How to Calculate Percentage: Formulas, Examples, and Shortcuts

By Faizan Ali · Updated September 08, 2026 · 8 min read

Key takeaways: A percentage is just a fraction out of 100, so every percentage question boils down to one of four shapes — finding X% of Y, finding what percent X is of Y, working out a percentage increase or decrease, or adding/subtracting a percentage from a number. Learn the four formulas below, watch out for the difference between percentage points and percent change, and you can handle almost any real-world percentage problem by hand or check your work with a percentage calculator.

What is a percentage, really?

"Percent" comes from the Latin per centum, meaning "per hundred." So 25% simply means 25 out of every 100. Written as a decimal, that's 0.25. Written as a fraction, it's 25/100, which simplifies to 1/4.

That one idea — percent = part ÷ whole × 100 — is the foundation for everything below. The four question types you'll run into are just this same idea rearranged depending on which piece is missing.

The four percentage question types

1. Finding X% of Y

This is the most common question: "What is 20% of 150?"

Formula: (percent ÷ 100) × number = result

Example: 20% of 150.

(20 ÷ 100) × 150 = 0.20 × 150 = 30

So 20% of 150 is 30. This shape shows up constantly — tips, discounts, taxes, commissions. You'll see it again in the sales-tax and tip sections below.

2. Finding what percent X is of Y

Sometimes you have two numbers and need to know the relationship between them: "36 is what percent of 240?"

Formula: (part ÷ whole) × 100 = percent

Example:

(36 ÷ 240) × 100 = 0.15 × 100 = 15%

36 is 15% of 240. This is the formula behind grading tests, tracking survey responses, and figuring out what share of a budget something takes up.

3. Percentage increase or decrease

This is where most people slow down, because it's easy to plug numbers into the wrong spot. The rule: always divide by the original (starting) value, not the new one.

Percentage increase formula:

((new value − original value) ÷ original value) × 100

Example: a product's price rises from $80 to $92.

((92 − 80) ÷ 80) × 100 = (12 ÷ 80) × 100 = 15%

Percentage decrease uses the same formula — the result just comes out negative, or you can phrase it as "decreased by" and drop the sign:

((old value − new value) ÷ old value) × 100

Example: a laptop drops from $1,200 to $960.

((1200 − 960) ÷ 1200) × 100 = (240 ÷ 1200) × 100 = 20%

That's a 20% decrease. Note that a 20% decrease followed by a 20% increase does not get you back to the original number — that asymmetry trips people up constantly, and it's the same reason stacked discounts don't add up the way you'd expect (more on that below).

4. Adding or subtracting a percentage from a number

This is the increase/decrease formula run in reverse — you know the percent and the starting number, and you want the resulting value directly.

Formula: original × (1 ± percent ÷ 100)

Example: add 15% to $200 (a price increase):

200 × (1 + 0.15) = 200 × 1.15 = $230

Example: subtract 30% from $200 (a discount):

200 × (1 − 0.30) = 200 × 0.70 = $140

This "multiply by the decimal factor" trick is worth memorizing — it's the fastest way to apply a tip, a discount, or a tax in one step. The tip calculator and discount calculator both use exactly this formula under the hood.

Percentage points vs. percent change (the classic reporting error)

This is the single most misused distinction in news and business writing, so it's worth its own section.

If an interest rate moves from 5% to 7%, that's a change of 2 percentage points. But as a percent change, it's much larger:

((7 − 5) ÷ 5) × 100 = 40%

So the same move can accurately be described as "up 2 percentage points" or "up 40%" — and those two phrasings sound wildly different even though they describe the same event. A percentage point is a flat, arithmetic difference between two percentages. A percent change is a relative difference. Mixing them up (saying a rate "rose 40%" when it actually rose 2 percentage points, or vice versa) is one of the most common errors in headlines about interest rates, tax rates, and survey results.

Why stacked discounts multiply, not add

Retailers love stacking discounts — "30% off, plus an extra 10% at checkout" — and it's tempting to think that adds up to 40% off. It doesn't.

