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Percentage Calculator

Calculate percentages, percentage increases, percentage decreases, and proportional fractions instantly. Multi-mode calculator for finding 'What is X% of Y', 'X is what % of Y', and percent change.

Percentages normalize ratios to a standardized base of 100, forming the mathematical foundation for retail markups, commercial profit margins, exam score evaluations, tax rates, and statistical growth metrics across daily life.

Find what percentage of a number equals instantly.

Arithmetic StandardsReviewed: January 2026

Percentage Normalization & Reversibility Rules

X% of Y = Y% of X (Reversible Commutativity)

A valuable mental math property is symmetry: 16% of 50 is identical to 50% of 16 (both equal 8). Percentage changes are asymmetric: a 50% loss requires a 100% gain to break even.

Reference: Standard Real Analysis & Applied Mathematics

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Core Percentage Formulas

Percentage = ([Part] ÷ [Whole]) × 100 | | | % Change = ([New - Old] ÷ [Old]) × 100

To find the percentage, divide the part by the whole and multiply by 100. To find percentage increase or decrease, subtract the old value from the new value, divide by the absolute original value, and multiply by 100.

Example Calculation

Input: Original Price: ₹800 | New Price: ₹1,000 | Difference: +₹200

Output: % Increase = ((1,000 - 800) ÷ 800) × 100 = +25.0%

Common Uses

  • • Retail Discount & Profit Margin Calculations
  • • Academic Test Score & Grade Percentage Conversions
  • • Financial Growth & Inflation Indexing
  • • Salary Increment & Compensation Revision Analysis

How the Percentage Calculator Works

1

Select Calculation Mode

Choose 'X% of Y', 'X is what % of Y', or 'Percentage Increase/Decrease'.

2

Input Values

Enter your starting base quantity and rate or comparison number.

3

View Exact & Step-by-Step Breakdown

Analyze the computed percentage, fractional decimal equivalent, and absolute difference.

Questions about this calculator

Subtract the sale price from the original price, divide the reduction by the original price, and multiply by 100. If an item falls from ₹2,000 to ₹1,500, the reduction is ₹500 and the discount is (500 ÷ 2,000) × 100 = 25%.

After an increase of r%, divide the final value by 1 + r/100 to recover the original. After a decrease of r%, divide by 1 − r/100. For example, ₹1,180 after an 18% increase started at ₹1,000.

Standard percentage change is undefined when the original value is zero because the formula divides by the original value. Report the absolute change instead and explain that no finite percentage change can be calculated from a zero baseline.

Percentage changes are calculated relative to their immediate baseline. If a ₹100 stock drops by 50%, its new price is ₹50. To return from ₹50 back to ₹100, the stock must increase by ₹50—which represents 100% of the new ₹50 base ($50 \div 50 \times 100 = 100\%$).

Divide the part by the total base quantity and multiply by 100. For example, to find what percentage 45 is of 180: $(45 \div 180) \times 100 = 0.25 \times 100 = 25\%$.

To find 10%, shift the decimal point one place to the left (10% of ₹840 is ₹84). To find 20%, double the 10% amount (₹84 × 2 = ₹168). To find 15%, take 10% (₹84) and add half of it (₹42) = ₹126.

Percentage points represent the simple arithmetic difference between two percentages. Percentage change measures the proportional relative shift. If an interest rate moves from 5% to 6%, it increased by 1 percentage point, but the relative percentage change in borrowing cost is $+20\%$ ($1 \div 5 \times 100$).

Understanding Percentage Calculations in Practice

The word percentage originates from the Latin per centum, meaning 'by the hundred'. In business, finance, and daily shopping, percentage math standardizes proportions so numbers can be compared objectively regardless of the original scale.

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Common Percentage Calculation Cheat Sheet

Calculation Type Mathematical Formula Practical Example Final Output
Find X% of Y $(X \div 100) \times Y$ 18% GST on ₹5,000 ₹900
X is what % of Y $(X \div Y) \times 100$ 420 marks out of 500 84.0%
Percentage Increase $((New - Old) \div Old) \times 100$ Salary from ₹50,000 to ₹65,000 +30.0%
Percentage Decrease $((Old - New) \div Old) \times 100$ Price cut from ₹1,200 to ₹900 -25.0%

Which Percentage Mode Should You Use?

Use “X% of Y” when you know the rate and base value, such as 18% of ₹5,000. Use “X is what % of Y” when comparing a part with a total, such as 420 marks out of 500. Use percentage change when comparing an old value with a new value over time.

Percentage Increase and Decrease Examples

If a salary rises from ₹40,000 to ₹46,000, the increase is ₹6,000. Dividing ₹6,000 by the original ₹40,000 and multiplying by 100 gives a 15% increase. If a price falls from ₹1,200 to ₹900, the ₹300 reduction divided by ₹1,200 gives a 25% decrease.

Common Percentage Mistakes

  • Use the original value as the denominator when calculating percentage change.
  • Do not confuse a change in percentage points with a relative percentage change.
  • A decrease and an equal percentage increase do not cancel because their base values differ.
  • Keep sufficient decimal precision during the calculation and round only the final result.

Learn more

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