Perform standard percentage calculations. Compute percentage increase, decrease, proportion ratios, and differences.
Percentage calculations appear in virtually every domain of daily life and professional work: retail discounts, tax computations, grade point averages, investment returns, survey statistics, nutritional labeling, and scientific data reporting. Despite their ubiquity, percentage calculations can be confusing because the same term 'percentage' describes several distinct mathematical operations.
This calculator handles all five fundamental percentage computation types: finding what percent A is of B, calculating a percentage of a number, computing percentage increase or decrease between two values, finding the original value before a percentage was applied (reverse percentage), and computing percentage points difference. Each calculation type is selected automatically based on your inputs and the formula is shown explicitly.
A critical distinction in statistical reporting is between percentage change and percentage points. If unemployment rises from 4% to 6%, it increased by 2 percentage points but by 50% in percentage change (since 6-4=2, and 2/4×100=50%). Confusing these two measures — as media reports frequently do — leads to misleading interpretations of magnitude.
Percentage change = ((New Value - Old Value) / Old Value) × 100. This measures relative change scaled to the original value. Percentage points simply subtract two percentage values directly. When analyzing economic indicators, interest rate movements, or polling data, always clarify which type of percentage comparison is being reported.
When multiple successive percentages are applied to a value, they cannot simply be added — they compound multiplicatively. A 20% increase followed by a 20% decrease does NOT return to the original value; it results in a 4% net decrease (1.2 × 0.8 = 0.96). This counterintuitive behavior of compound percentages is central to understanding compound interest, discounts stacking, and price adjustments.
Reverse percentage (finding the original value before a percentage was applied) is computed by dividing by the multiplier: if a price increased by 15% to reach $115, the original price was $115 / 1.15 = $100. This operation is essential for tax-inclusive price calculations (finding pre-tax amounts), markup pricing (finding supplier cost from selling price), and discount analysis (finding pre-discount prices).
Percentage of a number: Part = (Percent/100) × Whole. Example: 35% of 240 = (35/100) × 240 = 0.35 × 240 = 84. To find what percent A is of B: Percent = (A/B) × 100. Example: 84 is what percent of 240? (84/240) × 100 = 35%.
Percentage change = ((New Value - Old Value) / |Old Value|) × 100. A positive result indicates an increase; negative indicates a decrease. Example: price changed from $80 to $96: ((96-80)/80) × 100 = (16/80) × 100 = 20% increase. Note: the denominator is always the original (starting) value.
Reverse percentage finds the original value before a percentage was applied. If a value increased by X% to reach Y, the original = Y / (1 + X/100). If a value decreased by X% to reach Y, the original = Y / (1 - X/100). Example: a price with 20% markup is $120; original price = 120 / 1.20 = $100.
Because each percentage applies to a different base. A 50% increase on $100 gives $150. A 50% decrease on $150 gives $75 — a net 25% loss. Mathematically: 1.5 × 0.5 = 0.75. Percentage changes multiply as factors (1 + rate), not as simple additions. This is why compound interest calculations use exponential formulas, not simple addition of rates.
Percentage points measure the arithmetic difference between two percentages: if a score rises from 60% to 75%, it increased by 15 percentage points. Percent change measures the relative increase: 15/60 × 100 = 25% change. These give very different numbers for the same situation. Percentage points are used for absolute comparisons; percent change for relative comparisons.