Percentage Calculator: All Formulas Explained

What Is a Percentage?

A percentage is a number expressed as a fraction of 100. The word comes from Latin "per centum" — per hundred. When you say 25%, you mean 25 out of 100, or the fraction 25/100, or the decimal 0.25. These are all the same value expressed differently, and converting between them is the foundation of every percentage calculation.

To convert a percentage to a decimal, divide by 100 (move the decimal point two places left): 75% = 0.75, 8% = 0.08, 150% = 1.50. To convert a decimal to a percentage, multiply by 100 (move the decimal point two places right): 0.42 = 42%, 0.07 = 7%, 1.25 = 125%. Percentages above 100% are valid and common — they indicate a value greater than the reference amount.

The reason percentages are used so widely is normalization. Raw numbers are hard to compare: "Company A earned $2 million more this year" means different things depending on whether last year's revenue was $4 million or $400 million. Percentages normalize the comparison: a 50% increase versus a 0.5% increase tells the real story regardless of the absolute numbers involved.

The Three Basic Percentage Formulas

Nearly every percentage question is a variation of one of three formulas:

What is X% of Y? Multiply Y by X/100. What is 15% of 200? → 200 × 0.15 = 30. This is the formula for calculating tips, discounts, taxes, and commissions. "A 20% tip on $85" means $85 × 0.20 = $17.

X is what percent of Y? Divide X by Y, then multiply by 100. 45 is what percent of 180? → (45 ÷ 180) × 100 = 25%. This is the formula for finding what proportion one number is of another. "You scored 72 out of 90 on the test" → (72 ÷ 90) × 100 = 80%.

X is Y% of what number? Divide X by Y/100. 36 is 12% of what? → 36 ÷ 0.12 = 300. This is the reverse calculation — you know the result and the percentage, and you need the original number. "The discounted price is $68, and the discount was 15% — what was the original price?" → $68 ÷ (1 - 0.15) = $68 ÷ 0.85 = $80.

These three formulas cover the vast majority of real-world percentage questions. The key is identifying which formula applies: do you know two numbers and need the percentage, or do you know a number and a percentage and need the result?

Percentage Change and Difference

Percentage change measures how much a value has increased or decreased relative to its original value. The formula is: ((New - Old) ÷ Old) × 100. If a stock price goes from $40 to $52, the percentage change is ((52 - 40) ÷ 40) × 100 = 30% increase. If it drops from $52 to $40, the change is ((40 - 52) ÷ 52) × 100 = -23.08% decrease.

Notice that the same absolute change ($12) produces different percentages depending on the direction — 30% up but only 23% down. This asymmetry surprises people: a 50% loss requires a 100% gain to recover, not a 50% gain. If a $100 investment drops 50% to $50, it needs to double (100% gain) to return to $100.

Percentage difference compares two values without designating one as the "original." It uses the average of the two values as the denominator: |A - B| ÷ ((A + B) ÷ 2) × 100. This is used when comparing two independent measurements — the price of a product at two different stores, performance metrics of two systems, or survey results from two groups.

Compound percentage change: When percentages are applied sequentially, they compound. A 10% increase followed by a 10% increase is not 20% — it is 1.10 × 1.10 = 1.21, or a 21% total increase. This compounding effect is significant over many periods: a 7% annual return doubles an investment in about 10 years (the Rule of 72 — divide 72 by the growth rate to estimate the doubling time).

Business Applications

Markup and margin: These are related but different. Markup is the percentage added to cost to get the selling price: a $60 item with a 40% markup sells for $60 × 1.40 = $84. Margin is the percentage of the selling price that is profit: ($84 - $60) ÷ $84 × 100 = 28.6% margin. The same transaction has a 40% markup but a 28.6% margin. Confusing them is a common and costly mistake.

Discounts: Sequential discounts do not add up. A 30% discount followed by a 20% discount is not 50% off. It is 0.70 × 0.80 = 0.56, or 44% off the original price. A $100 item with "30% + 20% off" costs $56, not $50.

Interest rates: APR (Annual Percentage Rate) and APY (Annual Percentage Yield) differ because of compounding. A 12% APR compounded monthly means you pay 1% per month, but the actual annual cost is (1.01)¹² - 1 = 12.68% APY. Lenders advertise APR (lower number) while savings accounts advertise APY (higher number).

Tax calculations: Sales tax is straightforward multiplication. An 8.25% tax on $45.99 is $45.99 × 0.0825 = $3.79, for a total of $49.78. To find the pre-tax price from a total, divide by (1 + tax rate): $49.78 ÷ 1.0825 = $45.99.

Calculate Percentages Online

Our Percentage Calculator handles all common percentage operations in one place. Find what X% of Y is, determine what percentage one number is of another, calculate percentage increase or decrease, and work with markup and margin formulas. Enter your values and get instant results with the formula shown.

All calculations run locally in your browser. Use it for quick business math, financial planning, academic problems, or anytime you need a reliable percentage calculation without fumbling with a formula.