Mathematics
6 min read
•Updated 2026-09-17
How to Calculate Percentage: Formulas, Step-by-Step Math & Practical Examples
A complete authoritative guide to computing proportions, percentage differences, markups, discounts, and reverse percentages.
By AnyCalcHub Editorial Team
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1. The Core Percentage Formula
The word "percent" originates from the Latin phrase "per centum", meaning "by the hundred". A percentage represents a fraction where the denominator is always fixed at 100. To find what percentage one number (the part) is of another number (the whole), divide the part by the whole and multiply by 100.
Mathematical Formula
Percentage (%) = (Part / Whole) × 100
Step-by-Step Worked Example
Part45
Whole150
Step 1:Divide 45 by 150: 45 ÷ 150 = 0.30
Step 2:Multiply the decimal by 100: 0.30 × 100 = 30%
Final Result: 45 is 30% of 150
2. Percentage Increase and Decrease
When measuring how much a metric has changed over time—such as stock valuations, house prices, or inflation—we measure the difference relative to the starting (original) value.
Mathematical Formula
Percentage Change (%) = ((New Value - Old Value) / |Old Value|) × 100
Step-by-Step Worked Example
Old Value₹80
New Value₹100
Step 1:Find the absolute change: 100 - 80 = +20
Step 2:Divide by original value: 20 ÷ 80 = 0.25
Step 3:Multiply by 100: 0.25 × 100 = +25%
Final Result: A 25% price increase
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3. Reverse Percentage (Finding the Original Value)
Reverse percentage is used when you know the final amount after a percentage increase or decrease and need to find the original amount. Never simply subtract the percentage from the final amount, as percentage is asymmetric.
Mathematical Formula
Original Value = Final Value / (1 ± (Percentage / 100))
Step-by-Step Worked Example
Final Price₹1,180 (includes 18% GST)
Tax Rate18%
Step 1:Convert rate to decimal factor: 1 + 0.18 = 1.18
Step 2:Divide final price by factor: 1,180 ÷ 1.18 = 1,000
Final Result: Original pre-tax value is ₹1,000
Frequently Asked Questions
Common questions and mathematical nuances for this calculation.
Why does a 20% increase followed by a 20% decrease not return to the original number?
Because the base value changes. If 100 increases by 20%, it becomes 120. When 120 decreases by 20% (0.20 × 120 = 24), the result is 96, leaving a net 4% loss.
How do you convert a decimal to a percentage?
Multiply the decimal by 100 and append the % symbol. For example, 0.0825 × 100 = 8.25%.
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