Percentage Calculator

A percentage is a dimensionless ratio expressed as a fraction of 100, denoted by the symbol %. The word comes from the Latin "per centum," meaning "by the hundred." Mathematically, a percentage represents a proportion: 25% means 25 out of 100, or equivalently the fraction 25/100 = 1/4 = 0.25 in decimal form. This tool covers four fundamental percentage formulas that arise in everyday calculations.

The first formula, "What is X% of Y?", computes: Result = (X/100) x Y. For example, 15% of 200 = 0.15 x 200 = 30. The second formula, "X is what % of Y?", finds the ratio: Percentage = (X/Y) x 100. For example, 45 is what percent of 180? Answer: (45/180) x 100 = 25%. The third formula computes percentage change between two values: Change% = ((New - Old) / |Old|) x 100. Going from 80 to 100 is a (100-80)/80 x 100 = 25% increase. The fourth applies a percentage increase or decrease: Result = Value x (1 +/- X/100).

Understanding percentages is crucial because they normalize comparisons across different scales. Saying a stock rose by $5 is meaningless without context -- if the stock was $10, that is a 50% gain, but if it was $500, it is only 1%. Percentage change provides this context-independent comparison. Similarly, percentage points and percentages are different concepts: if an interest rate goes from 3% to 5%, the increase is 2 percentage points but a 66.7% increase relative to the original rate. This distinction matters greatly in finance, economics, and statistics.

This tool offers four independent calculation modes, each solving a different percentage problem:

1. "What is X% of Y?": Enter the percentage (X) and the base number (Y). The result shows the computed value. Example: 20% of 350 = 70.
2. "X is what % of Y?": Enter two numbers to find what percentage the first is of the second. Example: 42 is 60% of 70.
3. "Percentage Change": Enter the original value (From) and the new value (To). The result shows the percentage increase or decrease. Example: from 50 to 75 is a 50% increase.
4. "Percentage Increase / Decrease": Enter a percentage and a base value, then choose whether to apply an increase or decrease. Example: 15% increase of 200 = 230.

All four modes work independently and simultaneously. Results update in real time as you type, with up to 4 decimal places of precision.

• Sales tax calculation: Compute the tax on a purchase by finding X% of the pre-tax price. For an 8.5% sales tax on a $45 item: 0.085 x 45 = $3.83.
• Grade and score analysis: Determine what percentage score you achieved on a test: 38 out of 50 = (38/50) x 100 = 76%.
• Investment returns: Calculate the percentage gain or loss on an investment. Bought at $150, sold at $195: (195-150)/150 x 100 = 30% return.
• Salary and wage calculations: Compute a raise amount from a percentage increase, or determine what percentage raise a dollar amount represents relative to current salary.
• Nutrition and diet: Calculate what percentage of your daily caloric intake comes from a specific nutrient or meal.
• Business metrics: Compute conversion rates (signups/visitors x 100), profit margins ((revenue-cost)/revenue x 100), and year-over-year growth rates.
• Statistical analysis: Express proportions, relative frequencies, and confidence intervals as percentages for clearer communication of data findings.