Percentage Calculator
Calculate percentages instantly: find the percentage of a number, determine what percent one value is of another, or calculate percentage increase, decrease, and change. Three calculation modes in one tool.
Formulas, assumptions, and rounding are documented in our calculator methodology.
Calculation Type
The Three Percentage Formulas
1. What is X% of Y? Answer = Y × (X ÷ 100). Example: 15% of 60 = 60 × 0.15 = 9. 2. X is what percent of Y? Answer = (X ÷ Y) × 100. Example: 12 is what % of 80? (12 ÷ 80) × 100 = 15%. 3. Percent change from X to Y? Answer = [(Y − X) ÷ X] × 100. Example: from 80 to 100: [(100−80)÷80] × 100 = 25% increase.
Percent Change vs. Percentage Points
Percent change and percentage points are not the same thing. If an interest rate rises from 4% to 6%, it increased by 2 percentage points (the absolute arithmetic difference) but increased by 50% (the relative percentage change: [(6−4)÷4] × 100 = 50%). This distinction matters significantly in finance, polling, and statistics. 'Percent change' measures relative change; 'percentage points' measures absolute change in a percentage value.
Common Percentage Calculations by Context
Tax: total = price × (1 + tax rate). Reverse tax (finding pre-tax price): pre-tax = total ÷ (1 + tax rate). Tip: tip = bill × tip%. Discount: sale price = original × (1 − discount%). Grade: grade% = points earned ÷ points possible × 100. Investment return: return% = (current − original) ÷ original × 100. Markup: markup% = (selling price − cost) ÷ cost × 100.
Frequently Asked Questions
- Multiply the number by the percentage and divide by 100. Example: 25% of 80 = 80 × 25 ÷ 100 = 20. Equivalently: multiply by the decimal form of the percentage (25% = 0.25, so 80 × 0.25 = 20).
- Percentage increase = [(new value − old value) ÷ old value] × 100. Example: price went from $50 to $75. Change = $25. Percentage increase = (25 ÷ 50) × 100 = 50% increase.
- Percent change measures how much a value changed relative to the original value. It is directional: a positive result is an increase, negative is a decrease. Percent difference is symmetric — it measures the difference between two values relative to their average, with no direction. Use percent change when comparing before/after; use percent difference when comparing two independent values where neither is the baseline.
- Divide the part by the whole and multiply by 100. Example: 45 is what percent of 180? (45 ÷ 180) × 100 = 25%. This works for grades, completion rates, proportions, and any part-of-whole comparison.
- Discount amount = original price × (discount% ÷ 100). Sale price = original price − discount amount. Example: $120 item at 30% off. Discount = $120 × 0.30 = $36. Sale price = $120 − $36 = $84. Shortcut: sale price = original price × (1 − discount rate) = $120 × 0.70 = $84.
- Percentage decrease = [(original value − new value) ÷ original value] × 100. Example: a price drops from $200 to $150. Decrease = $50. Percentage decrease = (50 ÷ 200) × 100 = 25%. The result is expressed as a positive number representing the magnitude of the drop. This is the same as percentage change when the new value is smaller — the percent change formula returns a negative number, confirming a decrease.