Three percentage calculators in one tool. Calculate what X% of Y is, find what percentage one number is of another, or determine the percentage change between two values — all with instant results.
Percentages are one of the most frequently used concepts in everyday mathematics, yet they're a common source of confusion. There are three fundamentally different types of percentage questions, and each requires a different formula. This calculator handles all three in one place.
Type 1 — Finding a percentage of a number: "What is 20% of 85?" Formula: Result = (Percentage ÷ 100) × Number. Answer: 0.20 × 85 = 17. Use this for calculating tips, discounts, sales tax, or any portion of a whole.
Type 2 — Finding what percentage one number is of another: "25 is what percent of 200?" Formula: Result = (Part ÷ Whole) × 100. Answer: (25 ÷ 200) × 100 = 12.5%. Use this for test scores, market share calculations, or comparing values.
Type 3 — Percentage change: "What is the percentage change from 80 to 100?" Formula: Result = ((New − Old) ÷ |Old|) × 100. Answer: ((100 − 80) ÷ 80) × 100 = +25%. Use this for price changes, salary increases, population growth, or any before/after comparison.
A jacket costs $120 and is 35% off. Discount amount = 35% of $120 = 0.35 × 120 = $42 off. Final price = $120 − $42 = $78. Sales tax of 8.5% on $78 = 0.085 × 78 = $6.63. Total with tax = $84.63.
You scored 47 out of 60 on a test. What percentage is that? (47 ÷ 60) × 100 = 78.33%. To get an 85%, you'd need: 0.85 × 60 = 51 correct answers.
Your salary goes from $58,000 to $63,500. Percentage increase = ((63,500 − 58,000) ÷ 58,000) × 100 = (5,500 ÷ 58,000) × 100 = +9.48%. After inflation of 3.2%, your real raise is approximately 6.28%.
A 50% decrease followed by a 50% increase does NOT return to the original value. Starting at $100: −50% = $50, then +50% = $75. You're still down 25%. This asymmetry trips up many people in investment discussions. Similarly, a 100% increase doubles a number, but a 100% decrease brings it to zero — the percentages describe different things depending on direction.
Formula: ((New Value − Old Value) ÷ Old Value) × 100. Example: price goes from $40 to $52. Increase = ((52−40)÷40)×100 = 30%. The price increased by 30%.
These are often confused. If an interest rate goes from 4% to 5%, it increased by 1 percentage point but increased by 25% (because 1÷4×100=25%). Politicians and journalists sometimes use these interchangeably, which can be misleading. Be precise: use 'percentage points' for absolute differences between percentages.
If a price after a 20% discount is $80, what was the original price? Original = Final ÷ (1 − discount rate) = 80 ÷ 0.80 = $100. If a price after a 15% tax increase is $115, original = 115 ÷ 1.15 = $100.
Percent means 'per hundred.' Per mille means 'per thousand' (the ‰ symbol). 5% = 50‰. Per mille is used in some legal and financial contexts, particularly in Europe, and in blood alcohol content measurements. 0.08% BAC = 0.8‰.
Percentages are ubiquitous in finance: interest rates, return on investment, portfolio allocation, inflation rate, expense ratios, tax rates, loan-to-value ratios, and dividend yields are all expressed as percentages. Understanding percentage calculations is foundational to making informed financial decisions.