Each discount applies to whatever the price has already become, not the original price. So a $100 item with 30% off, then an extra 10% off, works out like this:

Step 1: 100 × (1 − 0.30) = 100 × 0.70 = $70
Step 2: 70 × (1 − 0.10) = 70 × 0.90 = $63

The final price is $63, meaning the real combined discount is 37%, not 40%. The gap grows as the discounts get bigger, which is exactly why it's worth running the numbers yourself before checkout rather than trusting the sticker math — the discount calculator handles multi-step discounts like this in one go.

How to reverse a discount (finding the original price)

Sometimes you know the sale price and the discount percentage, and you need to find what the item cost before the sale. This is a reverse percentage problem, and people often make the mistake of adding the percentage back onto the sale price — which gives the wrong answer.

Formula: sale price ÷ (1 − discount as a decimal) = original price

Example: an item is on sale for $76 after a 20% discount. What was the original price?

76 ÷ (1 − 0.20) = 76 ÷ 0.80 = $95

Check it: 20% of $95 is $19, and $95 − $19 = $76. That confirms it. Note that you divide by 0.80, not multiply the sale price by 1.20 — that's the mistake that gives a wrong answer here (76 × 1.20 = $91.20, not $95).

Mental-math shortcuts for percentages

You don't always need a calculator. Two shortcuts cover most everyday situations:

• 10% then halve. To get 10% of any number, just move the decimal point one place left (10% of 150 is 15). To get 5%, halve that (7.5). To get 15%, add the two together (15 + 7.5 = 22.5) — handy for tipping in restaurants that don't add a service charge automatically.
• The swap trick: x% of y = y% of x. This one feels like magic the first time you see it. 8% of 50 is awkward to picture, but 50% of 8 is instantly obvious — it's 4. Both give the exact same answer, because percentage is a fraction and multiplication doesn't care about order. Next time a percentage looks messy, try flipping which number is the "percent."

Worked example: calculating an exam grade

Say you scored 42 out of 56 on a test. What's your percentage grade?

(42 ÷ 56) × 100 = 0.75 × 100 = 75%

Now say your teacher curves the class and adds 5 percentage points to everyone's score. Your new grade is 80% — a straightforward addition, because percentage points add directly to a percentage. But if instead the teacher said "everyone's score increases by 5%," that means multiplying: 75 × 1.05 = 78.75%. Same phrase, very different math — which is exactly the percentage-points-versus-percent-change trap from earlier, showing up again in a grade book.

Frequently asked questions

How do you calculate a percentage of a number?

Divide the percentage by 100 to turn it into a decimal, then multiply by the number. For example, 20% of 150 is (20 ÷ 100) × 150 = 30. This is the most common percentage calculation and the basis for tips, discounts, and taxes.

What is the formula for percentage increase?

Subtract the original value from the new value, divide that difference by the original value, then multiply by 100: ((new − original) ÷ original) × 100. Always divide by the starting number, not the ending one, or the result will be wrong.

Why isn't a 20% decrease undone by a 20% increase?

Because each percentage is calculated on a different base number. A 20% decrease on $100 brings it to $80, but a 20% increase on $80 only adds $16, bringing it to $96 — not back to $100. This is the same reason stacked discounts don't simply add together.

What's the difference between percentage points and percent change?

A percentage point is a plain subtraction between two percentages (7% − 5% = 2 percentage points). Percent change compares that difference to the starting value ((7−5)/5 × 100 = 40%). The two numbers describe the same shift but can look very different, which is why financial and political reporting often specifies "percentage points" to avoid confusion.

How do I find the original price before a discount?

Divide the sale price by (1 minus the discount as a decimal). For a $76 item after a 20% discount, that's 76 ÷ 0.80 = $95. Don't just add the percentage back onto the sale price — that gives an incorrect result because the discount was originally taken off a larger number.

Try it yourself

Rather than redoing the arithmetic by hand every time, run your numbers through the free percentage calculator for any of the four question types above. If you're specifically working with a sale price, the discount calculator handles stacked discounts and reverse pricing automatically, the tip calculator splits a bill and tip in one step, and the loan calculator is useful when you need to work out interest as a percentage over time.