Percentage Calculator
Quickly solve everyday percentage calculations: find X% of Y, calculate what percentage X is of Y, find the original total, or compute percentage difference.
Input Parameters
0ms Local EngineResult = (20% / 100) × 500
- Convert 20% to decimal: 20 ÷ 100 = 0.2
- Multiply decimal by 500: 0.2 × 500 = 100
- 20% of 500 is 100
Understanding Percentage Calculations
A comprehensive guide to solving percentages, understanding the mathematical principles, and avoiding common calculation errors.
1. What is a Percentage?
A percentage represents a dimensionless fraction of 100. The word originates from the Latin per centum, meaning "by the hundred". Percentages provide a universal benchmark to compare ratios, proportions, marks, salary hikes, discounts, and statistical metrics regardless of scale.
2. The 4 Fundamental Percentage Operations
Result = (X ÷ 100) × Y
Example: 20% of 500 = 0.20 × 500 = 100
Result % = (X ÷ Y) × 100
Example: 100 is what % of 500 = (100/500) × 100 = 20%
Result = X ÷ (Y ÷ 100)
Example: 100 is 20% of what = 100 ÷ 0.20 = 500
Result % = (|X - Y| ÷ Avg) × 100
Where Avg = (|X| + |Y|) ÷ 2
3. Worked Real-World Examples
- Exam Scoring: A student scores 480 out of 600 marks. To find the percentage: (480 ÷ 600) × 100 = 80.00%.
- TDS Deduction: You receive a professional bill of ₹45,000 subject to 10% TDS. TDS amount = (10 ÷ 100) × 45,000 = ₹4,500. Net payable = ₹40,500.
- Reverse Sales Tax: If ₹180 represents 18% GST on an item, the base price is ₹180 ÷ 0.18 = ₹1,000.
- Confusing the Base: Calculating 20% of 100 gives 20. But reducing 120 by 20% does not bring you back to 100 (it brings you to 96) because the base has changed from 100 to 120.
- Zero Denominators: Attempting to divide by 0 when calculating "X is what % of Y" is mathematically undefined.
- Percentage vs Percentage Points: An increase from 5% interest rate to 6% interest rate is a 1 percentage point increase, but a 20% relative increase.
Calculations use standard IEEE 754 floating point arithmetic with rounding to 4 decimal places for precision display. Zero denominators are safely trapped to avoid invalid NaN or Infinity values.
Frequently Asked Questions on Percentages
Everything you need to know about everyday percentage arithmetic.
How do I calculate what X% of Y is?
How do I calculate what percentage X is of Y?
How do I find the total when I only know the percentage and partial value?
What is percentage difference and how does it differ from percentage change?
Why does the calculator return "Undefined" when the denominator is 0?
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