How to Calculate Percentages: Formulas & Examples
Percentages show up in shopping, school, salaries and the news — a 20%-off sale, a 15% tip, a 5% raise, a 92% score. The good news: almost every percentage question is one of just three types, and each has a one-line formula. This guide walks through all three with worked examples, the mental shortcuts that make them fast, and the mistakes that quietly produce wrong answers.
What a percentage really means
"Percent" comes from the Latin per centum — "per hundred". A percentage is simply a fraction whose denominator is 100, written with the % sign instead. So 25% is 25/100, which is the decimal 0.25.
That single idea unlocks everything below: to turn a percentage into a decimal, divide by 100; to turn a decimal back into a percentage, multiply by 100. Every formula here is just that rule applied in a different order.
Type 1 — a percentage of a number
This is the most common question: "what is 15% of 200?" The formula is result = (percentage / 100) x value. So 15% of 200 = 0.15 x 200 = 30. A tip, a tax amount and a commission all share this exact shape.
Mental shortcut: 10% of any number is that number with the decimal point moved one place left (10% of 200 = 20). Need 15%? Take 10% (20) plus half of it (10) = 30. Most real-world tipping needs nothing more.
Type 2 — X is what percent of Y?
Here you have two numbers and want the relationship between them: "42 out of 50 — what percent is that?" The formula flips it around: percentage = (X / Y) x 100. So 42 / 50 = 0.84, and x 100 = 84%.
A $250 expense against a $2,000 budget is 250 / 2000 x 100 = 12.5%. Same formula, any pair of numbers.
Type 3 — percentage change
To measure how much a value rose or fell in percentage terms, compare the change to where you started: change % = (new - old) / old x 100. A price rising from 80 to 100 is (100 - 80) / 80 x 100 = +25%.
Reverse those numbers — 100 down to 80 — and you get (80 - 100) / 100 x 100 = -20%, not -25%, because the starting point changed. Always divide by the original value.
Discounts, tips and tax
A discount takes a percentage off a price: final price = price x (1 - discount / 100). A $120 item at 25% off costs 120 x 0.75 = $90, a $30 saving. To add something instead — tax, a tip, a markup — multiply by (1 + rate): $120 plus 8% tax is 120 x 1.08 = $129.60.
Percentage points are not percentages
This trips up even careful readers. If an interest rate moves from 4% to 6%, that is a rise of 2 percentage points — but a 50% relative increase (2 / 4). When the thing you are measuring is itself a percentage, say "percentage points" for the raw gap and "percent" for the relative change.
Common mistakes to avoid
- A 50% rise followed by a 50% fall does not return to the start: 100 -> 150 -> 75. The base changes each step, so "up X% then down X%" always ends lower.
- In percentage change, divide by the original value, not the new one — this is the single most common source of wrong growth figures.
- Convert the percent to a decimal before multiplying: 15% of 64 is 0.15 x 64 = 9.6, not 15 x 64. An answer 100 times too big is usually this mistake.
- Always be clear what the percentage is "of" — the base matters as much as the rate.
Frequently asked questions
How do I calculate a discount quickly? Multiply the price by (1 minus the discount as a decimal). A 30%-off $50 item is 50 x 0.70 = $35.
Can a percentage be more than 100%? Yes — 100% is the whole, so anything larger is more than the original. Tripling a value is a 200% increase.
What is the fastest mental method? For 10%, move the decimal one place left; halve that for 5%. Combine them to build 15%, 20% or 25% in your head.
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Last updated: August 27, 2026