Percentage Calculator

Percentage calculations convert proportions into standardized values out of 100 ("per cent" means "per hundred"). The fundamental formula is: (Part / Whole) × 100 = Percentage. This calculator handles multiple percentage operations using algebraic transformations of this base formula.



For "What is X% of Y?", the calculator multiplies: (X / 100) × Y = Result. For "X is what percent of Y?", it divides: (X / Y) × 100 = Percentage. For percentage change, it calculates: ((New - Old) / Old) × 100, yielding positive results for increases and negative for decreases.



The interface provides specialized calculators for common scenarios: discounts (original price - percentage off), tips (bill amount + percentage tip), grade calculations (points earned / total points), and percentage point changes (difference between two percentages). JavaScript performs calculations in real-time as you type, displaying results with appropriate precision (typically 2 decimal places) and formatting (currency for money, percentages for rates).

1. Shopping & Discount Calculations
Calculate sale prices, discounts, and savings when shopping. "30% off $80" equals $56 final price with $24 saved. Compare discounts across stores ("20% off vs. $15 off on $75 item"). Calculate additional discounts on sale items ("20% off already-reduced 30% price"). Determine if bulk discounts offer real savings. Online shoppers use percentage calculators constantly for deal evaluation.



2. Financial Planning & Analysis
Calculate investment returns (portfolio grew 15%), interest rates (savings account yields 2.5% APY), tax amounts (8.5% sales tax on $200 purchase), loan payments (20% down payment on house), or budget allocations (30% of income to housing). Financial advisors calculate percentage changes in stock prices, retirement account growth, or expense ratios.



3. Academic & Grade Calculations
Calculate test scores (42 out of 50 = 84%), course grades (homework 30%, tests 50%, final 20% weighting), GPA conversions, or grade requirements ("What score do I need on the final to get an A?"). Students calculate current grades, professors calculate class averages, and academic departments analyze passing rates.



4. Business & Sales Metrics
Calculate profit margins (revenue - costs / revenue), sales growth (Q2 sales vs Q1), conversion rates (100 purchases / 5,000 visitors = 2%), commission earnings (5% commission on $50,000 sales), or market share changes. Business analysts calculate year-over-year growth, customer retention rates, or ROI percentages.



5. Health & Nutrition Tracking
Calculate daily value percentages for nutrition labels (25% DV for calcium), weight loss progress (lost 15 lbs = 10% of 150 lb starting weight), body fat percentage changes, or macronutrient ratios (30% protein, 40% carbs, 30% fat). Fitness apps and nutrition tracking rely heavily on percentage calculations for goals and progress.

• Understand the difference between percent and percentage points: If interest rates go from 5% to 8%, that's a 3 percentage point increase but a 60% relative increase ((8-5)/5 × 100). Percentage points measure absolute difference; percent change measures relative difference. Media often confuses these—be precise.



• Use the right base for comparisons: "Percentage increase" depends on which value is the base. If a stock goes from $50 to $75 (+50%), then back to $50, that's -33% (not -50%) because the base changed. Always identify: "percentage of what?" to avoid errors in comparisons.



• Check for compound vs. simple percentage changes: A 20% increase followed by 20% decrease doesn't return to original value. $100 × 1.20 = $120, then $120 × 0.80 = $96. Successive percentage changes multiply, they don't add/subtract. Calculate compound changes by multiplying factors: (1 + r₁)(1 + r₂)...



• Verify discount stacking calculations: Most stores apply discounts sequentially, not additively. "30% off + additional 20% off" is NOT 50% off. It's 30% off first ($100 → $70), then 20% off that ($70 → $56), totaling 44% off, not 50%. Calculate stacked discounts by multiplying: $100 × 0.70 × 0.80.



• Round appropriately for context: Money rounds to 2 decimals ($15.75, not $15.748), percentages often use 1-2 decimals (15.7%, not 15.6782%). However, scientific calculations may need more precision. Match rounding to context—overly precise numbers (84.3728% on a test) look odd when 84% or 84.4% suffices.



• Use percentages for comparison, absolute numbers for context: "Sales increased 50%!" sounds impressive, but if sales went from 2 to 3 units, that's not meaningful. Always consider absolute values alongside percentages. Small bases produce dramatic percentages; large bases make small percentages significant.



• Memorize common fraction-percentage equivalents: 1/4 = 25%, 1/3 ≈ 33.3%, 1/2 = 50%, 2/3 ≈ 66.7%, 3/4 = 75%. Quick mental math: 10% = move decimal left one place ($45 × 10% = $4.50), 20% = double that, 5% = half of 10%. Estimate tips and discounts without calculators.