Percentage is one of the most frequently used calculations in everyday life — from shopping discounts to exam scores, salary hikes to GST, investment returns to nutritional labels. Yet many people struggle when the question changes from "what is 20% of 500?" to "500 is what percentage of 2,000?" This guide covers all six core percentage calculation types with clear formulas and worked examples.
What is a Percentage?
A percentage is a ratio expressed as a fraction of 100. The word comes from Latin per centum — "by the hundred." When you say 45%, you mean 45 out of every 100, or 45/100 = 0.45 as a decimal. Percentages allow comparison between quantities with different bases — which is why they appear everywhere from statistics to science to everyday shopping.
Type 1: Finding the Percentage of a Number
Question: What is X% of Y?
Result = (X ÷ 100) × YExample: What is 35% of 8,400?
= (35 ÷ 100) × 8,400 = 0.35 × 8,400 = 2,940
Real-world uses: GST calculation (18% of bill amount), discount amount, commission earned, tip at a restaurant.
Type 2: Finding What Percentage One Number Is of Another
Question: X is what percentage of Y?
Percentage = (X ÷ Y) × 100Example: You scored 68 out of 80 in an exam.
= (68 ÷ 80) × 100 = 85%
Real-world uses: Exam score percentage, market share, completion percentage, attendance rate.
Type 3: Percentage Increase
Question: What is the percentage increase from Old to New?
% Increase = [(New − Old) ÷ Old] × 100Example: Salary increased from ₹45,000 to ₹52,200.
= [(52,200 − 45,000) ÷ 45,000] × 100 = [7,200 ÷ 45,000] × 100 = 16%
Type 4: Percentage Decrease
Question: What is the percentage decrease from Old to New?
% Decrease = [(Old − New) ÷ Old] × 100Example: Product was ₹1,200, now on sale for ₹900.
= [(1,200 − 900) ÷ 1,200] × 100 = [300 ÷ 1,200] × 100 = 25%
Type 5: Finding the Original Number from a Percentage
Question: X% of what number equals Y?
Original = Y ÷ (X ÷ 100) = (Y × 100) ÷ XExample: After a 20% discount, a shirt costs ₹640. What was the original price?
Sale price = 80% of original → Original = 640 ÷ 0.80 = ₹800
Common mistake: Adding 20% back to ₹640 = ₹768 — wrong! The percentage was taken off the original price, not the sale price.
Type 6: Percentage Difference Between Two Numbers
Question: What is the percentage difference between A and B?
% Difference = [|A − B| ÷ ((A + B) ÷ 2)] × 100Example: City A has 3,200 students; City B has 4,000.
= [800 ÷ 3,600] × 100 ≈ 22.2%
Quick Reference: All 6 Formulas
| Calculation Type | Formula |
|---|---|
| X% of Y | (X ÷ 100) × Y |
| X is what % of Y | (X ÷ Y) × 100 |
| % increase from A to B | [(B − A) ÷ A] × 100 |
| % decrease from A to B | [(A − B) ÷ A] × 100 |
| Original from % and result | Result ÷ (% ÷ 100) |
| % difference between A and B | [|A−B| ÷ avg(A,B)] × 100 |
Common Mistakes to Avoid
- Adding percentages directly: +50% then −50% on ₹100 gives ₹75, NOT ₹100.
- Confusing percentage points with % change: Interest rising from 4% to 6% is 2 percentage points but a 50% increase in the rate.
- Wrong base for reverse calculations: Always divide by the percentage decimal, don't add back to the discounted value.
Use our free Percentage Calculator to solve all six types instantly, or the Percentage Increase & Decrease Calculator to compute change between two values.