Percentage Formulas: A Complete Reference Guide

Percentages express a number as a fraction of 100. They make proportions, changes, and comparisons intuitive. Here are the three fundamental percentage operations with formulas and examples.

1. Find P% of X: Multiply X by P/100. Example: What is 20% of ₹1,200? Answer: 1,200 × 20/100 = ₹240. This is used for calculating discounts, tips, commissions, and proportional amounts.

2. Find what percent X is of Y: Divide X by Y and multiply by 100. Example: 45 is what percent of 60? Answer: (45/60) × 100 = 75%. This is used for test scores, completion rates, and composition analysis.

3. Find percentage change from X to Y: Divide (Y − X) by X and multiply by 100. A positive result means increase; negative means decrease. Example: Revenue grew from ₹50,000 to ₹62,000. Answer: (62,000 − 50,000) / 50,000 × 100 = +24%. This is used for growth rates, inflation, and performance tracking.

Common error: Confusing "percentage of" with "percentage change." If revenue goes from ₹100 to ₹150, the new value is 150% of the old value, but the percentage increase is 50%. These are different numbers answering different questions.

Reverse percentage: To find the original amount before a P% discount was applied to get amount A: Original = A / (1 − P/100). Example: After a 20% discount, an item costs ₹800. Original price = 800 / 0.80 = ₹1,000.

Use Tooler's Percentage Calculator for all three operations in one step.