How to Calculate Percentages: Formulas + Real-Life Examples

Percentages show up everywhere — restaurant tips, store sales, test grades, loan interest, news headlines. The good news? Once you understand the one big idea behind a percent, every type of problem looks the same. Here’s how to calculate percentages with confidence.

This guide walks you through the four main percent problems you’ll meet — finding a percent of a number, finding what percent one number is of another, finding the whole when given a part, and percent change. We’ll finish with mental-math shortcuts you can use at restaurants and in stores without reaching for your phone.

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The one idea behind every percent

A percent is just a fraction with 100 on the bottom. So 25% means 25 out of 100, which is the same as \(\tfrac{25}{100}\) or $0.25$.

If you can move between “percent → decimal → fraction” comfortably, you can solve any percent problem.

These six are worth memorizing for life — they open up most mental percent math.

Type 1 — Find a percent of a number

“What is 20% of 80?”

Convert the percent to a decimal and multiply:

\(0.20 \times 80 = 16\).

That’s it. 20% of 80 is 16.

Another worked example. What is 35% of 240? \(0.35 \times 240 = 84\).

Type 2 — Find what percent one number is of another

“What percent of 50 is 12?”

Divide, then multiply by 100:

\(\dfrac{12}{50} = 0.24 = 24\%\).

Another example. Last month you spent \$520 on groceries; this month you spent \$390. What percent of last month’s bill is this month’s? \(\tfrac{390}{520} = 0.75 = 75\%\). You spent 75% as much.

Type 3 — Find the whole when given a percent

“15 is 30% of what number?”

Divide the part by the decimal form of the percent:

\(\dfrac{15}{0.30} = 50\).

Another example. A student got 18 questions right, which was 60% of the test. How many questions total? \(\tfrac{18}{0.60} = 30\) questions.

Type 4 — Percent increase and decrease

Formula: \(\text{percent change} = \dfrac{\text{new} – \text{old}}{\text{old}} \times 100\%\).

Example: a shirt goes from \$40 to \$50. \(\dfrac{50-40}{40} \times 100\% = 25\%\) increase.

If the result is negative, it’s a decrease.

Reverse-direction example. A car loses 20% of its value in year one. Year one starts at \$30,000. What is it worth at the end? $0.80 \times 30{,}000 = \\(24{,}000\). (Notice: you’re paying 80% of the original.)

Real-life shortcuts

• 10% of anything: move the decimal point one place left. 10% of 73 = 7.3.
• 1% of anything: move it two places left. 1% of 460 = 4.6.
• 5% of anything: half of 10%. 5% of 73 = 3.65.
• Tip 15%: take 10% + half of that. For \$60, that’s \$6 + \$3 = \$9.
• Tip 20%: double the 10%. For \$60, that’s \$12.
• 20% off: 20% off is the same as paying 80% of the price.
• Sales tax (e.g., 8%): find 10% (move decimal), subtract 1% twice, or add 8% of the price directly.

Compound interest in one line

If something grows or shrinks by a percent repeatedly, multiply.

Example: a \$1000 investment grows 6% per year. After 3 years: $1000 \times 1.06^3 \approx \$1191.02$.

The “1.06” factor is just “100% + 6%” rewritten as a decimal.

Common mistakes

• Forgetting to convert percent to decimal before multiplying (16% is 0.16, not 16).
• Mixing up “percent of” and “percent off.”
• Using the new value as the base when calculating percent change — always use the original.
• Forgetting that a 50% increase followed by a 50% decrease does not return to the original.
• Confusing percentage points with percent. A jump from 8% to 10% is a 2 percentage point increase, but a 25% relative increase.

Quick practice

1. A jacket originally costs \$80. It’s marked 35% off. What’s the sale price? *Answer:* Discount = \$28. Sale price = \$52.
2. 42 is what percent of 70? Answer: 60%.
3. 18 is 24% of what number? Answer: 75.
4. A house grew in value from \$240,000 to \$282,000. What is the percent increase? Answer: 17.5%.
5. If you tip 20% on a \$56 dinner bill, what’s the total? *Answer:* \$67.20.
6. A laptop is on sale for 25% off and then another 10% off at checkout. If the original price is \$800, what is the final price? *Answer:* $800 \times 0.75 \times 0.90 = \$540$.
7. A student scored 85% on a 60-question test. How many questions did she get right? Answer: 51.
8. After a 30% raise, an hourly wage is now \$26 per hour. What was the original wage? *Answer:* \$20.

Reverse percents: working backward from a final amount

Reverse percents catch a lot of students off guard because the “base” is the original value — not the final value you’re looking at.

Example. A coat costs \$84 after a 30% discount. What was the original price?

The sale price represents 70% of the original. So: $\dfrac{84}{0.70} = \$120$ original price.

Another example. A house’s value rose 15% to \$345{,}000. What was the original?

The new value is 115% of the original. So: $\dfrac{345000}{1.15} = \$300{,}000$ original.

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When the problem says “after a 25% discount,” divide by 0.75. When it says “after a 25% increase,” divide by 1.25.

Percents on standardized tests

The SAT, ACT, GED, and TEAS all feature percent problems. The most common traps:

• Compound discounts. “30% off, then 20% off” is not the same as 50% off. It’s \(0.80 \times 0.70 = 56\%\) of the original (a 44% total discount).
• Percent points vs. percent change. A jump from 4% to 6% interest is a 2-percentage-point rise — but a 50% relative increase.
• Sales tax on a discount. Always discount first, then add tax — that’s how stores actually do it.

Practicing 10–15 percent word problems before test day is one of the single highest-yield study activities you can do.

