Percentage Calculator — Find Percentages of Any Number

The Formula

A percentage expresses a number as a fraction of 100. The "% of" formula multiplies the base by the percentage divided by 100. Percent change compares the difference between two values relative to the original.

Variable Definitions

How to Use This Calculator

1. 1

   Select the type of percentage calculation from the dropdown: "What is X% of Y?", "X is what % of Y?", "% change from X to Y", "Add X% to Y", or "Subtract X% from Y".

2. 2

   Enter your two numbers (X and Y). X is typically the percentage or first value; Y is the base or second value.

3. 3

   Read the result with the step-by-step calculation shown below. Each mode shows a different formula.

4. 4

   Check the real-world example to see how this applies in daily life — tips, grades, discounts, taxes, and price changes.

5. 5

   The decimal equivalent is shown for each calculation, which is useful for understanding the underlying ratio.

Quick Reference

Common Applications

• Shopping — calculate discounts, sale prices, and compare "percentage off" deals across different price points to find the best value
• Dining — compute tips as a percentage of the bill total, whether 15%, 18%, 20%, or a custom percentage
• Finance — track investment returns as percentage gains or losses, compare interest rates on loans and savings accounts
• Academics — convert test scores to letter grades by calculating the percentage of correct answers out of total questions
• Business — compute profit margins, tax rates, sales tax amounts, commission structures, and year-over-year growth rates

A 10×10 grid visually demonstrates that 20% means 20 out of every 100 units

Understanding the Concept

Percentages are one of the most common mathematical operations in daily life — used for tips, taxes, discounts, interest rates, grades, and statistics. The key insight is that a percentage is always relative: 20% of $50 ($10) is very different from 20% of $500 ($100). Always identify what the "whole" (100%) is before calculating. For percent change, the original value is always the denominator, which is why a 50% increase requires a 33% decrease to return to the original. A common real-world pitfall: stores advertise "50% off" on already-reduced items, but the second discount applies to the already-reduced price, not the original. Similarly, a "10% increase" followed by a "10% decrease" does not return to the starting value because the decrease applies to a larger base. This asymmetry between percentage increases and decreases is one of the most important and misunderstood concepts in personal finance.

Frequently Asked Questions

Sources & References