Percentage Calculator — Percent of, Change & More

This is the most common percentage calculation. To find X percent of Y, multiply Y by X and divide by 100: Result = Y × (X ÷ 100). For example, 15% of 200 equals 200 × 0.15 = 30. This formula is used constantly in everyday life — calculating a 20% restaurant tip on a $45 bill gives $9, or finding a 30% discount on a $120 jacket saves you $36. In business, it is used to calculate profit margins, commission amounts, tax on a sale price, and budget allocations. The key insight is that a percentage is simply a decimal in disguise: 15% = 0.15, 7.5% = 0.075. Multiplying by the decimal form is mathematically identical to multiplying by the fraction over 100.

To find what percent one number is of another, divide the part by the whole and multiply by 100: Percentage = (X ÷ Y) × 100. For instance, if a student scores 42 out of 56 on a test, their percentage score is (42 ÷ 56) × 100 = 75%. This formula answers questions like what share of the budget did department A spend, or what fraction of eligible voters turned out. It is also the basis of conversion ratios in chemistry and engineering. Always be careful to put the correct value in the denominator — it must be the reference whole quantity, not the part being measured.

Percentage change measures how much a value has grown or shrunk relative to its starting point: Change = ((New − Old) ÷ |Old|) × 100. A positive result is an increase; a negative result is a decrease. If a stock price rises from $80 to $92, the percentage change is ((92 − 80) ÷ 80) × 100 = 15%. If it falls from $80 to $68, the change is −15%. This formula is essential in finance for year-over-year revenue growth, in science for measuring experimental change, and in everyday comparisons such as price increases at the grocery store. Note that percentage increase and percentage decrease are not symmetric — a 50% decrease followed by a 50% increase does not return to the original value.

A fourth common operation is adding or subtracting a percentage to a base value: New Value = Original × (1 + Rate) for increase, or Original × (1 − Rate) for decrease. Adding 8% sales tax to a $250 item gives 250 × 1.08 = $270. Applying a 25% discount to a $200 product gives 200 × 0.75 = $150. This is also the core formula for compound growth — repeatedly applying a growth rate to a changing base. Loan repayments, savings account interest, and population growth projections all rely on this principle. Understanding the multiplicative nature of percentage changes prevents a common error: thinking that adding 25% and then removing 25% returns you to the start (it does not — 100 → 125 → 93.75).

When shopping, two percentage operations come up repeatedly. To apply a discount, multiply the original price by (1 − discount rate). A 40% off sale on a $90 item: 90 × 0.60 = $54. To add sales tax, multiply the discounted price by (1 + tax rate). If the local tax is 9%, the final cost becomes 54 × 1.09 = $58.86. When both apply, it is more efficient to combine them: 90 × 0.60 × 1.09 = $58.86. Comparing unit prices across different package sizes also uses percentage math — divide price by quantity to get the cost per unit, then compare across options. Understanding these calculations helps you verify receipts, evaluate coupon stacks, and make smarter purchasing decisions without relying on a cashier to do the math for you.

In personal finance, percentage calculations are indispensable. Annual percentage rate (APR) on a loan determines how much interest you pay each month. If you borrow $10,000 at 6% APR, simple annual interest is $600, or $50 per month. Investment returns are expressed as percentage change — a portfolio that grows from $5,000 to $5,750 has returned 15%. Compound annual growth rate (CAGR) uses the percentage change formula repeatedly across multiple years. Inflation rates, expressed as annual percentage changes in price levels, affect how you interpret salary increases — a 3% raise when inflation is 4% is effectively a pay cut in real terms. Tracking these numbers in percentage terms allows fair comparisons across different time periods and investment sizes.