Base}$$
  • Rate / Percentage Proportion: $$P = \frac{\text{Part}}{\text{Whole}} \times 100\%$$
  • Percent Change: $$\Delta\% = \frac{\text{New} - \text{Original}}{\text{Original}} \times 100\%$$
  • Percent Difference: $$\text{Diff}\% = \frac{|\text{Value}_1 - \text{Value}_2|}{\frac{\text{Value}_1 + \text{Value}_2}{2}} \times 100\%$$

2. Practical Applications

Percentages govern everyday commerce, taxation (sales tax, VAT), retail discounts, financial interest calculations (APR, APY), health statistics, and school grades.