How to Calculate Percentages: The Complete Guide with Real-World Examples
Master percentage calculations for discounts, tax, tips, grade changes, and more. Learn the three core percentage formulas with step-by-step examples.
What Is a Percentage?
A percentage is simply a ratio out of 100. The word itself comes from the Latin per centum, meaning "per hundred." When you say something is 45%, you mean 45 out of every 100 — or equivalently, 45/100 = 0.45 as a decimal.
Percentages appear everywhere in daily life: sales discounts, bank interest rates, exam scores, tax rates, nutritional labels, and weather forecasts. Mastering the three core percentage formulas will make you faster and more confident in all these situations.
The Three Core Percentage Formulas
1. Finding a Percentage of a Number
Formula: Result = (Percentage / 100) × Number
Example: What is 30% of 250?
Result = (30 / 100) × 250 = 0.30 × 250 = 75
2. Finding What Percentage One Number is of Another
Formula: Percentage = (Part / Whole) × 100
Example: What percentage is 45 of 180?
Percentage = (45 / 180) × 100 = 0.25 × 100 = 25%
3. Finding the Original Value
Formula: Original = Value / (Percentage / 100)
Example: ₹840 is 70% of what number?
Original = 840 / 0.70 = ₹1,200
Percentage Increase and Decrease
To calculate percentage change:
% Change = ((New − Old) / |Old|) × 100
If New > Old, it's an increase. If New < Old, it's a decrease.
Example: A salary rose from ₹40,000 to ₹46,000.
% Increase = ((46,000 − 40,000) / 40,000) × 100 = (6,000 / 40,000) × 100 = 15%
Real-World Applications
- Shopping discounts: 25% off ₹1,200 = ₹900 final price
- GST calculation: 18% GST on ₹1,000 = ₹180 tax, ₹1,180 total
- Grade calculation: 78 out of 120 = 65% score
- Bank interest: 7% per annum on ₹50,000 = ₹3,500/year interest
- Weight change: Lost 5 kg from 80 kg = 6.25% weight loss
Quick Mental Math Tips
To find 10% — move the decimal point one place left (10% of 350 = 35).
To find 5% — find 10% then halve it (5% of 350 = 17.5).
To find 20% — double the 10% value (20% of 350 = 70).
To find 15% — add 10% and 5% (15% of 350 = 35 + 17.5 = 52.5).
To find 1% — move the decimal two places left (1% of 350 = 3.5).
Common Mistakes to Avoid
Percentage vs. Percentage Points: If an interest rate rises from 5% to 8%, it rose by 3 percentage points. But it rose by 60% (as a percentage change).
Stacking Discounts: Two 20% discounts do not equal 40% off. Applying 20% off twice to ₹100: first 20% gives ₹80; second 20% of ₹80 gives ₹64. The effective discount is 36%, not 40%.
Use our free Percentage Calculator to instantly handle all these calculations without error.
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