Mental-math toolbox

• Switch the percent and the number. 18% of 50 is the same as 50% of 18 = 9. (Commutative property!) This trick works every time and saves real time.
• Use “of” = multiply. Whenever you see “percent of,” multiply.
• Round, then adjust. 19% of 80 ≈ 20% of 80 = 16. Then subtract 1% of 80 (which is 0.8) → 15.2.

These tricks let you do percent math at the register, at the restaurant, and on the SAT without a calculator.

FAQ

How do I convert a percent to a decimal?

Drop the % sign and divide by 100 (or move the decimal two places left). 47% = 0.47.

What’s the formula for percent change?

\(\dfrac{\text{new}-\text{old}}{\text{old}} \times 100\%\).

How do I calculate a tip without a calculator?

Find 10% (move the decimal left), then add half of that for 15%, or double it for 20%.

Why is percent change calculated using the original value?

Because the original value is the reference point — it’s what changed.

Are percents on the GED, ACT, and SAT?

Yes, frequently. Percent problems are among the highest-yield topics on every standardized test.

Why doesn’t a 20% increase plus a 20% decrease equal the original?

Because the base changes. A 20% increase grows the base; the 20% decrease then comes off a larger number, so you end up at 96% of the original.

What’s the difference between “X percent more” and “X percent of”?

“More” means added on top. “Of” means the result. “20% more than 80” = 96; “20% of 80” = 16.

How do I convert a fraction directly to a percent?

Divide the numerator by the denominator, then multiply by 100. \(\tfrac{3}{8} = 0.375 = 37.5\%\).

Why is the percent symbol “%”?

It comes from the Italian per cento (“per hundred”). The two zeros in the symbol are a nod to the “100” in that phrase. So “45%” literally means “45 per 100” — a fraction with a hidden denominator of 100.

What’s the difference between a percent and a percentile?

A percent is a part of a whole (“30% of students passed”). A percentile ranks you in a distribution (“you scored in the 80th percentile” means you outranked 80% of test-takers). They look alike but mean different things.

How can I quickly estimate a percent in my head?

Learn the 10% trick: divide by 10. Once you have 10%, you can scale up or down. 30% = 3 × 10%. 5% = half of 10%. 15% = 10% + 5%. With these three building blocks you can estimate any percent within a few seconds.

Brush up with our 6th-grade math worksheets or, if you’re prepping for the GED, our GED Math books cover percents in depth.

Recommended EffortlessMath Books

For a pre-algebra workbook that builds percent into a full year of work, Pre-Algebra for Beginners covers percent, ratio, and proportion with worked examples. For real-world word-problem practice, Mastering Grade 7 Math Word Problems includes tax, tip, discount, and percent-change problems with answer keys.

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Frequently Asked Questions

What is a percent in plain English?

A percent is just a fraction out of \(100\). \(25\%\) means \(25\) out of \(100\), which is \(\tfrac{25}{100} = 0.25 = \tfrac{1}{4}\). Percents, decimals, and fractions are three ways of writing the same number.

How do I find a percent of a number?

Convert and multiply. \(35\%\) of \(240 = 0.35 \times 240 = 84\). For a quick mental check: \(10\%\) of \(240\) is \(24\), so \(35\%\) should be three-and-a-half times that, or about \(84\). Matches.

How do I find what percent one number is of another?

Divide and multiply by \(100\). “What percent of \(50\) is \(12\)?” — \(\tfrac{12}{50} = 0.24 = 24\%\). Order matters: the part goes on top, the whole goes on the bottom.

How do I find the whole when I know the percent and the part?

Divide the part by the percent as a decimal. “\(15\) is \(30\%\) of what?” — \(\tfrac{15}{0.30} = 50\). “A student got \(18\) right, which was \(60\%\) of the test” — total questions \(= \tfrac{18}{0.60} = 30\).

How do I calculate a tip in my head?

\(10\%\): move the decimal one place left. On \(\$60\), that’s \(\$6\). \(20\%\): double the \(10\%\) — \(\$12\). \(15\%\): \(10\%\) plus half of that — \(\$6 + \$3 = \$9\). \(18\%\): \(10\%\) + \(5\%\) + \(3\%\) is close enough.

How do I find a percent discount?

A \(20\%\) off means you pay \(80\%\) of the price. \(0.80 \times \$50 = \$40\). Or compute the discount first: \(0.20 \times \$50 = \$10\), then \(\$50 – \$10 = \$40\). Same answer, two paths.

What’s percent change?

\(\dfrac{\text{new}-\text{old}}{\text{old}} \times 100\%\). Positive means increase, negative means decrease. Always use the OLD value as the base, not the new value.

Does a \(50\%\) increase followed by a \(50\%\) decrease return to the original?

No. \(\$100 \rightarrow +50\% \rightarrow \$150 \rightarrow -50\% \rightarrow \$75\). You end up below the start because the second percent is taken from a bigger number. Percent changes don’t simply cancel.

What’s the difference between “percent” and “percentage points”?

If an interest rate jumps from \(8\%\) to \(10\%\), that’s a \(2\) percentage-point increase OR a \(25\%\) relative increase (\(\tfrac{10-8}{8} = 0.25\)). News stories often mix these up; reading the wording carefully matters.

How do I compute compound growth?

Multiply by \(1 + r\) each period, where \(r\) is the rate as a decimal. \(\$1000\) at \(6\%\) per year for \(3\) years: \(1000 \times 1.06^3 \approx \$1191.02\). For decay, use \(1 – r\) — a car that loses \(20\%\) yearly: \(\$30{,}000 \times 0.80 = \$24{,}000\) after year one.

Related EffortlessMath Lessons

If a topic on this page feels rusty, these short lessons go deeper:

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• How to find percentage of numbers
• How to solve percent change
• Percent word problems and percent equations
• How to convert fractions to decimals
• How to calculate discount, tax, and tip