Percentage Calculator
Solve any percentage problem: percentage of, percentage change, and ratios.
1. Calculate Percentage: What is X% of Y?
2. Percentage Change: From Old Value to New Value
3. Ratio to Percentage: Part (X) is what % of Whole (Y)?
Mastering Percentage Calculations
The word percent originates from the Latin per centum, translating literally to "by the hundred." Expressing quantities as proportions of 100 allows standardized comparisons across disparate numbers, whether tracking inflation changes, comparing student exam marks, or tallying store discounts.
Core Formulas for the Three Primary Percentage Operations
Result = (X ÷ 100) × Y
Percentage Change = [ (New Value − Old Value) ÷ Old Value ] × 100
Percentage = (Part X ÷ Whole Y) × 100
Real-Life Worked Examples
- Store Discount: An item costs $350 with a 30% discount. 30% of $350 = (30 ÷ 100) × 350 = $105 savings. The final price is $245.
- Salary Increment: Your salary increases from $50,000 to $62,000. Change = [(62,000 − 50,000) ÷ 50,000] × 100 = +24% increase.
- Academic Score: A student scores 482 out of 600 in their board examination. (482 ÷ 600) × 100 = 80.33%.
Critical Distinction: Percentage vs. Percentage Points
News reports often confuse percentage change with percentage points. If an interest rate climbs from 10% to 12%, it has risen by 2 percentage points (12 − 10 = 2). However, relative to the starting rate of 10%, the percentage increase is actually 20% (2 ÷ 10 = 0.20). Understanding this nuance helps avoid financial misinterpretations.